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Research Article

Problem-solving interventions and depression among adolescents and young adults: A systematic review of the effectiveness of problem-solving interventions in preventing or treating depression

Roles Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, United States of America

Roles Conceptualization, Writing – original draft

Affiliation Centre for Evidence and Implementation, London, United Kingdom

Roles Data curation

Roles Conceptualization, Writing – review & editing

Affiliation Department of Psychology, Virginia Commonwealth University, Richmond, VA, United States of America

Roles Conceptualization, Methodology

Roles Conceptualization, Project administration, Writing – review & editing

Affiliation Centre for Evidence and Implementation, Melbourne, Victoria, Australia

Roles Conceptualization, Formal analysis, Methodology, Writing – original draft, Writing – review & editing

Affiliation Department of Social Work, Monash University, Melbourne, Victoria, Australia

• Kristina Metz, 
• Jane Lewis, 
• Jade Mitchell, 
• Sangita Chakraborty, 
• Bryce D. McLeod, 
• Ludvig Bjørndal, 
• Robyn Mildon, 
• Aron Shlonsky

• Published: August 29, 2023
• https://doi.org/10.1371/journal.pone.0285949
• Peer Review
• Reader Comments

Problem-solving (PS) has been identified as a therapeutic technique found in multiple evidence-based treatments for depression. To further understand for whom and how this intervention works, we undertook a systematic review of the evidence for PS’s effectiveness in preventing and treating depression among adolescents and young adults. We searched electronic databases ( PsycINFO , Medline , and Cochrane Library ) for studies published between 2000 and 2022. Studies meeting the following criteria were included: (a) the intervention was described by authors as a PS intervention or including PS; (b) the intervention was used to treat or prevent depression; (c) mean or median age between 13–25 years; (d) at least one depression outcome was reported. Risk of bias of included studies was assessed using the Cochrane Risk of Bias 2.0 tool. A narrative synthesis was undertaken given the high level of heterogeneity in study variables. Twenty-five out of 874 studies met inclusion criteria. The interventions studied were heterogeneous in population, intervention, modality, comparison condition, study design, and outcome. Twelve studies focused purely on PS; 13 used PS as part of a more comprehensive intervention. Eleven studies found positive effects in reducing depressive symptoms and two in reducing suicidality. There was little evidence that the intervention impacted PS skills or that PS skills acted as a mediator or moderator of effects on depression. There is mixed evidence about the effectiveness of PS as a prevention and treatment of depression among AYA. Our findings indicate that pure PS interventions to treat clinical depression have the strongest evidence, while pure PS interventions used to prevent or treat sub-clinical depression and PS as part of a more comprehensive intervention show mixed results. Possible explanations for limited effectiveness are discussed, including missing outcome bias, variability in quality, dosage, and fidelity monitoring; small sample sizes and short follow-up periods.

Citation: Metz K, Lewis J, Mitchell J, Chakraborty S, McLeod BD, Bjørndal L, et al. (2023) Problem-solving interventions and depression among adolescents and young adults: A systematic review of the effectiveness of problem-solving interventions in preventing or treating depression. PLoS ONE 18(8): e0285949. https://doi.org/10.1371/journal.pone.0285949

Editor: Thiago P. Fernandes, Federal University of Paraiba, BRAZIL

Received: January 2, 2023; Accepted: May 4, 2023; Published: August 29, 2023

Copyright: © 2023 Metz et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant methods and data are within the paper and its Supporting Information files.

Funding: This work was commissioned by Wellcome Trust and was conducted independently by the evaluators (all named authors). No grant number is available. Wellcome Trust had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. The authors declare no financial or other competing interests, including their relationship and ongoing work with Wellcome Trust. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Depression among adolescents and young adults (AYA) is a serious, widespread problem. A striking increase in depressive symptoms is seen in early adolescence [ 1 ], with rates of depression being estimated to almost double between the age of 13 (8.4%) and 18 (15.4%) [ 2 ]. Research also suggests that the mean age of onset for depressive disorders is decreasing, and the prevalence is increasing for AYA. Psychosocial interventions, such as cognitive-behavioural therapy (CBT) and interpersonal therapy (IPT), have shown small to moderate effects in preventing and treating depression [ 3 – 6 ]. However, room for improvement remains. Up to half of youth with depression do not receive treatment [ 7 ]. When youth receive treatment, studies indicate that about half of youth will not show measurable symptom reduction across 30 weeks of routine clinical care for depression [ 8 ]. One strategy to improve the accessibility and effectiveness of mental health interventions is to move away from an emphasis on Evidence- Based Treatments (EBTs; e.g., CBT) to a focus on discrete treatment techniques that demonstrate positive effects across multiple studies that meet certain methodological standards (i.e., common elements; 9). Identifying common elements allows for the removal of redundant and less effective treatment content, reducing treatment costs, expanding available service provision and enhancing scability. Furthermore, introducing the most effective elements of treatment early may improve client retention and outcomes [ 9 – 13 ].

A potential common element for depression intervention is problem-solving (PS). PS refers to how an individual identifies and applies solutions to everyday problems. D’Zurilla and colleagues [ 14 – 17 ] conceptualize effective PS skills to include a constructive attitude towards problems (i.e., a positive problem-solving orientation) and the ability to approach problems systematically and rationally (i.e., a rational PS style). Whereas maladaptive patterns, such as negative problem orientation and passively or impulsively addressing problems, are ineffective PS skills that may lead to depressive symptoms [ 14 – 17 ]. Problem Solving Therapy (PST), designed by D’Zurilla and colleagues, is a therapeutic approach developed to decrease mental health problems by improving PS skills [ 18 ]. PST focuses on four core skills to promote adaptive problem solving, including: (1) defining the problem; (2) brainstorming possible solutions; (3) appraising solutions and selecting the best one; and (4) implementing the chosen solution and assessing the outcome [ 14 – 17 ]. PS is also a component in other manualized approaches, such as CBT and Dialectical Behavioural Therapy (DBT), as well as imbedded into other wider generalized mental health programming [ 19 , 20 ]. A meta-analysis of over 30 studies found PST, or PS skills alone, to be as effective as CBT and IPT and more effective than control conditions [ 21 – 23 ]. Thus, justifying its identification as a common element in multiple prevention [ 19 , 24 ] and treatment [ 21 , 25 ] programs for adult depression [ 9 , 26 – 28 ].

PS has been applied to youth and young adults; however, no manuals specific to the AYA population are available. Empirical studies suggest maladaptive PS skills are associated with depressive symptoms in AYA [ 5 , 17 – 23 ]. Furthermore, PS intervention can be brief [ 29 ], delivered by trained or lay counsellors [ 30 , 31 ], and provided in various contexts (e.g., primary care, schools [ 23 ]). Given PS’s versatility and effectiveness, PS could be an ideal common element in treating AYA depression; however, to our knowledge, no reviews or meta-analyses on PS’s effectiveness with AYA specific populations exist. This review aimed to examine the effectiveness of PS as a common element in the prevention and treatment of depression for AYA within real-world settings, as well as to ascertain the variables that may influence and impact PS intervention effects.

Identification and selection of studies

Searches were conducted using PsycInfo , Medline , and Cochrane Library with the following search terms: "problem-solving", “adolescent”, “youth”, and” depression, ” along with filters limiting results to controlled studies looking at effectiveness or exploring mechanisms of effectiveness. Synonyms and derivatives were employed to expand the search. We searched grey literature using Greylit . org and Opengrey . eu , contacted experts in the field and authors of protocols, and searched the reference lists of all included studies. The search was undertaken on 4 th June 2020 and updated on 11 th June 2022.

Studies meeting the following criteria were included: (a) the intervention was described by authors as a PS intervention or including PS; (b) the intervention was used to treat or prevent depression; (c) mean or median age between 13–25 years; and (d) at least one depression outcome was reported. Literature in electronic format published post 2000 was deemed eligible, given the greater relevance of more recent usage of PS in real-world settings. There was no exclusion for gender, ethnicity, or country setting; only English language texts were included. Randomized controlled trials (RCTs), quasi-experimental designs (QEDs), systematic reviews/meta-analyses, pilots, or other studies with clearly defined comparison conditions (no treatment, treatment as usual (TAU), or a comparator treatment) were included. We excluded studies of CBT, IPT, Acceptance and Commitment Therapy (ACT), Dialectical Behaviour Therapy (DBT), and modified forms of these treatments. These treatments include PS and have been shown to demonstrate small to medium effects on depression [ 13 , 14 , 32 ], but the unique contribution of PS cannot be disentangled. The protocol for this review was not registered; however, all data collection forms, extraction, coding and analyses used in the review are available upon inquiry from the first author.

Study selection

All citations were entered into Endnote and uploaded to Covidence for screening and review against the inclusion/exclusion criteria. Reviewers with high inter-rater reliability (98%) independently screened the titles and abstracts. Two reviewers then independently screened full text of articles that met criteria. Duplicates, irrelevant studies, and studies that did not meet the criteria were removed, and the reason for exclusion was recorded (see S1 File for a list of excluded studies). Discrepancies were resolved by discussion with the team leads.

Data extraction

Two reviewers independently extracted data that included: (i) study characteristics (author, publication year, location, design, study aim), (ii) population (age, gender, race/ethnicity, education, family income, depression status), (iii) setting, (iv) intervention description (therapeutic or preventative, whether PS was provided alone or as part of a more comprehensive intervention, duration, delivery mode), (v) treatment outcomes (measures used and reported outcomes for depression, suicidality, and PS), and (vi) fidelity/implementation outcomes. For treatment outcomes, we included the original statistical analyses and/or values needed to calculate an effect size, as reported by the authors. If a variable was not included in the study publication, we extracted the information available and made note of missing data and subsequent limitations to the analyses.

RCTs were assessed for quality (i.e., confidence in the study’s findings) using the Cochrane Risk of Bias 2.0 tool [ 33 ] which includes assessment of the potential risk of bias relating to the process of randomisation; deviations from the intended intervention(s); missing data; outcome measurement and reported results. Risk of bias pertaining to each domain is estimated using an algorithm, grouped as: Low risk; Some concerns; or High risk. Two reviewers independently assessed the quality of included studies, and discrepancies were resolved by consensus.

We planned to conduct one or more meta-analyses if the studies were sufficiently similar. Data were entered into a summary of findings table as a first step in determining the theoretical and practical similarity of the population, intervention, comparison condition, outcome, and study design. If there were sufficiently similar studies, a meta-analysis would be conducted according to guidelines contained in the Cochrane Collaboration Handbook of Systematic Reviews, including tests of heterogeneity and use of random effects models where necessary.

The two searches yielded a total number of 874 records (after the removal of duplicates). After title and abstract screening, 184 full-text papers were considered for inclusion, of which 25 studies met the eligibility criteria and were included in the systematic review ( Fig 1 ). Unfortunately, substantial differences (both theoretical and practical) precluded any relevant meta-analyses, and we were limited to a narrative synthesis.

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https://doi.org/10.1371/journal.pone.0285949.g001

Risk of bias assessment

Risk of bias assessments were conducted on the 23 RCTs ( Fig 2 ; assessments by study presented in S1 Table ). Risk of bias concerns were moderate, and a fair degree of confidence in the validity of study findings is warranted. Most studies (81%) were assessed as ‘some concerns’ (N = 18), four studies were ‘low risk’, and one ‘high risk’. The most frequent areas of concern were the selection of the reported result (n = 18, mostly due to inadequate reporting of a priori analytic plans); deviations from the intended intervention (N = 17, mostly related to insufficient information about intention-to-treat analyses); and randomisation process (N = 13).

https://doi.org/10.1371/journal.pone.0285949.g002

Study designs and characteristics

Study design..

Across the 25 studies, 23 were RCTs; two were QEDs. Nine had TAU or wait-list control (WLC) comparator groups, and 16 used active control groups (e.g., alternative treatment). Eleven studies described fidelity measures. The sample size ranged from 26 to 686 and was under 63 in nine studies.

Selected intervention.

Twenty interventions were described across the 25 studies ( Table 1 ). Ten interventions focused purely on PS. Of these 10 interventions: three were adaptations of models proposed by D’Zurilla and Nezu [ 20 , 34 ] and D’Zurilla and Goldfried [ 18 ], two were based on Mynors-Wallis’s [ 35 ] Problem-Solving Therapy (PST) guide, one was a problem-orientation video intervention adapted from D’Zurilla and Nezu [ 34 ], one was an online intervention adapted from Method of Levels therapy, and three did not specify a model. Ten interventions used PS as part of a larger, more comprehensive intervention (e.g., PS as a portion of cognitive therapy). The utilization and dose of PS steps included in these interventions were unclear. Ten interventions were primary prevention interventions–one of these was universal prevention, five were indicated prevention, and four were selective prevention. Ten interventions were secondary prevention interventions. Nine interventions were described as having been developed or adapted for young people.

https://doi.org/10.1371/journal.pone.0285949.t001

Intervention delivery.

Of the 20 interventions, eight were delivered individually, eight were group-based, two were family-based, one was mixed, and in one, the format of delivery was unclear. Seventeen were delivered face-to-face and three online. Dosage ranged from a single session to 21, 50-minute sessions (12 weekly sessions, then 6 biweekly sessions); the most common session formar was once weekly for six weeks (N = 5).

Intervention setting and participants.

Seventeen studies were conducted in high-income countries (UK, US, Australia, Netherlands, South Korea), four in upper-middle income (Brazil, South Africa, Turkey), and four in low- and middle-income countries (Zimbabwe, Nigeria, India). Four studies included participants younger than 13 and four older than 25. Nine studies were conducted on university or high school student populations and five on pregnant or post-partum mothers. The remaining 11 used populations from mental health clinics, the community, a diabetes clinic, juvenile detention, and a runaway shelter.

Sixteen studies included participants who met the criteria for a depressive, bipolar, or suicidal disorder (two of these excluded severe depression). Nine studies did not use depression symptoms in the inclusion criteria (one of these excluded depression). Several studies excluded other significant mental health conditions.

Outcome measures.

Eight interventions targeted depression, four post/perinatal depression, two suicidal ideation, two resilience, one ‘problem-related distress’, one ‘diabetes distress’, one common adolescent mental health problem, and one mood episode. Those targeting post/perinatal depression used the Edinburgh Postnatal Depression Scale as the outcome measure. Of the others, six used the Beck Depression Inventory (I or II), two the Children’s Depression Inventory, three the Depression Anxiety Stress Scale-21, three the Centre for Epidemiologic Studies Depression Scale, one the Short Mood and Feelings Questionnaire, one the Hamilton Depression Rating Scale, one the depression subscale on the Schedule for Affective Disorders and Schizophrenia for School-Age Children, one the Strengths and Difficulties Questionnaire, one the Youth Top Problems Score, one the Adolescent Longitudinal Interval Follow-up Evaluation and Psychiatric Status Ratings, one the Kiddie Schedule for Affective Disorders and Schizophrenia, and one the Mini International Neuropsychiatric Interview.

Only eight studies measured PS skills or orientation outcomes. Three used the Social Problem-Solving Inventory-Revised, one the Problem Solving Inventory, two measured the extent to which the nominated problem had been resolved, one observed PS in video-taped interactions, and one did not specify the measure.

The mixed findings regarding the effectiveness of PS for depression may depend on the type of intervention: primary (universal, selective, or indicated), secondary or tertiary prevention. Universal prevention interventions target the general public or a population not determined by any specific criteria [ 36 ]. Selective prevention interventions target specific populations with an increased risk of developing a disorder. Indicated prevention interventions target high-risk individuals with sub-clinical symptoms of a disorder. Secondary prevention interventions include those that target individuals diagnosed with a disorder. Finally, tertiary prevention interventions refer to follow-up interventions designed to retain treatment effects. Outcomes are therefore grouped by intervention prevention type and outcome. Within these groupings, studies with a lower risk of bias (RCTs) are presented first. According to the World Health Organisation guidelines, interventions were defined as primary, secondary or tertiary prevention [ 36 ].

Universal prevention interventions

One study reported on a universal prevention intervention targeting resilience and coping strategies in US university students. The Resilience and Coping Intervention, which includes PS as a primary component of the intervention, found a significant reduction in depression compared to TAU (RCT, N = 129, moderate risk of bias) [ 37 ].

Selective prevention interventions

Six studies, including five RCTs and one QED, tested PS as a selective prevention intervention. Two studies investigated the impact of the Manage Your Life Online program, which includes PS as a primary component of the intervention, compared with an online programme emulating Rogerian psychotherapy for UK university students (RCT, N = 213, moderate risk of bias [ 38 ]; RCT, N = 48, moderate risk of bias [ 39 ]). Both studies found no differences in depression or problem-related distress between groups.

Similarly, two studies explored the effect of adapting the Penn Resilience Program, which includes PS as a component of a more comprehensive intervention for young people with diabetes in the US (RCT, N = 264, moderate risk of bias) [ 40 , 41 ]. The initial study showed a moderate reduction in diabetes distress but not depression at 4-, 8-, 12- and 16-months follow-up compared to a diabetes education intervention [ 40 ]. The follow-up study found a significant reduction in depressive symptoms compared to the active control from 16- to 40-months; however, this did not reach significance at 40-months [ 41 ].

Another study that was part of wider PS and social skills intervention among juveniles in state-run detention centres in the US found no impacts (RCT, N = 296, high risk of bias) [ 42 ]. A QED ( N = 32) was used to test the effectiveness of a resilience enhancement and prevention intervention for runaway youth in South Korea [ 43 ]. There was a significant decrease in depression for the intervention group compared with the control group at post-test, but the difference was not sustained at one-month follow-up.

Indicated prevention interventions

Six studies, including five RCTs and one QED, tested PS as an indicated prevention intervention. Four of the five RCTs tested PS as a primary component of the intervention. A PS intervention for common adolescent mental health problems in Indian high school students (RCT, N = 251, low risk of bias) led to a significant reduction in psychosocial problems at 6- and 12 weeks; however, it did not have a significant impact on mental health symptoms or internalising symptoms compared to PS booklets without counsellor treatment at 6- and 12-weeks [ 31 ]. A follow-up study showed a significant reduction in overall psychosocial problems and mental health symptoms, including internalizing symptoms, over 12 months [ 44 ]. Still, these effects no longer reached significance in sensitivity analysis adjusting for missing data (RCT, N = 251, low risk of bias). Furthermore, a 2x2 factorial RCT ( N = 176, moderate risk of bias) testing PST among youth mental health service users with a mild mental disorder in Australia found that the intervention was not superior to supportive counselling at 2-weeks post-treatment [ 30 ]. Similarly, an online PS intervention delivered to young people in the Netherlands to prevent depression (RCT, N = 45, moderate risk of bias) found no significant difference between the intervention and WLC in depression level 4-months post-treatment [ 45 ].

One RCT tested PS approaches in a more comprehensive manualized programme for postnatal depression in the UK and found no significant differences in depression scores between intervention and TAU at 3-months post-partum (RCT, N = 292, moderate risk of bias) [ 46 ].

A study in Turkey used a non-equivalent control group design (QED, N = 62) to test a nursing intervention against a PS control intervention [ 47 ]. Both groups showed a reduction in depression, but the nursing care intervention demonstrated a larger decrease post-intervention than the PS control intervention.

Secondary prevention interventions

Twelve studies, all RCTs, tested PS as a secondary prevention intervention. Four of the 12 RCTs tested PS as a primary component of the intervention. An intervention among women in Zimbabwe (RCT, N = 58, moderate risk of bias) found a larger decrease in the Edinburgh Postnatal Depression Scale score for the intervention group compared to control (who received the antidepressant amitriptyline and peer education) at 6-weeks post-treatment [ 48 ]. A problem-orientation intervention covering four PST steps and involving a single session video for US university students (RCT, N = 110, moderate risk of bias), compared with a video covering other health issues, resulted in a moderate reduction in depression post-treatment; however, results were no longer significant at 2-weeks, and 1-month follow up [ 49 ].

Compared to WLC, a study of an intervention for depression and suicidal proneness among high school and university students in Turkey (RCT, N = 46, moderate risk of bias) found large effect sizes on post-treatment depression scores for intervention participants post-treatment compared with WLC. At 12-month follow-up, these improvements were maintained compared to pre-test but not compared to post-treatment scores. Significant post-treatment depression recovery was also found in the PST group [ 12 ]. Compared to TAU, a small but high-quality (low-risk of bias) study focused on preventing suicidal risk among school students in Brazil (RCT, N = 100, low risk of bias) found a significant, moderate reduction in depression symptoms for the treatment group post-intervention that was maintained at 1-, 3- and 6-month follow-up [ 50 ].

Seven of the 12 RCTs tested PS as a part of a more comprehensive intervention. Two interventions targeted mood episodes and were compared to active control. These US studies focused on Family-Focused Therapy as an intervention for mood episodes, which included sessions on PS [ 51 , 52 ]. One of these found that Family-Focused Therapy for AYA with Bipolar Disorder (RCT, N = 145, moderate risk of bias) had no significant impact on mood or depressive symptoms compared to pharmacotherapy. However, Family-Focused Therapy had a greater impact on the proportion of weeks without mania/hypomania and mania/hypomania symptoms than enhanced care [ 53 ]. Alternatively, while the other study (RCT, N = 127, low risk of bias) found no significant impact on time to recovery, Family-Focused Therapy led to significantly longer intervals of wellness before new mood episodes, longer intervals between recovery and the next mood episode, and longer intervals of randomisation to the next mood episode in AYA with either Bipolar Disorder (BD) or Major Depressive Disorder (MDD), compared to family and individual psychoeducation [ 52 ].

Two US studies used a three-arm trial to compare Systemic-behavioural Family Therapy (SBFT) with elements of PS, to CBT and individual Non-directive Supportive therapy (NST) (RCT, N = 107, moderate risk of bias) [ 53 , 54 ]. One study looked at whether the PS elements of CBT and SFBT mediated the effectiveness of these interventions for the remission of MDD. It found that PS mediated the association between CBT, but not SFBT, and remission from depression. There was no significant association between SBFT and remission status, though there was a significant association between CBT and remission status [ 53 ]. The other study found no significant reduction in depression post-treatment or at 24-month follow-up for SBFT [ 54 ].

A PS intervention tested in maternal and child clinics in Nigeria RCT ( N = 686, moderate risk of bias) compared with enhanced TAU involving psychosocial and social support found no significant difference in the proportion of women who recovered from depression at 6-months post-partum [ 55 ]. However, there was a small difference in depression scores in favour of PS averaged across the 3-, 6-, 9-, and 12-month follow-up points. Cognitive Reminiscence Therapy, which involved recollection of past PS experiences and drew on PS techniques used for 12-25-year-olds in community mental health services in Australia (RCT, N = 26, moderate risk of bias), did not reduce depression symptoms compared with a brief evidence-based treatment at 1- or 2-month follow-up [ 56 ]. Additionally, the High School Transition Program in the US (RCT, N = 497, moderate risk of bias) aimed to prevent depression, anxiety, and school problems in youth transitioning to high school [ 57 ]. There was no reduction in the percentage of intervention students with clinical depression compared to the control group. Similarly, a small study focused on reducing depression symptoms, and nonadherence to antiretroviral therapy in pregnant women with HIV in South Africa (RCT, N = 23, some concern) found a significant reduction in depression symptoms compared to TAU, with the results being maintained at the 3-month follow-up [ 58 ].

Reduction in suicidality

Three studies measured a reduction in suicidality. A preventive treatment found a large reduction in suicidal orientation in the PS group compared to control post-treatment. In contrast, suicidal ideation scores were inconsistent at 1-,3- and 6- month follow-up, they maintained an overall lower score [ 50 ]. Furthermore, at post-test, significantly more participants in the PS group were no longer at risk of suicide. No significant differences were found in suicide plans or attempts. In a PST intervention, post-treatment suicide risk scores were lower than pre-treatment for the PST group but unchanged for the control group [ 12 ]. An online treatment found a moderate decline in ideation for the intervention group post-treatment compared to the control but was not sustained at a one-month follow-up [ 49 ].

Mediators and moderators

Eight studies measured PS skills or effectiveness. In two studies, despite the interventions reducing depression, there was no improvement in PS abilities [ 12 , 52 ]. One found that change in global and functional PS skills mediated the relationship between the intervention group and change in suicidal orientation, but this was not assessed for depression [ 50 ]. Three other studies found no change in depression symptoms, PS skills, or problem resolution [ 38 – 40 ]. Finally, CBT and SBFT led to significant increases in PS behaviour, and PS was associated with higher rates of remission across treatments but did not moderate the relationship between SBFT and remission status [ 53 ]. Another study found no changes in confidence in the ability to solve problems or belief in personal control when solving problems. Furthermore, the intervention group was more likely to adopt an avoidant PS style [ 46 ].

A high-intensity intervention for perinatal depression in Nigeria had no treatment effect on depression remission rates for the whole sample. Still, it was significantly effective for participants with more severe depression at baseline [ 55 ]. A PS intervention among juvenile detainees in the US effectively reduced depression for participants with higher levels of fluid intelligence, but symptoms increased for those with lower levels [ 42 ].The authors suggest that individuals with lower levels of fluid intelligence may have been less able to cope with exploring negative emotions and apply the skills learned.

This review has examined the evidence on the effectiveness of PS in the prevention or treatment of depression among 13–25-year-olds. We sought to determine in what way, in which contexts, and for whom PS appears to work in addressing depression. We found 25 studies involving 20 interventions. Results are promising for secondary prevention interventions, or interventions targeting clinical level populations, that utilize PS as the primary intervention [ 12 , 47 – 49 ]. These studies not only found a significant reduction in depression symptoms compared to active [ 48 , 49 ] and non-active [ 12 , 47 ] controls but also found a significant reduction in suicidal orientation and ideation [ 12 , 47 , 49 ]. These findings are consistent with meta-analyses of adult PS interventions [ 21 , 22 , 23 ], highlighting that PS interventions for AYA can be effective in real-world settings.

For other types of interventions (i.e., universal, selective prevention, indicated prevention), results were mixed in reducing depression. The one universal program was found to have a small, significant effect in reducing depression symptoms compared to a non-active control [ 37 ]. Most selective prevention programs were not effective [ 39 , 40 , 56 ], and those that did show small, significant effects had mixed outcomes for follow-up maintenance [ 41 , 42 ]. Most indicated prevention programs were not effective [ 30 , 31 , 45 – 47 ], yet a follow-up study showed a significant reduction in internalizing symptoms at 12-month post-treatment compared to an active control [ 44 ]. Given that these studies targeted sub-clinical populations and many of them had small sample sizes, these mixed findings may be a result of not having sufficient power to detect a meaningful difference.

Our review found limited evidence about PS skills as mediator or moderator of depression. Few studies measured improvements in PS skills; fewer still found interventions to be effective. The absence of evidence for PS abilities as a pathway is puzzling. It may be that specific aspects of PS behaviours and processes, such as problem orientation [ 59 ], are relevant. Alternatively, there may be a mechanism other than PS skills through which PS interventions influence depression.

Studies with PS as part of a wider intervention also showed mixed results, even amongst clinical populations. Although there was no clear rationale for the discrepancies in effectiveness between the studies, it is possible that the wider program dilutes the focus and impact of efficacious therapeutic elements. However, this is difficult to discern given the heterogeneity in the studies and limited information on study treatments and implementation factors. A broad conclusion might be that PS can be delivered most effectively with clinical populations in its purest PS form and may be tailored to a range of different contexts and forms, a range of populations, and to address different types of problems; however, this tailoring may reduce effectiveness.

Although the scale of impact is broadly in line with the small to moderate effectiveness of other treatments for youth depression [ 6 ], our review highlights shortcomings in study design, methods, and reporting that would allow for a better understanding of PS effectiveness and pathways. Studies varied in how well PS was operationalised. Low dosage is consistent with usage described in informal conversations with practitioners but may be insufficient for effectiveness. Fidelity was monitored in only half the studies despite evidence that monitoring implementation improves effectiveness [ 60 ]. There were references to implementation difficulties, including attrition, challenges in operationalizing online interventions, and skills of those delivering. Furthermore, most of the studies had little information about comorbidity and no analysis of whether it influenced outcomes. Therefore, we were unable to fully examine and conceptualize the ways, how and for whom PS works. More information about study populations and intervention implementation is essential to understand the potential of PS for broader dissemination.

Our review had several limitations. We excluded studies that included four treatments known to be effective in treating depression among AYA (e.g., CBT) but where the unique contribution of PS to clinical outcome could not be disentangled. Furthermore, we relied on authors’ reporting to determine if PS was included: details about operationalization of PS were often scant. Little evidence addressing the fit, feasibility, or acceptability of PS interventions was found, reflecting a limited focus on implementation. We included only English-language texts: relevant studies in other languages may exist, though our post-2000 inclusion criteria may limit this potential bias due to improved translation of studies to English over the years. Finally, the heterogeneity of study populations, problem severity, comparison conditions, outcome measures, and study designs, along with a relatively small number of included studies, limits confidence in what we can say about implementation and treatment outcomes.

Overall, our review indicates that PS may have the best results when implemented its purest form as a stand-alone treatment with clinical level AYA populations; tailoring or imbedding PS into wider programming may dilute its effectiveness. Our review also points to a need for continued innovation in treatment to improve the operationalizing and testing of PS, especially when included as a part of a more comprehensive intervention. It also highlights the need for study methods that allow us to understand the specific effects of PS, and that measure the frequency, dosage, and timing of PS to understand what is effective for whom and in what contexts.

Supporting information

S1 file. list of excluded studies..

https://doi.org/10.1371/journal.pone.0285949.s001

S2 File. PRISMA checklist.

https://doi.org/10.1371/journal.pone.0285949.s002

S1 Table. Individual risk of bias assessments using cochrane RoB2 tool by domain (1–5) and overall (6).

https://doi.org/10.1371/journal.pone.0285949.s003

Acknowledgments

All individuals that contributed to this paper are included as authors.

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CONCEPTUAL ANALYSIS article

Complex problem solving: what it is and what it is not.

• 1 Department of Psychology, University of Bamberg, Bamberg, Germany
• 2 Department of Psychology, Heidelberg University, Heidelberg, Germany

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011 ; Griffin and Care, 2015 ), to name only a few. One competence that seems to be of central importance is the ability to solve complex problems ( Mainzer, 2009 ). Mainzer quotes the Nobel prize winner Simon (1957) who wrote as early as 1957:

The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality. (p. 198)

The shift from well-defined to ill-defined problems came about as a result of a disillusion with the “general problem solver” ( Newell et al., 1959 ): The general problem solver was a computer software intended to solve all kind of problems that can be expressed through well-formed formulas. However, it soon became clear that this procedure was in fact a “special problem solver” that could only solve well-defined problems in a closed space. But real-world problems feature open boundaries and have no well-determined solution. In fact, the world is full of wicked problems and clumsy solutions ( Verweij and Thompson, 2006 ). As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes ( Schraw et al., 1995 ; but see Funke, 2010 ).

Well-defined problems have a clear set of means for reaching a precisely described goal state. For example: in a match-stick arithmetic problem, a person receives a false arithmetic expression constructed out of matchsticks (e.g., IV = III + III). According to the instructions, moving one of the matchsticks will make the equations true. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III + III) are defined clearly.

Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. For example: The goal state for solving the political conflict in the near-east conflict between Israel and Palestine is not clearly defined (living in peaceful harmony with each other?) and even if the conflict parties would agree on a two-state solution, this goal again leaves many issues unresolved. This type of problem is called a “complex problem” and is of central importance to this paper. All psychological processes that occur within individual persons and deal with the handling of such ill-defined complex problems will be subsumed under the umbrella term “complex problem solving” (CPS).

Systematic research on CPS started in the 1970s with observations of the behavior of participants who were confronted with computer simulated microworlds. For example, in one of those microworlds participants assumed the role of executives who were tasked to manage a company over a certain period of time (see Brehmer and Dörner, 1993 , for a discussion of this methodology). Today, CPS is an established concept and has even influenced large-scale assessments such as PISA (“Programme for International Student Assessment”), organized by the Organization for Economic Cooperation and Development ( OECD, 2014 ). According to the World Economic Forum, CPS is one of the most important competencies required in the future ( World Economic Forum, 2015 ). Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers ( Blech and Funke, 2010 ; Funke, 2010 ; Knauff and Wolf, 2010 ; Leutner et al., 2012 ; Selten et al., 2012 ; Wüstenberg et al., 2012 ; Greiff et al., 2013b ; Fischer and Neubert, 2015 ; Schoppek and Fischer, 2015 ), papers about measurement issues ( Danner et al., 2011a ; Greiff et al., 2012 , 2015a ; Alison et al., 2013 ; Gobert et al., 2015 ; Greiff and Fischer, 2013 ; Herde et al., 2016 ; Stadler et al., 2016 ), papers about applications ( Fischer and Neubert, 2015 ; Ederer et al., 2016 ; Tremblay et al., 2017 ), papers about differential effects ( Barth and Funke, 2010 ; Danner et al., 2011b ; Beckmann and Goode, 2014 ; Greiff and Neubert, 2014 ; Scherer et al., 2015 ; Meißner et al., 2016 ; Wüstenberg et al., 2016 ), one paper about developmental effects ( Frischkorn et al., 2014 ), one paper with a neuroscience background ( Osman, 2012 ) 1 , papers about cultural differences ( Güss and Dörner, 2011 ; Sonnleitner et al., 2014 ; Güss et al., 2015 ), papers about validity issues ( Goode and Beckmann, 2010 ; Greiff et al., 2013c ; Schweizer et al., 2013 ; Mainert et al., 2015 ; Funke et al., 2017 ; Greiff et al., 2017 , 2015b ; Kretzschmar et al., 2016 ; Kretzschmar, 2017 ), review papers and meta-analyses ( Osman, 2010 ; Stadler et al., 2015 ), and finally books ( Qudrat-Ullah, 2015 ; Csapó and Funke, 2017b ) and book chapters ( Funke, 2012 ; Hotaling et al., 2015 ; Funke and Greiff, 2017 ; Greiff and Funke, 2017 ; Csapó and Funke, 2017a ; Fischer et al., 2017 ; Molnàr et al., 2017 ; Tobinski and Fritz, 2017 ; Viehrig et al., 2017 ). In addition, a new “Journal of Dynamic Decision Making” (JDDM) has been launched ( Fischer et al., 2015 , 2016 ) to give the field an open-access outlet for research and discussion.

This paper aims to clarify aspects of validity: what should be meant by the term CPS and what not? This clarification seems necessary because misunderstandings in recent publications provide – from our point of view – a potentially misleading picture of the construct. We start this article with a historical review before attempting to systematize different positions. We conclude with a working definition.

Historical Review

The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986 ). The concept was introduced in Germany by Dörner and colleagues in the mid-1970s (see Dörner et al., 1975 ; Dörner, 1975 ) for the first time. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch (1991) and Frensch and Funke (1995a) that collected papers from different research traditions. Even though it looks as though the term was coined in the 1970s, Edwards (1962) used the term “dynamic decision making” to describe decisions that come in a sequence. He compared static with dynamic decision making, writing:

In dynamic situations, a new complication not found in the static situations arises. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. (p. 60)

The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Early work (see, e.g., Dörner, 1980 ) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Later, researchers used smaller dynamic systems as scenarios either based on linear equations (see, e.g., Funke, 1993 ) or on finite state automata (see, e.g., Buchner and Funke, 1993 ). In these contexts, CPS consisted of the identification and control of dynamic task environments that were previously unknown to the participants. Different task environments came along with different degrees of fidelity ( Gray, 2002 ).

According to Funke (2012) , the typical attributes of complex systems are (a) complexity of the problem situation which is usually represented by the sheer number of involved variables; (b) connectivity and mutual dependencies between involved variables; (c) dynamics of the situation, which reflects the role of time and developments within a system; (d) intransparency (in part or full) about the involved variables and their current values; and (e) polytely (greek term for “many goals”), representing goal conflicts on different levels of analysis. This mixture of features is similar to what is called VUCA (volatility, uncertainty, complexity, ambiguity) in modern approaches to management (e.g., Mack et al., 2016 ).

In his evaluation of the CPS movement, Sternberg (1995) compared (young) European approaches to CPS with (older) American research on expertise. His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states (p. 301): “I believe that although there are problems with the European approach, it deals with some fundamental questions that American research scarcely addresses.” So, even though the echo of the European approach did not enjoy strong resonance in the US at that time, it was valued by scholars like Sternberg and others. Before attending to validity issues, we will first present a short review of different streams.

Different Approaches to CPS

In the short history of CPS research, different approaches can be identified ( Buchner, 1995 ; Fischer et al., 2017 ). To systematize, we differentiate between the following five lines of research:

(a) The search for individual differences comprises studies identifying interindividual differences that affect the ability to solve complex problems. This line of research is reflected, for example, in the early work by Dörner et al. (1983) and their “Lohhausen” study. Here, naïve student participants took over the role of the mayor of a small simulated town named Lohhausen for a simulation period of ten years. According to the results of the authors, it is not intelligence (as measured by conventional IQ tests) that predicts performance, but it is the ability to stay calm in the face of a challenging situation and the ability to switch easily between an analytic mode of processing and a more holistic one.

(b) The search for cognitive processes deals with the processes behind understanding complex dynamic systems. Representative of this line of research is, for example, Berry and Broadbent’s (1984) work on implicit and explicit learning processes when people interact with a dynamic system called “Sugar Production”. They found that those who perform best in controlling a dynamic system can do so implicitly, without explicit knowledge of details regarding the systems’ relations.

(c) The search for system factors seeks to identify the aspects of dynamic systems that determine the difficulty of complex problems and make some problems harder than others. Representative of this line of research is, for example, work by Funke (1985) , who systematically varied the number of causal effects within a dynamic system or the presence/absence of eigendynamics. He found, for example, that solution quality decreases as the number of systems relations increases.

(d) The psychometric approach develops measurement instruments that can be used as an alternative to classical IQ tests, as something that goes “beyond IQ”. The MicroDYN approach ( Wüstenberg et al., 2012 ) is representative for this line of research that presents an alternative to reasoning tests (like Raven matrices). These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.

(e) The experimental approach explores CPS under different experimental conditions. This approach uses CPS assessment instruments to test hypotheses derived from psychological theories and is sometimes used in research about cognitive processes (see above). Exemplary for this line of research is the work by Rohe et al. (2016) , who test the usefulness of “motto goals” in the context of complex problems compared to more traditional learning and performance goals. Motto goals differ from pure performance goals by activating positive affect and should lead to better goal attainment especially in complex situations (the mentioned study found no effect).

To be clear: these five approaches are not mutually exclusive and do overlap. But the differentiation helps to identify different research communities and different traditions. These communities had different opinions about scaling complexity.

The Race for Complexity: Use of More and More Complex Systems

In the early years of CPS research, microworlds started with systems containing about 20 variables (“Tailorshop”), soon reached 60 variables (“Moro”), and culminated in systems with about 2000 variables (“Lohhausen”). This race for complexity ended with the introduction of the concept of “minimal complex systems” (MCS; Greiff and Funke, 2009 ; Funke and Greiff, 2017 ), which ushered in a search for the lower bound of complexity instead of the higher bound, which could not be defined as easily. The idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. Imagine starting with a simple system containing two variables with a simple linear connection between them; then, step by step, increase the number of variables and/or the type of connections. One soon reaches a point where the system can no longer be considered simple and has become a “complex system”. This point represents a minimal complex system. Despite some research having been conducted in this direction, the point of transition from simple to complex has not been identified clearly as of yet.

Some years later, the original “minimal complex systems” approach ( Greiff and Funke, 2009 ) shifted to the “multiple complex systems” approach ( Greiff et al., 2013a ). This shift is more than a slight change in wording: it is important because it taps into the issue of validity directly. Minimal complex systems have been introduced in the context of challenges from large-scale assessments like PISA 2012 that measure new aspects of problem solving, namely interactive problems besides static problem solving ( Greiff and Funke, 2017 ). PISA 2012 required test developers to remain within testing time constraints (given by the school class schedule). Also, test developers needed a large item pool for the construction of a broad class of problem solving items. It was clear from the beginning that MCS deal with simple dynamic situations that require controlled interaction: the exploration and control of simple ticket machines, simple mobile phones, or simple MP3 players (all of these example domains were developed within PISA 2012) – rather than really complex situations like managerial or political decision making.

As a consequence of this subtle but important shift in interpreting the letters MCS, the definition of CPS became a subject of debate recently ( Funke, 2014a ; Greiff and Martin, 2014 ; Funke et al., 2017 ). In the words of Funke (2014b , p. 495):

It is funny that problems that nowadays come under the term ‘CPS’, are less complex (in terms of the previously described attributes of complex situations) than at the beginning of this new research tradition. The emphasis on psychometric qualities has led to a loss of variety. Systems thinking requires more than analyzing models with two or three linear equations – nonlinearity, cyclicity, rebound effects, etc. are inherent features of complex problems and should show up at least in some of the problems used for research and assessment purposes. Minimal complex systems run the danger of becoming minimal valid systems.

Searching for minimal complex systems is not the same as gaining insight into the way how humans deal with complexity and uncertainty. For psychometric purposes, it is appropriate to reduce complexity to a minimum; for understanding problem solving under conditions of overload, intransparency, and dynamics, it is necessary to realize those attributes with reasonable strength. This aspect is illustrated in the next section.

Importance of the Validity Issue

The most important reason for discussing the question of what complex problem solving is and what it is not stems from its phenomenology: if we lose sight of our phenomena, we are no longer doing good psychology. The relevant phenomena in the context of complex problems encompass many important aspects. In this section, we discuss four phenomena that are specific to complex problems. We consider these phenomena as critical for theory development and for the construction of assessment instruments (i.e., microworlds). These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

The first phenomenon is the emergency reaction of the intellectual system ( Dörner, 1980 ): When dealing with complex systems, actors tend to (a) reduce their intellectual level by decreasing self-reflections, by decreasing their intentions, by stereotyping, and by reducing their realization of intentions, (b) they show a tendency for fast action with increased readiness for risk, with increased violations of rules, and with increased tendency to escape the situation, and (c) they degenerate their hypotheses formation by construction of more global hypotheses and reduced tests of hypotheses, by increasing entrenchment, and by decontextualizing their goals. This phenomenon illustrates the strong connection between cognition, emotion, and motivation that has been emphasized by Dörner (see, e.g., Dörner and Güss, 2013 ) from the beginning of his research tradition; the emergency reaction reveals a shift in the mode of information processing under the pressure of complexity.

The second phenomenon comprises cross-cultural differences with respect to strategy use ( Strohschneider and Güss, 1999 ; Güss and Wiley, 2007 ; Güss et al., 2015 ). Results from complex task environments illustrate the strong influence of context and background knowledge to an extent that cannot be found for knowledge-poor problems. For example, in a comparison between Brazilian and German participants, it turned out that Brazilians accept the given problem descriptions and are more optimistic about the results of their efforts, whereas Germans tend to inquire more about the background of the problems and take a more active approach but are less optimistic (according to Strohschneider and Güss, 1998 , p. 695).

The third phenomenon relates to failures that occur during the planning and acting stages ( Jansson, 1994 ; Ramnarayan et al., 1997 ), illustrating that rational procedures seem to be unlikely to be used in complex situations. The potential for failures ( Dörner, 1996 ) rises with the complexity of the problem. Jansson (1994) presents seven major areas for failures with complex situations: acting directly on current feedback; insufficient systematization; insufficient control of hypotheses and strategies; lack of self-reflection; selective information gathering; selective decision making; and thematic vagabonding.

The fourth phenomenon describes (a lack of) training and transfer effects ( Kretzschmar and Süß, 2015 ), which again illustrates the context dependency of strategies and knowledge (i.e., there is no strategy that is so universal that it can be used in many different problem situations). In their own experiment, the authors could show training effects only for knowledge acquisition, not for knowledge application. Only with specific feedback, performance in complex environments can be increased ( Engelhart et al., 2017 ).

These four phenomena illustrate why the type of complexity (or degree of simplicity) used in research really matters. Furthermore, they demonstrate effects that are specific for complex problems, but not for toy problems. These phenomena direct the attention to the important question: does the stimulus material used (i.e., the computer-simulated microworld) tap and elicit the manifold of phenomena described above?

Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. In creativity research, “little c” and “BIG C” are used to differentiate between everyday creativity and eminent creativity ( Beghetto and Kaufman, 2007 ; Kaufman and Beghetto, 2009 ). Everyday creativity is important for solving everyday problems (e.g., finding a clever fix for a broken spoke on my bicycle), eminent creativity changes the world (e.g., inventing solar cells for energy production). Maybe problem solving research should use a similar differentiation between “little p” and “BIG P” to mark toy problems on the one side and big societal challenges on the other. The question then remains: what can we learn about BIG P by studying little p? What phenomena are present in both types, and what phenomena are unique to each of the two extremes?

Discussing research on CPS requires reflecting on the field’s research methods. Even if the experimental approach has been successful for testing hypotheses (for an overview of older work, see Funke, 1995 ), other methods might provide additional and novel insights. Complex phenomena require complex approaches to understand them. The complex nature of complex systems imposes limitations on psychological experiments: The more complex the environments, the more difficult is it to keep conditions under experimental control. And if experiments have to be run in labs one should bring enough complexity into the lab to establish the phenomena mentioned, at least in part.

There are interesting options to be explored (again): think-aloud protocols , which have been discredited for many years ( Nisbett and Wilson, 1977 ) and yet are a valuable source for theory testing ( Ericsson and Simon, 1983 ); introspection ( Jäkel and Schreiber, 2013 ), which seems to be banned from psychological methods but nevertheless offers insights into thought processes; the use of life-streaming ( Wendt, 2017 ), a medium in which streamers generate a video stream of think-aloud data in computer-gaming; political decision-making ( Dhami et al., 2015 ) that demonstrates error-proneness in groups; historical case studies ( Dörner and Güss, 2011 ) that give insights into the thinking styles of political leaders; the use of the critical incident technique ( Reuschenbach, 2008 ) to construct complex scenarios; and simulations with different degrees of fidelity ( Gray, 2002 ).

The methods tool box is full of instruments that have to be explored more carefully before any individual instrument receives a ban or research narrows its focus to only one paradigm for data collection. Brehmer and Dörner (1993) discussed the tensions between “research in the laboratory and research in the field”, optimistically concluding “that the new methodology of computer-simulated microworlds will provide us with the means to bridge the gap between the laboratory and the field” (p. 183). The idea behind this optimism was that computer-simulated scenarios would bring more complexity from the outside world into the controlled lab environment. But this is not true for all simulated scenarios. In his paper on simulated environments, Gray (2002) differentiated computer-simulated environments with respect to three dimensions: (1) tractability (“the more training subjects require before they can use a simulated task environment, the less tractable it is”, p. 211), correspondence (“High correspondence simulated task environments simulate many aspects of one task environment. Low correspondence simulated task environments simulate one aspect of many task environments”, p. 214), and engagement (“A simulated task environment is engaging to the degree to which it involves and occupies the participants; that is, the degree to which they agree to take it seriously”, p. 217). But the mere fact that a task is called a “computer-simulated task environment” does not mean anything specific in terms of these three dimensions. This is one of several reasons why we should differentiate between those studies that do not address the core features of CPS and those that do.

What is not CPS?

Even though a growing number of references claiming to deal with complex problems exist (e.g., Greiff and Wüstenberg, 2015 ; Greiff et al., 2016 ), it would be better to label the requirements within these tasks “dynamic problem solving,” as it has been done adequately in earlier work ( Greiff et al., 2012 ). The dynamics behind on-off-switches ( Thimbleby, 2007 ) are remarkable but not really complex. Small nonlinear systems that exhibit stunningly complex and unstable behavior do exist – but they are not used in psychometric assessments of so-called CPS. There are other small systems (like MicroDYN scenarios: Greiff and Wüstenberg, 2014 ) that exhibit simple forms of system behavior that are completely predictable and stable. This type of simple systems is used frequently. It is even offered commercially as a complex problem-solving test called COMPRO ( Greiff and Wüstenberg, 2015 ) for business applications. But a closer look reveals that the label is not used correctly; within COMPRO, the used linear equations are far from being complex and the system can be handled properly by using only one strategy (see for more details Funke et al., 2017 ).

Why do simple linear systems not fall within CPS? At the surface, nonlinear and linear systems might appear similar because both only include 3–5 variables. But the difference is in terms of systems behavior as well as strategies and learning. If the behavior is simple (as in linear systems where more input is related to more output and vice versa), the system can be easily understood (participants in the MicroDYN world have 3 minutes to explore a complex system). If the behavior is complex (as in systems that contain strange attractors or negative feedback loops), things become more complicated and much more observation is needed to identify the hidden structure of the unknown system ( Berry and Broadbent, 1984 ; Hundertmark et al., 2015 ).

Another issue is learning. If tasks can be solved using a single (and not so complicated) strategy, steep learning curves are to be expected. The shift from problem solving to learned routine behavior occurs rapidly, as was demonstrated by Luchins (1942) . In his water jar experiments, participants quickly acquired a specific strategy (a mental set) for solving certain measurement problems that they later continued applying to problems that would have allowed for easier approaches. In the case of complex systems, learning can occur only on very general, abstract levels because it is difficult for human observers to make specific predictions. Routines dealing with complex systems are quite different from routines relating to linear systems.

What should not be studied under the label of CPS are pure learning effects, multiple-cue probability learning, or tasks that can be solved using a single strategy. This last issue is a problem for MicroDYN tasks that rely strongly on the VOTAT strategy (“vary one thing at a time”; see Tschirgi, 1980 ). In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT.

What is CPS?

In the early days of CPS research, planet Earth’s dynamics and complexities gained attention through such books as “The limits to growth” ( Meadows et al., 1972 ) and “Beyond the limits” ( Meadows et al., 1992 ). In the current decade, for example, the World Economic Forum (2016) attempts to identify the complexities and risks of our modern world. In order to understand the meaning of complexity and uncertainty, taking a look at the worlds’ most pressing issues is helpful. Searching for strategies to cope with these problems is a difficult task: surely there is no place for the simple principle of “vary-one-thing-at-a-time” (VOTAT) when it comes to global problems. The VOTAT strategy is helpful in the context of simple problems ( Wüstenberg et al., 2014 ); therefore, whether or not VOTAT is helpful in a given problem situation helps us distinguish simple from complex problems.

Because there exist no clear-cut strategies for complex problems, typical failures occur when dealing with uncertainty ( Dörner, 1996 ; Güss et al., 2015 ). Ramnarayan et al. (1997) put together a list of generic errors (e.g., not developing adequate action plans; lack of background control; learning from experience blocked by stereotype knowledge; reactive instead of proactive action) that are typical of knowledge-rich complex systems but cannot be found in simple problems.

Complex problem solving is not a one-dimensional, low-level construct. On the contrary, CPS is a multi-dimensional bundle of competencies existing at a high level of abstraction, similar to intelligence (but going beyond IQ). As Funke et al. (2018) state: “Assessment of transversal (in educational contexts: cross-curricular) competencies cannot be done with one or two types of assessment. The plurality of skills and competencies requires a plurality of assessment instruments.”

There are at least three different aspects of complex systems that are part of our understanding of a complex system: (1) a complex system can be described at different levels of abstraction; (2) a complex system develops over time, has a history, a current state, and a (potentially unpredictable) future; (3) a complex system is knowledge-rich and activates a large semantic network, together with a broad list of potential strategies (domain-specific as well as domain-general).

Complex problem solving is not only a cognitive process but is also an emotional one ( Spering et al., 2005 ; Barth and Funke, 2010 ) and strongly dependent on motivation (low-stakes versus high-stakes testing; see Hermes and Stelling, 2016 ).

Furthermore, CPS is a dynamic process unfolding over time, with different phases and with more differentiation than simply knowledge acquisition and knowledge application. Ideally, the process should entail identifying problems (see Dillon, 1982 ; Lee and Cho, 2007 ), even if in experimental settings, problems are provided to participants a priori . The more complex and open a given situation, the more options can be generated (T. S. Schweizer et al., 2016 ). In closed problems, these processes do not occur in the same way.

In analogy to the difference between formative (process-oriented) and summative (result-oriented) assessment ( Wiliam and Black, 1996 ; Bennett, 2011 ), CPS should not be reduced to the mere outcome of a solution process. The process leading up to the solution, including detours and errors made along the way, might provide a more differentiated impression of a person’s problem-solving abilities and competencies than the final result of such a process. This is one of the reasons why CPS environments are not, in fact, complex intelligence tests: research on CPS is not only about the outcome of the decision process, but it is also about the problem-solving process itself.

Complex problem solving is part of our daily life: finding the right person to share one’s life with, choosing a career that not only makes money, but that also makes us happy. Of course, CPS is not restricted to personal problems – life on Earth gives us many hard nuts to crack: climate change, population growth, the threat of war, the use and distribution of natural resources. In sum, many societal challenges can be seen as complex problems. To reduce that complexity to a one-hour lab activity on a random Friday afternoon puts it out of context and does not address CPS issues.

Theories about CPS should specify which populations they apply to. Across populations, one thing to consider is prior knowledge. CPS research with experts (e.g., Dew et al., 2009 ) is quite different from problem solving research using tasks that intentionally do not require any specific prior knowledge (see, e.g., Beckmann and Goode, 2014 ).

More than 20 years ago, Frensch and Funke (1995b) defined CPS as follows:

CPS occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multi-step activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver’s cognitive, emotional, personal, and social abilities and knowledge. (p. 18)

The above definition is rather formal and does not account for content or relations between the simulation and the real world. In a sense, we need a new definition of CPS that addresses these issues. Based on our previous arguments, we propose the following working definition:

Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.

The main differences to the older definition lie in the emphasis on (a) the self-regulation of processes, (b) creativity (as opposed to routine behavior), (c) the bricolage type of solution, and (d) the role of high-stakes challenges. Our new definition incorporates some aspects that have been discussed in this review but were not reflected in the 1995 definition, which focused on attributes of complex problems like dynamics or intransparency.

This leads us to the final reflection about the role of CPS for dealing with uncertainty and complexity in real life. We will distinguish thinking from reasoning and introduce the sense of possibility as an important aspect of validity.

CPS as Combining Reasoning and Thinking in an Uncertain Reality

Leading up to the Battle of Borodino in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war to his friend Pierre. Pierre expects war to resemble a game of chess: You position the troops and attempt to defeat your opponent by moving them in different directions.

“Far from it!”, Andrei responds. “In chess, you know the knight and his moves, you know the pawn and his combat strength. While in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. In chess, you can see all of your opponent’s possible moves. In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Many a time, you cannot even know whether your troops will follow your orders…”

In essence, war is characterized by a high degree of uncertainty. A good commander (or politician) can add to that what he or she sees, tentatively fill in the blanks – and not just by means of logical deduction but also by intelligently bridging missing links. A bad commander extrapolates from what he sees and thus arrives at improper conclusions.

Many languages differentiate between two modes of mentalizing; for instance, the English language distinguishes between ‘thinking’ and ‘reasoning’. Reasoning denotes acute and exact mentalizing involving logical deductions. Such deductions are usually based on evidence and counterevidence. Thinking, however, is what is required to write novels. It is the construction of an initially unknown reality. But it is not a pipe dream, an unfounded process of fabrication. Rather, thinking asks us to imagine reality (“Wirklichkeitsfantasie”). In other words, a novelist has to possess a “sense of possibility” (“Möglichkeitssinn”, Robert Musil; in German, sense of possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible). This sense of possibility entails knowing the whole (or several wholes) or being able to construe an unknown whole that could accommodate a known part. The whole has to align with sociological and geographical givens, with the mentality of certain peoples or groups, and with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far.

Thinking is a means to eliminate uncertainty. This process requires both of the modes of thinking we have discussed thus far. Economic, political, or ecological decisions require us to first consider the situation at hand. Though certain situational aspects can be known, but many cannot. In fact, von Clausewitz (1832) posits that only about 25% of the necessary information is available when a military decision needs to be made. Even then, there is no way to guarantee that whatever information is available is also correct: Even if a piece of information was completely accurate yesterday, it might no longer apply today.

Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.

If we are to believe Tuchman’s (1984) book, “The March of Folly”, most politicians and commanders are fools. According to Tuchman, not much has changed in the 3300 years that have elapsed since the misguided Trojans decided to welcome the left-behind wooden horse into their city that would end up dismantling Troy’s defensive walls. The Trojans, too, had been warned, but decided not to heed the warning. Although Laocoön had revealed the horse’s true nature to them by attacking it with a spear, making the weapons inside the horse ring, the Trojans refused to see the forest for the trees. They did not want to listen, they wanted the war to be over, and this desire ended up shaping their perception.

The objective of psychology is to predict and explain human actions and behavior as accurately as possible. However, thinking cannot be investigated by limiting its study to neatly confined fractions of reality such as the realms of propositional logic, chess, Go tasks, the Tower of Hanoi, and so forth. Within these systems, there is little need for a sense of possibility. But a sense of possibility – the ability to divine and construe an unknown reality – is at least as important as logical reasoning skills. Not researching the sense of possibility limits the validity of psychological research. All economic and political decision making draws upon this sense of possibility. By not exploring it, psychological research dedicated to the study of thinking cannot further the understanding of politicians’ competence and the reasons that underlie political mistakes. Christopher Clark identifies European diplomats’, politicians’, and commanders’ inability to form an accurate representation of reality as a reason for the outbreak of World War I. According to Clark’s (2012) book, “The Sleepwalkers”, the politicians of the time lived in their own make-believe world, wrongfully assuming that it was the same world everyone else inhabited. If CPS research wants to make significant contributions to the world, it has to acknowledge complexity and uncertainty as important aspects of it.

For more than 40 years, CPS has been a new subject of psychological research. During this time period, the initial emphasis on analyzing how humans deal with complex, dynamic, and uncertain situations has been lost. What is subsumed under the heading of CPS in modern research has lost the original complexities of real-life problems. From our point of view, the challenges of the 21st century require a return to the origins of this research tradition. We would encourage researchers in the field of problem solving to come back to the original ideas. There is enough complexity and uncertainty in the world to be studied. Improving our understanding of how humans deal with these global and pressing problems would be a worthwhile enterprise.

Author Contributions

JF drafted a first version of the manuscript, DD added further text and commented on the draft. JF finalized the manuscript.

Authors Note

After more than 40 years of controversial discussions between both authors, this is the first joint paper. We are happy to have done this now! We have found common ground!

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for the continuous support of their research over many years. Thanks to Daniel Holt for his comments on validity issues, thanks to Julia Nolte who helped us by translating German text excerpts into readable English and helped us, together with Keri Hartman, to improve our style and grammar – thanks for that! We also thank the two reviewers for their helpful critical comments on earlier versions of this manuscript. Finally, we acknowledge financial support by Deutsche Forschungsgemeinschaft and Ruprecht-Karls-Universität Heidelberg within their funding programme Open Access Publishing .

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Keywords : complex problem solving, validity, assessment, definition, MicroDYN

Citation: Dörner D and Funke J (2017) Complex Problem Solving: What It Is and What It Is Not. Front. Psychol. 8:1153. doi: 10.3389/fpsyg.2017.01153

Received: 14 March 2017; Accepted: 23 June 2017; Published: 11 July 2017.

Reviewed by:

Copyright © 2017 Dörner and Funke. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Joachim Funke, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

Enhancing cognitive dimensions in gifted students through future problem-solving enrichment programs

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• Published: 09 September 2024
• Volume 5 , article number  248 , ( 2024 )

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• Khaled Elballah 1 ,
• Norah Alkhalifah 2 ,
• Asma Alomari 2 &
• Amal Alghamdi 2  

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This study has undertaken a scrutiny of research pertaining to enrichment programs based on future problem-solving skills, aimed at enhancing the cognitive dimensions of gifted students between the years 2010 and 2023. The study used a sample of 10 studies; 3 correlational studies and 7 quasi-experimental studies. The study employed the descriptive-analytical approach by following a meta-analysis method. The study aimed to discern the effectiveness of enrichment programs based on future problem-solving skills in developing the cognitive dimensions of the gifted. The study's findings have indicated a significant impact of enrichment programs based on future problem-solving skills in the development of the cognitive dimensions of the gifted, as per both correlational and quasi-experimental designs. Moreover, statistically significant differences were found related to the variables of educational level and gender in accordance with both correlational and quasi-experimental designs. The study also advocates the need for further research in this domain to facilitate the generalization of the novel findings of this study within the gifted field.

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1 Introduction

The special needs of gifted students and the challenges they encounter compel us to offer them tailored education that aligns with their potential. According to relevant literature, numerous programs and practices are employed in educating gifted students. In recent years, gifted education has witnessed substantial growth in programs, providing students with various enrichment opportunities. Among these opportunities are enrichment programs that come in various forms, often interactive and centered around higher-order thinking skills. This allows students requiring additional intellectual stimulation to remain engaged and interested in their classrooms [ 3 ]. Enrichment programs focusing on future problem-solving skills are a significant component of gifted education. Many studies have called attention to such problem-based programs. Given the challenges faced by modern societies due to rapid and continuous changes, gifted individuals in the twenty-first century find it imperative to possess future problem-solving skills. These skills involve individuals actively exploring the future by connecting the past with the present, attempting to anticipate the future based on current information and data, and creating current and future solutions to these issues. Future thinking is an active process encompassing all situations, involving planning toward future objectives, passing through stages of imagination, prediction, visualization, planning, and decision-making [ 2 ].

Enrichment programs centered on future problem-solving skills focus on enhancing cognitive processes, such as creative thinking, critical thinking, future-oriented thinking, imaginative thinking, and motivation for achievement. These programs are suitable for experienced students and support the educational process interactively. Their curriculum encompasses essential steps that students should follow when solving future problems. These steps start with identifying future challenges, selecting the most prominent challenges, generating solutions and ideas, setting criteria and applying them, and conclude with developing an action plan, equipping students with the tools and strategies to address these problems [ 48 ]. In this regard, [ 20 , 33 ] underline the significance of future problem-solving enrichment programs in gifted education, emphasizing that it represents a novel and captivating approach for gifted students to enhance their self-efficacy, acclimate to higher-order thinking skills, and cultivate their creative self. This, in turn, improves their creative thinking, mitigates the potential for boredom and monotony, and broadens their knowledge while introducing them to new areas of interest. Johnsen [ 28 ] posits that gifted education programs must prioritize offering rich experiences characterized by depth, challenge, and flexibility. They should challenge the capabilities of gifted students and develop their higher-order thinking skills, focusing on holistic development of their mental, skill-based, emotional, and independent thinking capacities in problem-solving situations. Such characteristics can be found in enrichment programs that revolve around genuine future problems to nurture these skills.

Regarding research, several studies have directed their attention to exploring future problem-solving competencies. For instance, [ 20 ] assert the effectiveness of enrichment programs centered on future problem-solving in enhancing students' creative self-efficacy. Additionally [ 7 ], affirms the effectiveness of an enrichment program based on the Kolb model in developing problem-solving skills among gifted students in the cognitive dimensions.

On another side, studies have examined the characteristics of gifted students participating in future-thinking problem-based programs [ 55 ]. Conducted a study that revealed that children participating in a program based on diverse future-thinking skills acquired the ability for profound observation, extensive general knowledge, exceptional verbal, logical, detailed, and creative thinking, and a flexible approach to problem-solving. Despite the positive impact identified by numerous previous studies in the context of future problem-solving programs, there have been variations, particularly concerning gender, educational level, and other skills, as evidenced by the findings of certain studies [ 11 ]. Furthermore, this methodological approach has not garnered significant attention from researchers in Arab countries, despite the researchers' affirmation of the importance of sequential analyses [ 47 ]. Emphasize that Meta analyses can provide unique contributions to the field of gifted education. Firstly, the results are reliable, stemming from replicable methodological steps [ 25 ]. Secondly, by summarizing the current state of evidence, Meta analyses offer researchers the opportunity to place their insights within the larger context. Thirdly, Meta analyses allow researchers to examine the effects of a large number of independent variables and potential influences simultaneously [ 45 ]. Asserts that Meta analyses are a more comprehensive method for conducting program evaluations in gifted education, as it enables the study of a wide array of independent and moderating variables simultaneously, facilitating a better understanding of the results of various studies.

1.1 Research questions

This study employed a meta-analytic approach to synthesize findings concerning problem-solving skills in the domain of gifted education. The purpose was to address the following inquiries:

What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs?

To what extent does the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school)?

What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs?

To what extent does the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school)?

1.2 Significance of the study

The significance of this study resides in its substantive contribution to the field of gifted education research, mitigating the rare of studies employing such analytical methodologies. Furthermore, it answers the clarion call voiced by numerous scholars in the Arab world regarding the importance of conducting meta-analytical studies within the educational field [ 1 ]. This study will play a pivotal role in the realization of the directives set forth by the American Psychological Research Guide, which underscores the criticality of employing meta-analysis as an adjunctive statistical method for scrutinizing statistical significance. Through this meta-analysis, we shall elucidate the effective factors upon the education of gifted students. Consequently, it will bestow unparalleled contributions to the field of gifted education by means of descriptive multivariate analyses, which proffer a more comprehensive evaluation of gifted education programs. They empower researchers to scrutinize a wide spectrum of independent variables and moderating variables concurrently [ 50 ].This study will serve as the cornerstone upon which plans for the development and activation of the roles of gifted care programs in fostering cognitive dimensions are constructed. This is because any developmental blueprints hinge upon a comprehensive portrayal of the existing reality from all its facets. Moreover, this study will offer guidance for future research endeavors and inquiries into enrichment program typologies.

1.3 Research terminologies

1.3.1 meta-analysis.

This study uses the meta-analysis methodology, defined as statistical analysis for a comprehensive spectrum of research findings. Its principal objective resides in the synthesis of abstracts or information extracted from an expansive body of research, with the overarching intention of fostering cohesion among studies that share a common thematic concern. This methodological approach serves to facilitate a more profound understanding of the rapid proliferation of antecedent research endeavors. The nomenclature employed to signify meta-analysis has demonstrated a degree of lexical diversity, encompassing designations such as transcendental analysis and meta-analysis [ 15 ].

1.3.2 Enrichment programs

Enrichment programs, as defined by [ 6 ], refer to an assemblage of educational programs used by educators to nurture the development of students' competencies. These proficiencies encompass a varied spectrum, including cognitive aptitudes, social skills, and other skills that enhance the educational experiences of students.

1.3.3 Future problem-solving skills

Future problem-solving, as elucidated by [ 4 ], draws upon Torrance's (2003) definition of this term, characterizing it as the acumen employed for the analysis and formulation of strategies directed at the resolution of problems, challenges, or difficulties, and undefined obstacles projected to manifest in the future, extending over a temporal future of no less than twenty-five years.

1.3.4 Gifted students

The National Association for Gifted Children (NAGC) has defined gifted and talented students as those who perform—or can perform—at higher levels than others of the same age, experience, and environment in one or more areas. These talented people must modify their educational experience to learn and achieve their potential. Furthermore, gifted and talented students can have the following features:

They come from all ethnic and cultural groups and from all economic classes.

It requires obtaining adequate educational opportunities to achieve their potential.

May have learning and processing disorders that require specialized intervention and adaptation.

Need support and guidance to develop socially, emotionally and in different areas [ 35 ].

1.3.5 Cognitive dimensions

Cognitive dimensions, as expounded by [ 9 ], encompass an array of concepts, ideas, and systematically organized mental operations resident within a child's cognitive consciousness. These operations discriminate the cognitive realm and are predicated upon skills such as recall, categorization, and decision-making. These skills, in turn, are rooted in the skills of thinking, conceptualization, and organizational aptitude.

1.4 Study procedures

1.4.1 study design.

The study used the descriptive-analytical approach applying the meta-analysis method, as it was suitable for the nature of this study. Meta-analysis is considered an advanced approach for comprehensive summarization of previous studies and research. It significantly contributes to the interpretation of the huge literature that extends beyond the confines of academia. It is a descriptive-analytical methodology aimed at extracting underlying findings from multiple outcomes derived from individual studies with specific attributes. This involves conducting a survey of studies related to the subject matter of the study, examining their theoretical framework, as well as the research problem, hypotheses, procedures, and results. Subsequently, criteria were established for selecting studies that warrant reanalysis and the appropriate decisions [ 19 ].

1.4.2 Study sample

The sample comprised ten research articles published between 2010 and 2023 in diverse international journals.

Shokraneh [ 45 ] recommended documenting the strategies and steps employed in meta-analysis to facilitate repetition or new updates for meta-analysis. In this study, the analytical strategies and steps adopted were as follows:

2.1 Firstly, data collection

Studies published between 2010 and 2023 were included, using a two-stage process. The first stage involved conducting computer-based research using the following keywords: "gifted," "gifted education programs," "gifted education," "gifted student," "thinking skills," "future problem-solving skills," "gifted programs," "cognitive dimensions," "cognitive resilience," "decision-making," "achievement," and "metacognition." Studies that included these keywords in their titles or abstracts were initially selected and individually reviewed to identify additional references.

Manual searches were conducted across several journals, with articles related to gifted students, including but not limited to the Journal of Secondary, Journal for the Education of the Gifted, Roeper Review, Gifted Child Quarterly, Gifted Education, Journal of Advanced Academics, Journal of King Saud University, Journal of Umm Al-Qura University, International Journal of Educational Research at the United Arab Emirates University, Educational Journal at Taif University, and Dar Al-Mandhuma Database. Additionally, searches were conducted on the Google Scholar scientific researcher database, ERIC database, and the Google search engine. The previous search results yielded a total of 288 research articles. In the second stage, criteria for including studies in the current research were applied, resulting in a reduction to ten research articles.

2.2 Secondly, inclusion and exclusion criteria

The study applied inclusion criteria based on the following guidelines:

Selection of studies published between 2010 and 2023 in Arabic and foreign journals.

Selection of complete studies (open-access journals).

Selection of studies with clearly defined correlational or quasi-experimental methodologies.

Selection of studies that explicitly stated the sample size.

Selection of studies that employed educational tests as Pearson correlation coefficients, "t-tests," and "F-tests."

Selection of studies with available statistical data indicating the relationship between the interventions of enrichment programs based on future problem-solving skills for gifted students and the development of their cognitive dimensions or their impact (correlation coefficients, sample size, mean, standard deviation). The previous studies were examined, resulting in the inclusion of ten studies investigating the impact of enrichment program interventions based on future problem-solving skills for gifted students and the development of their cognitive dimensions, according to the criteria specified above. It is to be noted that articles removed during the systemic process included the duplicated articles, articles identified as ineligible for the research by the automation tools and other articles that were removed for some other reasons such as missing information or bad quality of the articles or irrelevant to the study topic. It is also important to note that 41 articles were excluded from the analysis because of the missing information or bad quality of the articles or irrelevant to the study topic.

3 PRISMA flow diagram of the systematic search

Figure 1 describes the process stages used to select the articles used in this research. It is to be noted that two sources have been used in the process of selecting of data namely articles from databases and registrars. Furthermore, it is to be noted that articles removed during the systemic process included the duplicated articles, articles identified as ineligible for the research by the automation tools and other articles that were removed for some other reasons such as missing information or bad quality of the articles or irrelevant to the study topic.

PRISMA flow diagram of the systematic search

Table 1 describes the studies in the research sample included in the meta-analysis.

3.1 Thirdly, the encoding of study characteristics

A coding protocol was established to reflect information regarding the principal attributes of the study, experimental conditions if applicable, and the participants and samples. The features of the outcomes [ 21 ]. Consequently, the encoding of the modified variables in the present study stands as follows:

3.1.1 A—Study design

The encoding of the study design was categorized into:

Correlational research: If these studies investigate the correlational relationship between interventions of enrichment programs for gifted students and the development of their cognitive dimensions.

Quasi-experimental research: If these studies explore the impact of enrichment programs based on future problem-solving skills for gifted students in developing their cognitive dimensions.

3.1.2 B—Participant type

The encoding of participant type was categorized as (males, females, males and females together).

3.1.3 C—Educational level

The encoding of educational stage was categorized as (elementary, middle, secondary).

3.2 Fourthly, data analysis strategy

The study used effect size criteria provided by [ 17 ], and in accordance with that, the effect size is categorized as follows: from 0 to 0.10 weak, from 0.11 to 0.30 modest, from 0.31–0.50 moderate, from 0.51to 0.80 large, and represents greater than 0.81 as very large.

Furthermore, the common effect size of previous studies was calculated by determining the model used and represented by the random or fixed-effects model, which is determined by the test of heterogeneity that detects whether the observed variance in effect sizes (Q) significantly differs from the variance due to sampling error [ 21 ]. Accordingly, it is necessary to find the value of Q and compare it to the degree of freedom value (df = n-1) in the Chi-square value tables as follows: If the value of Q is less than the Chi-square value, it is interpreted that the effect sizes of the studies are homogeneous, and the common effect size is calculated according to the fixed-effects model. However, if the value of Q is greater than the Chi-square value, it is interpreted that the effect sizes of the studies are not homogeneous, and the common effect size is calculated according to the random-effects model.

In the current study, the random-effects model was used to align with the study's objectives, and the test of heterogeneity was conducted, as well as the application of categorical moderator analysis to examine whether the common effect size of enrichment programs based on future problem-solving skills for gifted students in the development of their cognitive dimensions showed significant differences based on study type, participant type, and educational stage. Moreover, it was determined whether the moderator was significant based on the level of significance value (Q) in the light of the random-effects model.

3.3 Fifthly, effect size calculation

The effect size in quasi-experimental studies was calculated as the difference between the means of the experimental and control groups divided by the common standard deviation. Additionally, Pearson's correlation coefficient was used as a measure of effect size for correlational studies.

3.4 Sixthly, publication bias assessment

Publication bias refers to the irregular representation of studies published in the literature, resulting from a higher probability of publishing studies with significant effects. This bias can influence the results of meta-analysis [ 42 ]. Researchers in meta-analysis studies have examined a set of peer-reviewed scientific studies published in journals, although there are similar studies that have not had the opportunity to be published in those journals for one reason or another, raising doubts about the possibility of bias in the results they reach. Hence, the importance of assessing publication bias becomes evident. For this purpose, Egger's regression test was used, which is a test of regression analysis for non-symmetrical funnel plot. It relies on the value "t" and its significance, so if the "t" value is not significant, it indicates no bias.

3.5 Seventhly, heterogeneity assessment

Heterogeneity analysis is a common approach in meta-analysis. It examines the likelihood of observing the variation displayed by effect sizes if sampling error is what makes them different [ 21 ]. In the current research, heterogeneity was evaluated using the Cochran's Q test, and the I 2 statistic [ 27 ]. The Q statistic follows a Chi-square distribution with degrees of freedom (n-1), while the I 2 statistic represents a percentage of the total variation across studies attributed to heterogeneity rather than chance. The test also examines the null hypothesis of homogeneity, stating that all studies evaluate the same effect [ 27 ].

3.6 Data analysis

The researchers of the current study used the Comprehensive Meta-Analysis (CMA) V.3.3.07 software to analyze the data extracted from previous studies (n = 10).

4.1 First question results

“What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs?"

To answer this question, the researchers used the following:

The heteroscedasticity test was employed to ascertain whether the observed variability in effect sizes within the research and study sample significantly deviated from the expected variability attributable to sampling error. This determination was crucial in identifying the appropriate model for aggregating effect sizes, as illustrated in Table  2 .

Table 2 clearly demonstrates the outcome of the heterogeneity test, which attests to its statistical significance (P = 0.037). The observed value stands at Q = 10.39 with degrees of freedom df = 2, markedly exceeding the critical Chi-squared (X 2 ) table value at a 95% confidence level. Furthermore, the heterogeneity ratio index (I 2  = 80.14%) underscores a substantial degree of heterogeneity among the various studies, indicating a dearth of common effect size. This, in turn, suggests a marked incongruity among the studies. Given the considerable variation in effect sizes across different studies, it is imperative to subject them to analysis in accordance with the random effects model. In this model, the common effect is construed as the mean value of these respective effects [ 16 ].

Moreover, the tabulated data in Table  2 unveil that the common effect size, as posited by the random effects model, is estimated at 0.531 with a standard error of 0.004 and a 95% confidence interval spanning from 0.317 to 0.694. This estimate is consistent with the characterization of a substantial effect size, as delineated by [ 17 ]. Consequently, the influence of enrichment programs tailored for intellectually gifted students, particularly concerning the development of their cognitive dimensions through the utilization of a correlational design, is indeed of considerable large.

In the assessment of publication bias, researchers employed the regression analysis test by Egger, yielding a coefficient "t" (1.15), with one degree of freedom, with P value of 0.455. This value bears no statistical significance, signifying the absence of publication bias.

4.2 Second question results

“To what extent does the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school)”

To answer this question the researchers used Analysis of Modified Variables, as follows:

The researchers employed a modified analysis to discern whether the impact of enrichment program interventions on the cognitive dimensions of gifted students varies depending on the type of participants (males, females, both), and the educational level (primary, middle, secondary). This revelation is elucidated through Table  3 .

It is evident from Table  3 that statistically significant disparities in the effect size of enrichment program interventions on the cognitive dimensions of gifted students are attributed to the gender of the participants (males, females, both), in favor of females (P = 0.004), and the educational stage (primary, middle, secondary), in favor of the secondary level (P < 0.001).

4.3 Third question results

“What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs?”

An assessment of heterogeneity test was employed to ascertain whether the observed variability in effect sizes within the research and study sample significantly deviated from the expected variability attributable to sampling error. This determination was crucial in identifying the appropriate model for aggregating effect sizes, as illustrated in Table  4 .

Table 4 reveals that the heterogeneity test results signify significance (< 0.001 = p). The value (Q = 139.1) is accompanied by degrees of freedom (6), surpassing the critical Chi-squared value (X 2 ) and indicating a 95% confidence interval. Moreover, the heterogeneity ratio (I 2  = 96%) indicates a substantial degree of heterogeneity among studies. This suggests that the research and study samples do not share a common effect size, highlighting their inherent heterogeneity. Given the variation in effect sizes across studies, it is imperative to analyze them according to the random-effects model, where the common effect is the average of these effects [ 16 ]. Furthermore, Table  4 demonstrates that the common effect size, according to the random-effects model, is 0.745 with a standard error of 0.003 and a 95% confidence interval ranging from 0.436 to 0.789. This places the common effect size within the realm of substantial effect sizes, as indicated by [ 17 ]. Consequently, the impact of enrichment programs for gifted students on cognitive dimensions development, employing a quasi-experimental design, is large.

Publication Bias Assessment: The researchers employed Egger's regression analysis test, yielding a "t" value of 0.3211 with degrees of freedom (5) at a p- value 0.7623. This statistically non-significant value suggests an absence of publication bias.

4.4 Fourth question results

“To what extent does the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school)?”

To answer this question, the researchers used the Analysis of the modified variables: Researchers employed modified analysis to discern whether the effect of enrichment program interventions for gifted students on the development of their cognitive dimensions differs depending on the type of participants (males, females, males and females together), and the academic stage (primary, intermediate, secondary). This is evident from Table  5 ,

It is apparent from Table  5 that there are statistically significant differences in the average effect size according to the type of participants (males, females, males and females together), in favor of both males and females together (P < 0.001). Additionally, statistically significant differences were found according to the academic level (primary, intermediate, secondary) in favor of the secondary level (P = 0.001).

5 Discussion

The primary aim of the present study was to conduct a rigorous analysis with the intent of elucidating the impacts of enrichment program interventions on the development of prospective problem-solving skills and the cognitive dimensions within a cohort of gifted students. This was achieved through the employment of both correlational and quasi-experimental research designs, with the purpose of unveiling the moderating factors intrinsic to these effects. For this purpose, a total of ten research inquiries were subjected to scrutiny, encompassing three correlational studies and seven quasi-experimental investigations conducted from 2010 to 2023. The ensuing discourse will center upon the findings pertaining to each of the study's research questions, which are as follows:

This section starts with the first question enquiring about the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs. The results, in response to this question, have determined that the common effect size, as per the random-effects model, attains a value of 0.531 with a standard error of 0.004 and 95% confidence intervals (0.317, 0.694). This effect size, for future problem-solving program interventions, resides within the realm of substantial effects, in accordance with what [ 17 ] has elucidated. Consequently, the influence of future problem-solving program interventions on the development of cognitive dimensions in gifted students, utilizing the correlational design, is indeed large. Researchers expound that future problem-solving programs are efficacious in the cultivation of cognitive dimensions among gifted students, guiding them towards success in both their personal and professional lives. It is noteworthy that education specialists must direct enrichment programs to meet the needs of gifted students in this field and design programs commensurate with the knowledge and skills of gifted students at various educational stages. Moreover, these programs must be oriented toward enhancing critical and creative thinking skills among gifted students in both academic and non-academic domains, while providing the requisite resources to accomplish these objectives. Interest in the development of future problem-solving programs for gifted students is steadily increasing, as problem-solving is deemed an exceedingly crucial skill in the modern age. Cognitive dimensions for problem-solving skills encompass critical and creative thinking, idea and problem analysis, theoretical and practical thinking, and the ability to make appropriate decisions [ 24 , 46 ]. Research suggests that future problem-solving programs contribute to the development of critical and creative thinking capabilities among gifted students. Indeed, [ 8 ] study demonstrated that enrichment programs for future problem-solving assist gifted students in developing their analytical and critical thinking skills, thereby enhancing their academic performance. Future problem-solving programs also aid in the development of theoretical and practical thinking. A study conducted in 2021 revealed that enrichment programs for future problem-solving help gifted students enhance their ability to analyze problems theoretically and practically, thereby enabling them to make sound decisions in diverse situations [ 54 ]

Furthermore, the current study's findings align with those conducted by [ 43 ], which showed that enrichment programs for future problem-solving facilitate gifted students in developing their ability to make appropriate decisions, thereby assisting them in achieving success in their personal and professional lives.

Then, we discuss the second question enquiring about the extent to the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school. To respond to this question, researchers used a modified analysis to discern whether the impact of future problem-solving intervention programs for gifted students on the cultivation of their cognitive dimension skills, as per correlational designs, indicated statistically significant differences in effect size attributed to the participant variables (males, females, males and females together), favoring the female participants, and the educational stage (elementary, middle, secondary), favoring the secondary stage. Researchers expound upon these findings by acknowledging the divergent aptitudes and requirements of gifted students across various educational stages. Indeed, students in the lower echelons may necessitate a greater emphasis on fundamental skills, while those in the higher echelons yearn for more substantial challenges. The nature of talent also varies among students participating in enrichment programs, with some demonstrating academic inclinations and others displaying artistic or socio-emotional proclivities. These differences significantly influence their responses to program interventions. The enrichment programs exhibit variances in terms of content, session duration, resource availability, and the expertise of supervisors, all of which contribute to disparities in the magnitude of the effect. Thus, disparities in the effect size of enrichment programs can be attributed to multiple variables related to the nature of the students, program content, and methodologies, as elucidated by experimental designs in this domain. Studies conducted in this domain [ 5 , 56 ] have demonstrated the pivotal role played by participant characteristics in determining the effect size of enrichment programs on the cognitive dimensions of gifted students. Results have shown statistically significant differences in the effect size of enrichment programs in favor of females. This might be attributed to gender disparities in educational interests, proclivities, and career aspirations, all of which influence the responses of gifted students to enrichment program interventions. Regarding the educational stage, studies [ 32 , 38 ] have indicated substantial variations in the effect size of enrichment programs across different educational stages. It has been revealed that the secondary stage yields superior results in the development of cognitive dimensions in gifted students compared to other stages. This can be attributed to variations in academic achievement levels and cognitive maturity among different educational stages, which impact the responses of gifted students to enrichment program interventions.

Enrichment programs for gifted students aim to provide educational opportunities that transcend standard curricula and intellectually challenge advanced learners. The effectiveness of such programs has been the subject of diverse research studies. Many studies have shown that participation in enrichment programs positively impacts the academic performance of gifted students. Research conducted by [ 29 ] found that students who participated in enrichment programs exhibited higher academic achievements, increased motivation, and enhanced critical thinking skills compared to their non-participating peers. Enrichment programs often offer opportunities for gifted students to explore their talents and develop advanced skills in specific fields. Research conducted by [ 39 ] elucidated that specialized enrichment programs focusing on specific areas such as mathematics, science, or the arts can accelerate learning and develop expertise.

The third question enquiring about the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs, is then discussed. Hence, to address this question, an analysis of heterogeneity was employed to discern whether the observed variability in the research sample exhibited significant disparities beyond the anticipated variance due to observational error. The findings unequivocally elucidate the significant influence of enrichment programs for gifted students on the cultivation of their cognitive dimensions. These programs center their focus on stimulating critical and imaginative thinking in gifted students, who are the quintessence of cognitive evolution. They proffer challenges that nurture their loftier intellectual capacities and kindle unconventional problem-solving approaches and innovative ideation, thereby augmenting their cognitive capital [ 26 , 44 ]. Furthermore, these educational initiatives encompass projects and experiential learning activities, affording students the opportunity to construct knowledge through practical application. The enrichment programs hone gifted students' acquisition of advanced cognitive skills, encompassing critical thinking, problem resolution, and decision-making, thereby impacting the evolution of their cognitive dimensions [ 40 , 41 ]. Researchers elucidate that enrichment programs for gifted students wield a formidable influence on the augmentation of their cognitive dimensions. These programs are geared toward nurturing critical and creative thinking, which constitute the bedrock of cognitive development. They instill challenges designed to foster higher mental faculties, stimulating students to employ alternative methods in problem-solving and conceiving fresh ideas, thereby amplifying their cognitive endowment.

These programs hinge upon skills-based learning, affording gifted students opportunities to construct knowledge through experiential acquisition. They train students in the acquisition of elevated cognitive skills such as critical thinking and problem resolution, which significantly contribute to the enhancement of their cognitive dimensions. For these reasons, a multitude of studies have demonstrated the efficacy of enrichment programs in advancing the cognitive dimensions of gifted students.

The study's results concur with several extant research endeavors, much like the study conducted by [ 30 , 34 ], which evinced that the enrichment training program substantially facilitated the acquisition of critical thinking and problem-solving skills among gifted students. A study by [ 34 ] revealed a marked increase in the levels of critical and creative thinking among gifted students. The findings of a study by [ 31 ] demonstrated that enrichment programs significantly contributed to the enhancement of cognitive thinking skills, such as critical thinking and problem-solving, among gifted students.

Finally, this result related to question four, enquiring of to what extent the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school is discussed. To respond to this question, researchers undertook an elucidation of results, which unveiled statistically significant discrepancies in the mean effect size upon participant type (males, females, males and females together), favoring both males and females jointly. Furthermore, statistically meaningful distinctions about the educational level (elementary, middle, secondary) were unearthed, favoring the secondary level.

The findings in these studies revealed statistically significant disparities in the mean magnitude of the impact based on participant type and educational level. Concerning participant type, studies discovered disparities in the impact size of enrichment programs in favor of both males and females jointly, indicating that enrichment programs can be beneficial to both genders alike. Researchers expound this by suggesting that gifted individuals in the realm of sciences, such as critical and creative thinking, foster within themselves the zeal and enthusiasm to further their learning in this domain. The enrichment program proffers a diverse array of educational enriching activities, thus aiding in honing the students' skills in various scientific fields. The selection of students partaking in the enrichment program is contingent upon their distinguished prowess in the sciences, signifying their aptitude to assimilate and apply advanced scientific concepts more effectively. Regarding educational level, studies [ 14 , 22 ] found disparities in the impact size of enrichment programs in favor of the secondary level, implying that enrichment programs may be more efficacious in nurturing the cognitive abilities of gifted students in subsequent educational stages. This may be attributable to variations in mental and educational maturity levels and interests across educational stages.

This can be expounded upon by positing that gifted students possess greater experience in various academic subjects and exhibit higher levels of mental and intellectual maturity, rendering them more adept at comprehending and applying complex concepts and skills offered in enrichment programs.

Additionally, the educational interests of gifted students evolve across educational stages, as they become more specialized in specific fields and develop particular skills. Hence, enrichment programs that concentrate on these fields and skills may be more effective in enhancing their intellectual capacities [ 36 ]. These findings align with the study conducted by [ 23 ] to evaluate the effectiveness of the enrichment program employed by high school students in advancing their athletic intelligence and sports thinking. The results demonstrated significant enhancements in the levels of athletic intelligence and sports thinking among students who participated in the enrichment program. They also concur with a study by [ 8 ] assessing the efficacy of the enrichment program utilized by elementary and middle school students in improving their scientific skills. The study aimed to evaluate the effectiveness of the scientific enrichment program in enhancing the levels of scientific, intellectual, and creative thinking among gifted students in elementary and middle schools. The results of the enrichment program were assessed using scientific intelligence and scientific and creative thinking assessments, and the results of students who participated in the enrichment program were compared with those of a group of students who did not participate. The results indicated that the enrichment program achieved positive results in improving the levels of scientific intelligence and scientific and creative thinking in students.

6 Conclusion

In this study, the researchers analyzed the outcomes of previous research published between the years 2010 and 2023. These works delved into the future problem-solving skills within the domain of nurturing the gifted. This analysis was conducted via the meta-analysis approach, which hinges on the examination of results from prior studies, coupled with quantitative evaluation through various statistical procedures. These include impact assessment, magnitude assessment, and control of potential publication bias. After thorough examination of databases and journals, as many as 288 studies relevant to the study's title and objectives were identified. Studies that did not align with the prescribed study criteria were excluded, resulting in a reduction of the studies to ten. The study primarily focused on ascertaining the effectiveness of interventions pertaining to future problem-solving programs in developing the cognitive dimensions of gifted students. This evaluation was conducted according to correlational and quasi-experimental designs. Furthermore, the investigation sought to determine the average variance in the impact size of these future problem-solving interventions on the development of cognitive dimensions among gifted students, categorized by participant gender (male, female, and mixed) and academic stage (primary, middle, and secondary). The study's findings in this regard indicated that the effectiveness of future problem-solving program interventions, under both correlational and quasi-experimental research designs, demonstrated a high degree of effectiveness. As for the examination of the average variance in the impact size of future problem-solving program interventions on the development of cognitive dimensions, considering the participant type and academic stage, the results displayed disparities based on the research designs. Studies adopting correlational research designs pointed to differences based on academic stage, favoring the secondary stage, and gender-based differences favoring females concerning participant type. On the other hand, studies employing quasi-experimental research designs showed variations based on academic stage consistent with the findings from correlational research, favoring the secondary stage. However, concerning the participant type, there were statistically significant differences favoring both males and females.

7 Recommendations

In light of the findings derived, the researchers proffer the following suggestions:

Studies of this nature, as pursued in the current research, are exceedingly scarce in the realm of gifted education, and their outcomes cannot be universally extrapolated. Hence, an imperative requirement manifests for the execution of further investigations to validate result precision.

Those entrusted with the formulation of enrichment programs for the gifted ought to be rooted in the cultivation of future problem-solving competencies, while taking into account a multitude of factors, notably their alignment with the age bracket, gender, and societal cultural context. It has been observed that differential impact surfaces across the more advanced developmental stages.

8 Future proposed studies

Future studies suggest that meta-analysis studies are needed to reveal the effect of future problem-solving skills on other variables (psychological, social, and emotional) through experimental and correlational designs. It is also recommended that more meta-analysis studies on enrichment programs based on future problem-solving on studies published in peer-reviewed journals to clarify the effect of culture and form a clear picture of the results.

9 Limitations of the study

Like any other study, this research has some limitations. For example, the study targeted only the previous literature available in Arabic and English, ignoring her studies conducted in different languages, which may have some biases. It is to be noted that the studies related to males were very few compared to those about females or both sexes. The study included only those with open sources due to the difficulties in accessing non-open source articles. Furthermore, while searching, about 32 reports were not retrieved, which might have some influence on the study findings.

Data availability

The data used to support the findings of this study are available upon request. However, please note that the data for this article were generated as part of a project funded by King Faisal University. Due to the nature of the funding and to protect intellectual property rights, the data cannot be shared without prior permission from King Faisal University.

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This work was supported by the Deanship of Scientific Research, Vice President for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. 241554].

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Contribution: The contributions of each author to the research paper are as follows: Khaled Elballah—Formal Analysis—Funding Acquisition Norah Alkhalifah—Investigation.—Research Methodology Asma Alomari—Conceptualization—Data Curation Amal Alghamdi—Project Administration—Resources—Software.

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Elballah, K., Alkhalifah, N., Alomari, A. et al. Enhancing cognitive dimensions in gifted students through future problem-solving enrichment programs. Discov Sustain 5 , 248 (2024). https://doi.org/10.1007/s43621-024-00470-5

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Teams Solve Problems Faster When They’re More Cognitively Diverse

• Alison Reynolds
• David Lewis

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• AR Alison Reynolds  is a member of faculty at the UK’s Ashridge Business School where she works with executive groups in the field of leadership development, strategy execution and organization development. She has previously worked in the public sector and management consulting, and is an advisor to a number of small businesses and charities.
• DL David Lewis  is Director of London Business School’s Senior Executive Programme and teaches on strategy execution and leading in uncertainty. He is a consultant and works with global corporations, advising and coaching board teams.  He is co-founder of a research company focusing on developing tools to enhance individual, team and organization performance through better interaction.

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Get ready to turn your classroom into a problem-solving playground! Join us as we explore exciting strategies that spark curiosity, unleash creativity, and empower students to tackle challenges with confidence!

• Nurturing curiosity and inquiry

Cultivate a sense of wonder by motivating students to ask questions and explore their interests. This approach enhances their critical thinking abilities and fosters a desire to comprehend the world around them. {1}

• Teaching students to deconstruct problems

Assist students in learning to divide problems into smaller, more manageable parts. This strategy helps simplify complex issues, making them less intimidating and teaches them to tackle challenges in a systematic way. {1}

• Encouraging brainstorming and innovative thinking

Facilitate brainstorming sessions where students feel free to express their ideas without criticism. Engaging in creative activities, such as drawing or storytelling, can also enhance their ability to devise original solutions. {1}

• Modelling problem-solving behaviour

Show effective strategies when encountering challenges, as children frequently learn by observing adults. This can be accomplished by:

• Identifying problems for the class to see
• Brainstorming solutions collaboratively
• Deciding on the best solution together
• Testing the solution and discussing outcomes
• Adjusting as needed to improve results
• Offering opportunities for decision-making

Empower students to make choices using decision-making exercises which allow them to practise weighing options and considering consequences. {1}

• Applying project-based learning

Engage students in project-based learning to actively develop their problem-solving skills through various classroom projects. This approach allows teachers to observe and document students’ strategies while providing opportunities for targeted feedback to enhance their abilities. Address observations collectively with the group or offer individualised support to help students refine their problem-solving techniques. {2}

• Using an inquiry-based learning approach

Provide students with intriguing situations in an inquiry-based approach to spark their curiosity and motivate exploration. Use open-ended questions to prompt students to develop responses that require problem-solving, encouraging them to consider multiple perspectives and navigate disagreements. {2}

• Prioritising student agency

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• Published: 10 September 2024

Research on origin-based cold storage location and routing optimization of fresh agricultural products based on hybrid whale algorithm

• Xueyan Zhou 1 , 2 ,
• Fengjie Xie 1 &
• Jing Fang 1  

Scientific Reports volume  14 , Article number:  21078 ( 2024 ) Cite this article

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• Engineering
• Mathematics and computing

With the focus on the insufficient origin-based cold storage in China, this study investigates the location and routing problem (LRP) of origin-based cold storage for fresh agricultural products. This study considers the loss of fresh agricultural products in different environments during transportation and presents a cold storage LRP model. To address this issue, a hybrid whale algorithm with heuristic rules is designed, and the effectiveness of the algorithm is verified by standard instances. Finally, taking Chenggu County as a practical case, the influence of cold storage capacity and farmers’ demand for refrigeration are analysed. Experimental results show that the proposed algorithm has a good effect in solving medium-scale LRP. As the storage capacity increases, the total cost of the system can be increased by 0.086%. As farmers’ demand for refrigeration increases, the total cost of the system can be increased by 34.034%. Farmers’ demand has a greater impact on the system’s total costs than the cold storage capacity. When optimizing the cold storage layout, changes in fresh agricultural product output in the next few years can be roughly predicted, and the most economical optimization scheme can be obtained.

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Introduction.

With the upgrading of urban and rural residents’ consumption, people’s demand for fresh agricultural products is increasing. People’s requirements for the freshness and timeliness are also increasing. Cold chain logistics is the key to improve the quality of fresh agricultural products and effectively losses. Cold chain logistics in urban areas of China have significantly advanced technology and services. However, there are still many problems in the cold chain of fresh agricultural products in rural areas, restricting the upward movement of fresh agricultural products. The origin-based cold storage is the core node of the origin-based cold chain. However, the number of origin-based cold storage facilities in China is insufficient, and the problem of resource imbalance is prominent. Owing to the lack of a cold chain of origin, the cold chain disconnection is easy to occur in each link of fresh agricultural products “the first kilometer”. Large changes in temperature lead to an increased decay risk in the storage and transportation of fresh agricultural products, which easily leads secondary accidents. According to statistics, the loss rate of fruits, vegetables, and potatoes in China is as high as 15–25%, with an annual loss of nearly 200 million tons 1 . At the same time, fresh agricultural products are listed in the mature peak season, which is restricted by the cold storage capacity of fresh agricultural products. The problems of “difficult sale” and seasonal fluctuation of prices are prominent, and the situation of increasing farmers’ production without increasing their income occurs from time to time. Therefore, the construction of origin-based cold storage has important practical significance.

The construction of origin-based cold storage is a strategic issue. Once completed, it cannot be changed in a short period of time. Unreasonable cold storage locations not only reduce turnover rates, but also increase the operating costs of origin-based cold storage. Second, unreasonable transportation routes for refrigerated trucks will increase the transportation cost and increase the loss of agricultural products 2 . In previous studies, the location allocation problem 3 (LAP) and the vehicle routing problem 4 (VRP) were commonly discussed separately. Herein, the location and routing collaborative optimization of the cold storage is based on the characteristics of perishable and high demand timeliness of fresh agricultural products, combined with two NP-hard problems. Through the location and routing coordination optimization of cold storage, the cold chain of origin layout is improved, the cold chain transportation efficiency is improved, and the loss rate of fresh agricultural products is reduced. It is of great significance to promote farmers’ income and increase the added value of fresh agricultural products.

Many scholars have conducted in-depth research on location and routing problem (LRP). Niu et al. 5 studied the optimization of the location of waste treatment centers and the garbage collection path, and established a three-objective optimization model to achieve a balance between total cost, carbon emissions, and residents’ satisfaction. At present, the research object of this problem has been extended to many aspects, but few studies have focused on “the first kilometer” origin-based cold storage. In addition, most of the existing studies have neglected the consideration of the loss of fresh agricultural products. For farmers with small and scattered demand for refrigeration, the LRP of origin-based cold storage is more complicated and requires further studies. Therefore, this study aims at the new scenario of “the first kilometer” origin-based cold storage service for scattered farmers, considering multiple factors such as cold storage capacity, fuel consumption, vehicle load, time window constraints, and fresh agricultural product loss and establishes an origin-based cold storage LRP model. The decision variables include the location of the cold storage, the farmers served by the cold storage, and the routing of farmers served by refrigeration trucks. The objective function is the system total cost after considering the above factors, such as the cold storage location (construction and operation), transportation, damage, refrigeration, and penalty costs. Moreover, a hybrid whale algorithm is designed to support the model.

The main innovations and contributions are as follows: (1) Focusing on “the first kilometer” origin-based cold storage as the research object, the LRP of the origin-based cold storage is studied; (2) the loss of fresh agricultural products in different environments during transportation is considered in detail, and the minimum loss cost is optimized as the objective function; (3) considering the time window constraints of farmers, the actual high requirements of farmers for the timeliness of fresh agricultural products after being picked must be meet; and (4) according to the characteristics of the model, a hybrid whale algorithm is designed. By designing chromosomes that can express all decision information and developing corresponding initialization and search strategies, the integrated optimization of location and routing is realized. Finally, through the practical case and sensitivity analyses, the validity of the model and algorithm is verified, and the influence of the change in cold storage capacity and farmers’ demand on the results is analyzed, providing management significance and practical enlightenment for the cost reduction and efficiency increase of cold storage operators in the producing area.

The remainder of this study is organized as follows: “ Literature review ” section reviews the existing related literature. In “ Model development ” section introduces the origin-based cold storage location and routing optimization model of fresh agricultural products. In “ Algorithm design ” section describes a hybrid whale algorithm and presents its effectiveness verification through standard instances. In “ Practical case application ” section presents the actual data as a practical case to verify and puts forward relevant suggestions. In “ Conclusion ” section concludes the study and outlines future works.

Literature review

Regarding the origin-based cold storage LRP of fresh agricultural products in this study, the research work is summarized in the following three aspects:

Cold chain of fresh agricultural products.

Nowadays, the logistics industry is rapidly developing, and the cold chain logistics of agricultural products has become the focus of the industry. Therefore, some scholars have studied this problem. For instance, Chunrong and Katarzyn 6 studied the optimization of the cold chain distribution route of urban agricultural products from the perspective of low carbon. They proposed the joint distribution mode of agricultural products under low carbon to reduce the circulation level of agricultural products and the impact of cold chain distribution activities on the environment. When Liu and Hou 7 studied the distribution of fresh agricultural products in urban areas, they optimized the freshness of the agricultural products at delivery, the maximum distribution distance, and the limited cold chain logistics budget as three-objective functions. The results indicated that the ability to accurately predict and control the freshness through the distance range can reduce the occurrence of customer complaints about the quality of the delivered products. Zhu et al. 8 studied the problem of “the first kilometer” cold chain logistics network design of fresh agricultural products under government subsidies. They designed effective solutions to this problem, providing management inspiration for managers. Tao 9 took the necessity of sinking the cold chain logistics service network of agricultural products as the starting point. Focusing on Jiangsu as an actual case, she analyzed the problems existing in the sinking of Jiangsu agricultural products cold chain logistics service network into rural areas. In addition, she proposed countermeasures to solve the problems, which promoted the development of cold chain logistics for Jiangsu agricultural products. Moreover, Zhang and Ding 10 determined that the cold chain logistics of fresh agricultural products in China presents the origin paradox of “the cold chain of origin is weak, the policy support is increased, the farmers do not use the cold chain, which leads to the origin weaker.” The mechanism and internal reasons of the origin cold chain paradox are systematically analyzed, and the countermeasures and suggestions to promote the development of the origin cold chain are put forward. Furthermore, Xie 11 constructed a cold chain logistics mode of fresh agricultural products from “the first kilometer” to “the last kilometer”. In addition, the links in this mode were analyzed. Hence, establishing a combined distribution network of production warehouse and sales warehouse is important to realize the standardization and scale of the agricultural product supply chain.

LRP has always been one of the popular topics in academic research. LRP has been applied to emergency rescue 12 , 13 , reverse logistics 5 , 14 , green logistics 15 , 16 , electric vehicle charging facility layout 17 , 18 , medical waste recycling 19 , 20 , and other fields. Peng 21 considered multiple fuzzy factors and introduced a customer fuzzy time window with variable coefficients, and established a multiobjective set allocation integrating a multilevel LRP model. She proposed an archive-type multiobjective simulated annealing improvement algorithm based on master–slave parallel framework embedded tabu search to solve the model. The experimental results demonstrate the preciseness and reference significance of the multilevel LRP model with multiple fuzzy factors. Wang et al. 22 discussed the problems of large greenhouse gas emissions in “the last mile” logistics distribution activities of rural logistics and the shortage of electric vehicles with respect to endurance mileage and carrying capacity. The planning problem of county-rural three-level logistics distribution network considering dynamic and static carbon emissions and oil-electric hybrid fleet configuration was studied, and an innovative two-stage hybrid algorithm was proposed to address it.

In addition, there are some scholars studying the LRP of fresh product cold chain industry. For instance, Zhang et al. 23 focus on the fresh cold chain prewarehouse as the research object and proposed a new comprehensive cost calculation method of carbon emissions. They analyzed the prewarehouse mode under the background of energy conservation and emission reduction. Ding and Chen 24 began by constructing a fresh logistics network and studied the spatial layout of the nodes of fresh and cold chain distribution centers. The decision-making factors have three aspects: node location, routing planning, and inventory control. Considering that the demand is difficult to determine, an integrated optimization model of the location-routing-inventory under fuzzy random demand is constructed. Fu and Tang 25 proposed applying a “high-speed rail + cold chain logistics” as a mode to transport fresh agricultural products. Focusing on high-speed rail freight, the LRP model of cold chain logistics distribution centers for fresh agricultural products with the lowest total cost and the best routing was constructed. Liu et al. 26 constructed a bi-objective model of cold chain logistics LRP based on the lowest logistics comprehensive cost and carbon emission by focusing on the cold storage self-pickup cabinet facilities of fresh e-commerce in the “to cabinet” mode as the research object.

The above research objects are all conducted in urban areas. There are few research results on the LRP of fresh agricultural products cold chain industry in rural areas. Most scholars studied from the LAP or VRP. For instance, Liang et al. 2 studied the LAP of cold storage with the goal of improving the satisfaction of e-commerce farmers. Ma and Wang 1 considered the loss of fresh agricultural products in “the first kilometer” process in the study of precooling station location, and considered the number, location, type, and capacity of precooling stations as decision variables. Wang et al. 27 focus on the postharvest grading and precooling of fresh agricultural products as the research object. In addition, they comprehensively considered unique collaborative scenarios such as the optimal precooling time of fresh agricultural products and the service order of precooling after grading. The collaborative scheduling optimization model of mobile hierarchical precooling resources is constructed. Zhang et al. 28 used the maximum coverage model to rationally plan the locations of precooling stations in concentrated areas of agricultural production bases in Xinxiang City, Henan Province. Moreover, they combined the entropy weight method to improve the traditional maximum coverage model to optimize the location layout of precooling stations. Ge and Zhang 29 predicted the collection demand of farmers, proposed a proactive scheduling strategy, and optimized the logistics collection routing of fresh products based on this strategy. Li et al. 30 combined the characteristics of agricultural product production and precooling in villages and towns in China. In addition, they proposed a coordinated precooling mechanism that comprehensively applied two precooling modes of fixed facilities and mobile facilities. Moreover, they constructed a multitype precooling facility LRP model for agricultural products in villages and towns. Considering the maximum pre-cooling delay time, an improved genetic algorithm (GA) was designed to solve the model according to its characteristics. The research results have important theoretical significance and practical value for the optimization of multitype precooling service network layout in villages and towns in China.

Algorithms for the LRP.

LRP is a combination of two NP-hard problems: LAP and VRP. At present, many scholars have applied various heuristic algorithms to solve LAP and VRP. For instance, Ricardo et al. 31 used computational recursive switching techniques to optimize the placement of fixed-point vaccination sites. Moreover, they compared the predicted participation with the best-placed vaccination sites with the actual locations used in previous activities, providing the best solution by minimizing the average walking distance or maximizing the expected participation algorithm. Quan et al. 32 proposed an improved differential search algorithm by combining a learning strategy and a dynamic Cauchy mutation strategy to solve the pollution VRP of logistics distribution in an open medical consortium. Yilin et al. 33 used solutions based on deep neural networks and non-DNN solutions (sweep algorithm) to solve the VRP, and compared the results, indicating that deep reinforcement learning can provide more efficient solutions for decision-makers.

For the solution of the LRP, most scholars use a two-stage method to reduce the complexity of the problem 34 , 35 . In the process of solving the LRP, if the facility location problem and the VRP are solved separately, the problem will lose the essence of the overall optimization. Therefore, this study will solve the LRP of the origin-based cold storage of fresh agricultural products from the perspective of joint optimization. LRP is a NP-hard problem, and most scholars use heuristic algorithms to solve it, such as GA 30 , 36 , particle swarm optimization algorithm 37 , 38 , ant colony algorithm 39 , 40 , neighborhood search algorithm 41 , 42 , and so forth.

The whale optimization algorithm (WOA) 43 was used by some scholars to solve the LAP or VRP owing to its few parameters, simple structure and strong search ability. For instance, Hui et al. 44 designed an improved genetic whale optimization algorithm that combines the crossover and mutation ideas of GA, and proposes a whale individual position update mechanism under a hybrid strategy. The algorithm is used to solve the VRP of ship segment transportation task. Pham et al. 45 combined WOA with gray wolf optimization algorithm and proposed a hybrid whale optimization algorithm to solve VRP. Xiao et al. 46 and Cai and Du 47 used the WOA to solve the VRP of AGV and unmanned vehicles. Moreover, Liang et al. 48 utilized the WOA to solve the LAP of electric vehicle charging facilities.

Research gap.

By studying the literature on the three research directions, namely, cold chain of fresh agricultural products, LRP, and algorithms for the LRP, there are some research gaps: (1) In the field of cold chain logistics of agricultural products, there has been an extensive qualitative analysis of the operation mode, management strategy, and policy support of cold chain logistics. However, quantitative research on “the first kilometer” of agricultural product cold chain is relatively scarce. This link is directly related to the initial quality of agricultural products and the efficiency of the subsequent supply chain. The existing literature rarely considers the loss of agricultural products, which is an important problem to be solved upstream of agricultural products. Therefore, it is important to quantitatively analyze the process of fresh agricultural products from the field to the cold storage, such as the time and cost-effectiveness of precooling, packaging, loading, and other links, and to consider the perishable characteristics of fresh agricultural products. (2) With respect to LRP, although the existing literature has widely discussed the LRP optimization strategies in different application scenarios, the research objects of cold chain logistics of fresh agricultural products are mainly concentrated in urban areas; hence, the attention to rural areas is insufficient. The construction of cold chain logistics facilities and the optimization of service networks in rural areas are of great significance for improving the overall efficiency of agricultural product supply chain and ensuring food safety. Therefore, future research should pay more attention to the LRP of cold chain logistics in rural areas. In addition, in the existing research on LRP, few studies have focused on “the first kilometer” origin-based cold storage as the research object. As the key node of cold chain logistics of fresh agricultural products, the location and routing decision of cold storage directly affect the preservation effect and logistics cost of fresh agricultural products. Therefore, it is an important direction of future research to study the LRP optimization model of cold storage and consider location decisions under various constraints. (3) With respect to algorithm research, the whale algorithm, as a new optimization algorithm, has achieved initial results in the application of LAP or VRP; however, there are few studies on joint optimization problems. In addition, the whale algorithm has some drawbacks in practical applications, such as the local optimal solution problem and the limitation of convergence speed. Therefore, it is an important direction of future research to improve the computational efficiency and optimization performance of the algorithm by introducing new heuristic strategies, improving the search mechanism of the algorithm or combining with other optimization algorithms.

In summary, this study aims to fill the forementioned research gaps. Through in-depth research on the LRP of cold storage in rural areas and considering the loss of agricultural products, as well as the improvement of WOA, the theory and practice of LRP of cold storage in fresh agricultural products in rural areas are promoted, with the main innovations and contributions are as follows: (1) Focusing on “the first kilometer” origin-based cold storage as the research object, the LRP of the origin-based cold storage is studied; (2) the loss of fresh agricultural products in different environments during transportation is considered in detail, and the minimum loss cost is optimized as the objective function; (3) considering the time window constraints of farmers, the actual high requirements of farmers for the timeliness of fresh agricultural products after being picked must be meet; and (4) according to the characteristics of the model, a hybrid whale algorithm is designed. By designing chromosomes that can express all decision information and developing corresponding initialization and search strategies, the integrated optimization of location and routing is realized. Finally, through the practical case and sensitivity analyses, the validity of the model and algorithm is verified, and the influence of the change in cold storage capacity and farmers’ demand on the results is analyzed, providing management significance and practical enlightenment for the cost reduction and efficiency increase of cold storage operators in the producing area.

Model development

Problem description.

This study focuses on “the first kilometer” origin-based cold storage service for scattered farmers as the research object, and studies the LRP of origin-based cold storage with a time window. Figure  1 presents the location and routing optimization diagram of the origin-based cold storage. In a rural area, there are several alternative cold storage points with known locations and several farmer services points with known locations, refrigeration demands and service time window requirements. From the cold storage operator’s perspective, at least one suitable location is selected from the alternative cold storage points to construct the cold storage. Under the condition of satisfying the load capacity and time window limit, the collection routing planning of each refrigerated truck was conducted, and the loss of fresh agricultural products was subdivided into each link of the transportation process for calculation and optimization as one of the objective functions. Finally, the total system costs of the origin-based cold storage are reduced, and the refrigeration demand of fresh agricultural products at multiple farmer service points within the origin-based cold storage is met.

Location and routing optimization diagram.

Model assumptions

In order to facilitate the analysis of origin-based cold storage LRP, the following assumptions are made:

The location of the farmer service points (hereinafter referred to as the service points), the alternative points of the origin-based cold storage, and the refrigeration demands are determined, and each service point can only be served by one cold storage.

The origin-based cold storage cannot meet the large demand of service points without restriction, so the origin-based cold storage has a capacity limit.

The speed of a vehicle during transportation is determined and fixed. Each vehicle can start from only one origin-based cold storage and return to the original cold storage after serving all the service points on the route.

Each route is served only by a single vehicle, and any service point only has one vehicle through.

The load of the vehicle in any route arc is less than or equal to the vehicle capacity.

This study sets the following parameters and variables, as shown in Table 1 .

Model construction

According to the problem description and model assumptions, the cold storage operator should select at least one of the alternative points of the cold storage to construct the origin-based cold storage, which needs to consider factors such as distance, demands, and loss of fresh agricultural products. Simultaneously, the service relationship between cold storage and service points is determined, and the reasonable planning of the collection routing is conducted to meet the needs of all service points. Finally, the model with the minimum total system costs of cold storage is constructed. The total system costs of origin-based cold storage are location, transportation, damage, refrigeration and penalty costs.

Location Costs C 1 : Location costs of the origin-based cold storage are composed of construction costs and operation costs. The location costs C1 in this model can be expressed as:

Transportation Costs C 2 : Transportation costs are the costs spent in collecting fresh agricultural products. These include fixed and variable costs. The fixed costs are the purchase and maintenance costs of the transportation vehicle, and the maintenance costs are the maintenance and repair costs of vehicle. The variable costs under constant speed are vehicle fuel costs, which are proportional to distribution distance.

Damage Costs C 3 : Owing to the perishable nature of fresh agricultural products, with the extension of time and the influence of external heat, temperature in the carriage of transport vehicles changes, and the quality of fresh agricultural products will decline, which is irreversible. Therefore, there will be certain damage costs associates with the transportation process. Fresh agricultural products will possibly two types of damage during transportation. The first is the damage caused by time accumulation during transportation, and the second is the damage caused by the sudden increase of temperature, such as by opening the door when the transport vehicle is at the service point, reducing the freshness of the agricultural products.

This study introduces the corruption function of fresh agricultural products to measure the costs of damage: \(\varphi \left(t\right)={\varphi }_{0}{e}^{-\partial t}\) ;

In the formula: \(\varphi \left(t\right)\) is the quality of fresh agricultural products at time t; \({\varphi }_{0}\) is the initial quality of fresh agricultural products; \(\partial\) is the corruption rate, and its value is related to the characteristics of the product itself, so the corruption part of the fresh product quality is \({\varphi }_{0}\left(1-{e}^{-\partial t}\right)\) .

The damage costs of time accumulated =

The damage costs of opening the door =

Refrigeration Costs C 4 : Refrigerated carriages will bear heat load during products transportation; hence, it will produce refrigeration costs. These costs are generated during the transportation process, from the origin-based cold storage to the product consolidation task. The refrigeration costs are determined by the heat Q 1 transfer from the outside to the inside of the carriage and the heat Q 3 transfer into the carriage when opening the door.

The simplified formula \({Q}_{2}=\beta {Q}_{1}\) is often used in the actual calculation of the heat Q 2 transfer into the carriage through solar radiation, where β is a scale factor, β = 0.1 in the area with general sunshine intensity, and β = 0.2 in the area with strong sunshine intensity.

The heat Q 3 transfer into the carriage when opening the door is generated by convection of cold and hot air during loading. Because the cold and hot air are in direct contact, there is no heat transfer coefficient U, and the heat transfer area is the area of the door S c .

The refrigeration costs in transportation process =

The refrigeration costs of door opening process =

Penalty Costs C 5 : The vehicle should reach the service points within a certain time period to ensure the quality of fresh agricultural products, and the penalty costs will be incurred before or after the farmer’s service time window.

Based on Eqs. ( 1 )–( 13 ), the optimization model of origin-based cold storage system is as follows:

In the above formula, constraint formula ( 14 ) indicates the minimum total system costs of the origin-based cold storage; constraint formula ( 15 ) indicates to build at least one origin-based cold storage; constraint formula ( 16 ) indicates that each service point is serviced by only one origin-based cold storage; constraint formula ( 17 ) indicates that each service point can only have one delivery vehicle to serve it; constraint formula ( 18 ) indicates that the total amount of agricultural products received by each origin-based cold storage does not exceed its maximum storage capacity; constraint formula ( 19 ) indicates that the total amount of agricultural products loaded by each refrigerated truck is less than the maximum capacity of the vehicle; constraint formula ( 20 ) indicates that there is no routing between the same origin-based cold storage and service points; constraint formula ( 21 ) indicates that there is no routing between different cold storages; constraint formula ( 22 ) indicates the balance constraint of vehicle entry and exit, and the vehicles arriving and leaving at each service point are the same; constraint formula ( 23 ) indicates that each vehicle has at most one service routing; constraint formula ( 24 ) indicates the service time window constraint; constraint formulas ( 25 )–( 27 ) are decision variable.

Algorithm design

The WOA simulates the unique search method and hunting mechanism of humpback whales, including three important phases: encircling prey, bubble-net attacking and searching for prey.

Encircling prey

The search range of the whale is the global solution space, and it is necessary to determine the location of the prey in order to surround it. Since the position of the optimal solution in the search space is unknown, the WOA algorithm assumes that the current optimal candidate solution is the target prey or close to the optimal solution. After defining the optimal whale position, other whales will attempt to update their position to the optimal whale. The position update formula is expressed by Eq. ( 29 ):

where A and C are coefficient vectors, X*(t) is the current optimal solution, X(t) is the individual, t is the current iteration number, | | is the absolute value.

The vector A and C are calculated as follows:

where a decreases linearly from 2 to 0 in the iterative process, r1 and r2 are random vectors in [0,1].

The selection of this phases depends on the parameter A and the probability p of the predator–prey mechanism, where p is a random number with a range of [0, 1]. For each individual, if p  < 0.5 and |A|< 1, the location is updated by encircling prey.

Searching for prey

In order to ensure that all whales can fully search in the solution space, WOA updates the position according to the distance between whales to achieve the purpose of random search. Therefore, when p  < 0.5 and |A|≥ 1, the search individual will swim to the random whale. The position update formula is shown in Eq.  33 :

Bubble-net attacking

When p  ≥ 0.5, the bubble-net is used for predation. The position update between the humpback whale and the prey is expressed by the logarithmic spiral equation. The position update formula is shown in Eq. ( 35 ):

where D′ is the distance between the current search individual and the current optimal solution, b is the spiral shape parameter, the range of l is a random number uniformly distributed in [− 1, 1].

Hybrid whale optimization algorithm (HWOA)

Chromosomes coding.

When solving the LRP, a chromosome represents a feasible solution, and the encoding of the solution directly determines the difficulty and quality of the algorithm. In this study, natural number coding is used in the design of chromosome coding. When generating the initial solution of cold storage location and vehicle distribution routing, a routing is randomly generated first, and segmentation points with a label of 0 are inserted. Moreover, the routing is divided into several segments to indicate the opening of several cold storages. Afterward, the precise code of the cold storage is randomly selected at the beginning and end of each routing segment for insertion, and the preinserted segmentation points are deleted to represent a complete initial solution.

The initial decoding of 3 alternative origin-based cold storage points and 10 service points are used as example. Values 1–10 represents the service point, 11–13 represents the alternative origin-based cold storage points, as shown in Fig.  2 . The first step is to initialize the coding of the service point service order, in which the shadow part marks the location of the segmentation point. The second step is to randomly select the cold storage code and fill it into the complete vehicle routing, in which the shadow part represents the cold storage coding position. As shown in the Fig.  2 , in the candidate cold storage 11–13, cold storage 11 and 13 were opened.

Chromosome coding diagram.

Initializing the population

Reasonable population initialization improves the convergence efficiency of the algorithm. In the initial population, the diversity of the population is increased by combining random generation with a heuristic algorithm. Taking population 100 as an example, 70 individuals were randomly generated, and the other 30 individuals were randomly generated first. The nearest neighbor method was then used to optimize the service routing. To make the individuals in the population feasible, it is necessary to judge the individual constraints, and adjust the part of the gene if constraints are not met.

When the population is initialized, it mainly involves the cold storage capacity constraint (the total amount of agricultural products received by each origin-based cold storage does not exceed its maximum storage capacity) and the time window constraint (the time to reach each service point shall not exceed the time window limit of this service point). Therefore, after the chromosome sequence is randomly generated, the above constraints are checked in turn for each service routing. First, the capacity constraint is determined. If the constraint is not satisfied, the service point exceeding the capacity range is moved to the next cold storage service routing and the chromosome is updated. Afterward, the time window constraint is determined. The service points in the routing are reordered according to the left time window size. Figure  3 presents the specific process.

Initializing the population diagram.

Improved search strategy

In the improved search operation, the crossover and mutation operators in the GA are introduced to ensure the diversity of feasible solutions. The crossover operation is realized by 2-opt exchange. In the genes of the chromosome representing the service point, two service point positions are randomly selected for exchange and their fitness values are calculated. The number of exchanges conducted on each chromosome n is 1/5 of the number of service points. By repeatedly conducting exchanges, the offspring with the best fitness value is selected. Figure  4 shows the cross-operation process with several service points of 20.

Crossover operation process.

In this study, four search mechanisms are used in the mutation process: routing gene reversal, routing gene insertion, location gene insertion, and location gene mutation. The first two mechanisms work on the routing gene, and the latter two mechanisms work on the location gene. The probability of selecting each mutation operator is equal.

Routing gene reversal : Randomly select two positions i and j (i ≠ 1 and i < j) representing the service point from the coding arrangement of the solution, and then insert the chromosome fragments between the two service points into the original position after reverse arrangement, as shown in Fig.  5 a.

Routing gene mutation operation process.

Routing gene insertion : Randomly select two positions i and j (i ≠ 1 and i < j) representing the service point from the encoding arrangement of the solution, and then insert the element at the j position into the following position of the i element, as shown in Fig.  5 b.

Location gene insertion : Because the location genes in the middle position of the chromosome are always connected, the two connected location genes in the middle position are divided into a group, then a group is randomly selected from the grouping of the location genes, then a service point i is randomly selected from the service points of the two cold stores, and then this group of location genes is inserted behind the i element, as shown in Fig.  6 a.

Location gene mutation operation process.

Location gene replacement : After extracting the location gene of the chromosome, cold storage i is randomly selected from the open cold storage, and then a cold storage j is randomly selected from the unopened cold storage. Replace i with j and insert it back to the original location of i, as shown in Fig.  6 b.

Local search strategy

To better improve the optimization ability of the algorithm, the population is evaluated after optimization, and the top 10% of the individuals in the population perform iterative local search operations to evaluate the offspring obtained by the search. Finally, the roulette wheel selection is utilized to select a certain number of excellent individuals from the offspring and put them back into the original population. When performing a local search, the population needs to readjust the coding strategy first. The vehicle routing extracted by each individual is used as a new chromosome. Figure  7 presents the specific adjustment operation of a chromosome, in which each row presents the routing of a vehicle.

Readjustment of chromosome coding strategy process.

In the local search, this study adopts three kinds of neighborhood operations. (1) First is the multisequence exchange neighborhood operation, as shown in Fig.  8 a. The process can be described as follows: first select two parents P1 and P2; the child inherits 1/3 of the total routing of the parent P1. The remaining unserved points are arranged according to the service order of the parent P2. Afterward, the unserved points are assigned to the cold storage to generate a new vehicle routing and then inserted into the child. When the cold storage is allocated, it is first allocated from the open cold storage. When the open cold storage cannot meet the demand of the service point, a new cold storage is opened. (2) Second is the exchange neighborhood operation, as shown in Fig.  8 b. The process can be described as follows: randomly select two service points in two different routings from the total routing of the parent, and replace the position. (3) Third is the mutation neighborhood operation, as shown in Fig.  8 c. The process can be described as follows: 1/3 of the routing was randomly selected from the total routing of the parent, and a cold storage was reselected to replace the cold storage of the original routing.

Three neighbourhood operation example processes.

Algorithm process

In summary, Fig.  9 presents the overall process of the hybrid whale algorithm, and the specific steps are as follows:

Initialize the algorithm parameters such as the initial population number N, the maximum number of iterations (Gmax), and so forth.

Initialize the whale population according to the initialization strategy, evaluate the fitness value of each whale individual, and identify the optimal individual as the global optimal individual (Xbest).

Determine whether the maximum number of iterations is reached. If it is not satisfied, proceed to step 4. If it is satisfied, generate the current optimal solution, and the algorithm ends.

The iteration process begins, and the individuals in the population are traversed in turn. A random number p between 0 and 1 is generated. If p  < 0.5, then proceed to step 5; otherwise, proceed to step 6.

If |A|< 1, the current individual performs cross-operation and replaces the current individual with the offspring. If |A|≥ 1, the globally optimal individual performs a crossover operation and replaces the current individual with its offspring.

The current individual performs a mutation operation and replaces the current individual with the offspring.

Evaluate the population, identify the current optimal individual, and replace if it is better than the global optimal individual; the individuals with the top 10% fitness value in the population were selected as population 2.

Population 2 performs local search operations to obtain a new population, finds the current optimal individual of the new population, and replaces if it is better than the historical global optimal individual.

After the iteration process is completed, the roulette wheel selection is used to select the corresponding number of excellent individuals and put them back to the original population.

Repeat the above steps until the algorithm reaches the termination condition and generates the result.

Hybrid whale algorithm flowchart.

Verify the efficiency of the algorithm

Taguchi method parameter setting.

The algorithm is very sensitive to the setting of parameters, and different parameter values can determine the effectiveness of the algorithm. Therefore, we need to determine the reasonable parameter values before running the algorithm. HWOA contains two main parameters, which are population number N and the maximum number of iterations Gmax. In this study, the experimental method of Taguchi design is used to optimize the parameters to determine their values. The target value of Taguchi method is divided into three groups: ‘the smaller the better’, ‘the larger the better’ and ‘nominally the best’. The objective function of this study is to minimize the cost, select the type of ‘the smaller the better’, and the corresponding signal-to-noise (SN) ratio is shown in ( 36 ).

In the formula, n is the number of executions of the algorithm at each parameter level, and Ft is the response value, that is, the objective function value of the t-times experiment. The N and Gmax are set to four levels respectively. The four levels of N are: 100, 200, 300, 400. The four levels of iterations are 100, 300, 500, 700. The two can form a total of 16 combinations L16 (4 2 ). Under each parameter combination, HWOA uses the standard LRP example 50–5–1a proposed by Prins et al. 49 to run independently for 10 times, and the calculated experimental values are analyzed by Taguchi design. The analysis results are shown in Table 2 , and the corresponding mean and SN ratio are shown in Figs.  10 and 11 .

SN ratio interaction diagram.

Date means interaction diagram.

It can be seen from Fig.  10 that when N is 300 and Gmax is 300, the SN ratio is the largest. Similarly, in Fig.  11 , when the N is 300 and Gmax is 300, the date means is the smallest. Therefore, according to the Taguchi experimental analysis, N is set to 300, and Gmax is 300.

Instances verification

To test the performance of HWOA to solve the LRP, this study utilized the standard LRP instances proposed by Prins et al. 49 to conduct simulation experiments. Eight test datasets are selected from them, and the parameters are set according to the original dataset. At the same time, the algorithm is compared with WOA and GA. In this study, MATLAB R2022a under Windows 11 system is used to code the HWOA and the experiment of related instances.

In this study, N and Gmax of the three algorithms are set to 300, and the coding methods of the three algorithms adopt the coding rules proposed in this study. The parameters of GA are set as follows: the selection probability is 0.8, the crossover probability is 0.5, and the mutation probability is 0.1. Because the original WOA cannot solve the discrete problem, the search strategy of this study is adopted. In the same computing environment, the comparison results of the optimal values of the three algorithms after 10 times of each group of instances are shown in Table 3 .

As shown in Table 3 , when solving small-scale instances, all three algorithms can find the optimal solution. WOA takes the least time, followed by GA, and finally HWOA. When solving medium-scale examples, WOA has the fastest calculation time, but the accuracy of the calculation results is the worst. The accuracy of GA calculation results is better than that of WOA, but the calculation time is the slowest. The proposed HWOA achieved the highest accuracy, and the calculation time is better than that of GA and worse than that of WOA. It can be seen that the WOA algorithm is highly competitive in solving small-scale examples using the change rules in this study. However, as the size of the example increases, the accuracy of WOA decreases. Considering the accuracy of the calculation results, the calculation time of HWOA is within an acceptable range. Therefore, HWOA is suitable for solving medium-scale LRP.

Practical case application

Practical case introduction.

Chenggu County, Hanzhong City, Shaanxi Province is the largest producer of citrus fruit in the northwest. At present, the citrus planting area is about 230,000 mu, the annual output is 320,000 tons, and the annual output value is exceeding 800 million yuan. However, the number and capacity of cold storages in local areas cannot meet the current citrus production. Therefore, this study takes the citrus planting belt in Chenggu County as the research object, and takes the village-level units with a total output of more than 150 tons as service points. A total of 35 service points were obtained, with a total demand of 8752.68 tons. There are 7 alternative cold storage points available. The number of farmer service points is 1–35, and the number of alternative cold storage points is 36–42. The location information of farmer service points and alternative cold storage points is shown in Fig.  12 , and the specific information of each point is shown in Table 4 .

Location distribution map of each point.

Combined with existing literature 1 , 50 , 51 and the actual situation of Chenggu County, the basic data of the model are set as follows: the construction costs of the origin-based cold storage are 150,000 yuan, the operation costs of the origin-based cold storage are 50 yuan/day, the maximum storage capacity of the origin-based cold storage is 40 t, the operation accounting period is 5 years, the annual operation time is 6 months, the maximum load of the refrigerated truck is 8t, and the driving speed is set to 50 km/h. The relevant data settings such as purchase costs, maintenance costs and transportation costs of refrigerated trucks are shown in Table 5 . The unit price of fresh agricultural products is 1.2 yuan/kg. The hourly loss rates of fresh agricultural products during transportation and door opening are 0.2% and 0.3%, respectively. The ambient temperature is set at 20 °C, the temperature in the refrigerated truck carriage is 4 °C. The heat transfer coefficient of the carriage is 0.7, and the sunshine intensity is 0.1. The penalty costs earlier than the time window are 30 yuan/h, and the penalty costs later than the time window are 50 yuan/h.

Practical case results and analysis

In this study, a total of 35 farmer service points and 7 alternative cold storage points in Chenggu County citrus planting belt are selected as datasets for calculation. This is a medium-scale LRP, and the proposed HWOA has been verified several times. It has strong competitiveness in solving medium-scale LRP. Therefore, according to the above parameter values, the HWOA is used to solve the problem on MATLAB2022a. The algorithm sets the population size to 300 and the maximum number of iterations to 500. When the optimal value does not change for 200 consecutive generations or the population chromosomes are completely consistent, the calculation is completed and the results are generated.

The algorithm was run 30 times in the environment of Intel®Core™i5-13400F, and good results were obtained. Figure  13 presents the convergence of the optimal solution in 30 operations. It can be seen that the algorithm converges in about 100 generations and takes 102.0 s. Table 6 presents the optimal calculation scheme, and Fig.  14 presents the location and vehicle routing of the optimal scheme. Combining the results presented in Table 6 and Fig.  14 , it can be concluded that under the current parameter value, Chenggu County should build origin-based cold storage at alternative points No. 39 and No. 42, respectively. Moreover, cold storage No. 39 needs to serve 26 farmers and invest on 5 refrigerated trucks; the No. 42 cold storage needs to serve 9 farmers and invest on 2 refrigerated trucks. The total system costs of cold storage are 40964.199 million yuan.

Convergence curves of the HWOA.

Optimal scheme diagram.

The origin-based cold storage capacity is directly related to the costs. The cold storage with a small storage capacity has small construction costs, and it can serve a small number of farmers. The cold storage with a large storage capacity has large construction costs, and it can serve a large number of farmers. Therefore, exploring the impact of cold storage capacity on the final result can provide a scientific basis for cold storage operators to make decisions.

The types and planting scales of fresh agricultural products in different regions vary. If the planting products are rare or the planting scale is small, the yield is small. On the contrary, if the planting products are more common or the planting scale is larger, the yield is larger. Moreover, even in the same area, the planting conditions and scales of different farmers are still different. Therefore, the refrigeration demand of farmers varies greatly, which has a direct impact on the final result.

In this study, the capacity of cold storage and the farmers’ refrigeration demands are utilized as variables; both of them are reduced by 50% and 25%, increased by 25% and 50%. Four sets of data are generated respectively, and the results are recalculated. Comparing the four new results with the original results, the influence of capacity and demand on the layout of origin-based cold storage and the vehicle routing of refrigerated trucks is analyzed.

The influence of origin-based cold storage capacity.

Table 7 presents the impacts of four sets of data on cold storage capacity on various costs, and Fig.  15 presents the impacts on cold storage location and vehicle routing results. When the storage capacity is reduced by 50%, the construction costs and operation costs of a single cold storage are reduced by 50%. Moreover, the second row of Table 7 presents the costs of origin-based cold storage in each region, and Fig.  15 a presents the LRP result. Furthermore, it is necessary to build three cold storages to meet the farmers’ needs. With the increased number of cold storages, the related transportation costs from the farmers’ service points to the cold storage reduced, and the total costs of building this cold storage are also less than the total costs of building the original cold storage; hence, the total costs are significantly reduced.

The impact of changes in cold storage capacity on the location and vehicle routing results of the cold storage.

When the storage capacity is reduced by 25%, the construction and operation costs of a single cold storage are reduced by 25%. The third row of Table 7 presents the costs of origin-based cold storage in each part, and Fig.  15 b presents the LRP results. In addition, it is necessary to build two cold storages to meet the farmers’ needs. Moreover, the number of cold storages remains the same; however, the service relationship has improved, and there is no significant difference in the related transportation costs. Because the total costs of building this cold storage are less than the total costs of building the original cold storage, the total costs are reduced.

When the storage capacity increases by 25% and 50%, the construction and operation costs of a single cold storage increase by 25% and 50%. The fifth and sixth rows of Table 7 present the costs of origin-based cold storage in each part. Figure  15 c,d present the LRP results. In both cases, one cold storage can be built to meet the farmers’ needs, and the location and vehicle routing results of the cold storage remain the same. As the number of cold storages decreased, the related transportation costs increased, and the costs of building a single cold storage increased; however, the number of cold storages decreased. The costs of building a cold storage with a large storage capacity are less than the costs of building two original storage cold storages; the increasing transportation costs are less than the costs of reducing the number of cold storages, and the total costs are still reduced.

In summary, it is the best scheme to build one cold storage with a storage capacity of 50t in Chenggu County because the total system costs are still low. With the change of storage capacity, the final results accordingly change. Therefore, the scale and quantity of origin-based cold storage can be considered according to the local actual situation, and the construction scheme with the lowest costs can be sought.

The impact of farmers’ refrigeration demand.

Table 8 presents the impact of the four sets of data on farmers’ demand on various costs, and Fig.  16 presents the impact on cold storage location and vehicle routing results. The second and third rows of Table 8 present the costs of LRP in each stage when the demand is reduced by 50% and 25%, and Fig.  16 a,b presents the LRP results. Moreover, the construction of one cold storage can meet the farmers’ needs. As the number of cold storages decreases, the number of refrigerated trucks decreases, the number of farmers served by one refrigerated truck increases, and the service relationship changes. The costs are reduced compared with the original, and the smaller the farmers’ demands, the smaller the total costs.

The impact of changes in demand on the location and vehicle routing results of the cold storage.

The fifth and sixth rows of Table 8 present the costs of cold storage LRP in each stage when the demand increases by 25% and 50%. Figure  16 c,d present the LRP results. The construction of two cold storages can meet the farmers’ needs. Moreover, the number of cold storages remains the same, and the number of refrigerated trucks has increased. Except for the location costs ( C 1 ), which remain the same owing to the same number of cold storages, the other costs have increased than those of the original; thus, the total costs have increased. The larger the demand, the greater the number of vehicles, and the higher the total cost.

To sum up, with the change of farmers’ demands, only the change in cold storage location and vehicle routing can minimize the total minimum costs. When optimizing the LRP of cold storage in the region, it is necessary to predict the production and sales of local fresh agricultural products to make rational use of the layout of origin-based cold storage and improve the utilization rate of cold storage.

“The first kilometer” of the cold chain is the challenging and critical part of the upstream transportation of fresh agricultural products, as well as the key to ensuring the final product quality. In this study, considering the loss of fresh agricultural products during transportation to the origin-based cold storage after picking, the LRP of the cold storage of fresh agricultural products are studied. With the goal of minimizing the total system costs, the LRP model of the cold storage of fresh agricultural products is constructed, and HWOA is designed to solve the problem. The designed algorithm realizes the improvement of WOA, which is a better algorithm to solve such problems. Good results are obtained in different instances. In practical case, the location layout of origin-based cold storage for fresh agricultural products and the route planning for refrigerated trucks have been successfully implemented. Afterward, this study explores the impact of changes in cold storage capacity and farmers’ cold storage demand on the total system costs and the location and vehicle routing results of cold storage. It provides theoretical references for cold storage operators in location selection and vehicle routing for serving farmers.

The results show that: (1) The algorithm designed in this study achieves the improvement of WOA. The results of different instances show that HWOA is suitable for solving medium-scale LRP and has good performance. (2) The change of cold storage capacity has an important influence on the results. With the increase of the proportion of cold storage capacity change from 0.5 to 1.5, the system total costs can be increased by 0.086%. After calculation, it is the best scheme to build a cold storage with a storage capacity of 50t in Chenggu County of Hanzhong City, and the system total costs are the lowest. (3) With the increase of farmers’ demands for refrigeration, the number of cold storage and vehicles increases, and the total costs increase. As the proportion of farmers’ demands for refrigeration increases from 0.5 to 1.5, the system total costs can increase by 34.034%.

Through the calculation and analysis, the following management implications are obtained: (1) When planning the origin-based cold storage, the demand for storage capacity should be accurately evaluated to avoid overinvestment or insufficient storage capacity. Considering the impact of changes in cold storage capacity on the total costs, it is recommended to establish a flexible storage capacity adjustment mechanism to adjust the storage capacity in a timely manner according to market changes and seasonal demand. (2) Strengthen the prediction of farmers’ cold storage demand, and use historical data and market analysis to predict future demand changes and to achieve efficient resource allocation in advance. In addition, it is recommended to develop coping strategies in advance, such as the establishment of standby cold storage, a flexible vehicle scheduling system, and so forth, to cope with demand fluctuations. (3) Improve the efficiency of cold storage and vehicle use through technological upgrading and management innovation, and ensure that the cost is reduced as much as possible while meeting the demand. Farmers are encouraged to provide feedback to better understand changes in demand and improve services.

However, this study also has some limitations. First, the model assumes that the scale and capacity of the origin-based cold storage are fixed, and the scale of the origin-based cold storage is not optimized. Second, the model assumes that the farmers’ demand is fixed, and does not consider farmers’ uncertain demand in an actual situation. Third, the algorithm may encounter computational efficiency problems when dealing with large-scale data. Fourth, this study mainly focuses on the construction of theoretical models and algorithm optimization, and the replicability in practical applications must be further verified. Given the above limitations, we propose the following suggestions: First, future research can consider optimizing the scale of origin-based cold storage as a decision variable to more accurately determine the most suitable cold storage scale in the region. Second, considering the uncertain demand, the LRP model of fresh agricultural product cold storage with uncertain demand is constructed. Third, more efficient algorithms or parallel computing techniques can be explored to improve the ability to process large-scale data. Fourth, it is recommended to implement and test the model in actual cases to evaluate its performance in the real environment, and to adjust and optimize it based on feedback.

This study provides an innovative solution for the LRP of cold storage of fresh agricultural products, and provides a valuable reference for relevant enterprises and management departments. Future research should continue to deepen the exploration in this field to promote the continuous optimization and development of fresh agricultural product cold chain.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

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Acknowledgements

The Fundamental Research Funds for the Central Universities, CHD (300102213508), the Young Talents Promotion Program of Shaanxi Association for Science and Technology (20230238).

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X.Z. and J.L. wrote the main manuscript text. F.X. and J.F. prepared practical case data and content review.

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The influencing factors of clinical nurses’ problem solving dilemma: a qualitative study

a Department of Nursing, Shanghai Pulmonary Hospital, Tongji University, Shanghai, China

b Tongji University School of Medicine, Shanghai, China

c Beijing Tiantan Hospital, Capital Medical University, Beijing, China

Problem solving has been defined as “a goal-directed sequence of cognitive and affective operations as well as behavioural responses to adapting to internal or external demands or challenges. Studies have shown that some nurses lack rational thinking and decision-making ability to identify patients’ health problems and make clinical judgements, and have poor cognition and response to some clinical problems, easy to fall into problem-solving dilemma. This study aimed to understand the influencing factors of clinical nurses’ problem solving dilemma, to provide a basis for developing training strategies and improving the ability of clinical nurses in problem solving.

A qualitative research was conducted using in-depth interviews from August 2020 to December 2020. A total of 14 participants from a tertiary hospital in Shanghai, China were recruited through purposive sampling combined with a maximum variation strategy. Data were analysed with the conventional content analysis method.

Three themes and seven subthemes were extracted: nurse’s own factors (differences in knowledge structure and thinking, differences in professional values, poor strain capacity); improper nursing management (low sense of organizational support, contradiction between large workload and insufficient manpower allocation); patient factors (the concept of emphasizing medicine and neglecting to nurse, individual differences of patients).

The influencing factors of clinical nurses’ problem-solving dilemma are diverse. Hospital managers and nursing educators should pay attention to the problem-solving of clinical nurses, carry out a series of training and counselling of nurses by using the method of situational simulation, optimize the nursing management mode, learn to use new media technology to improve the credibility of nurses to provide guarantee for effective problem-solving of clinical nurses.

Introduction

Nursing education in China can be divided into two main levels: vocational education and higher education. Vocational education includes technical secondary schools and junior colleges, while higher education includes undergraduate, master’s and doctoral education. Vocational education aims at training students to master basic nursing service skills and to be able to take the post to engage in daily nursing work (Sun & Zong, 2017 ). Higher nursing education started late, and undergraduate education has always followed the “three-stage” education model of clinical medicine (basic medical courses, specialized courses and clinical practice). Most courses are centred on subject knowledge, and all clinical practice takes the form of centralized practice (Li, 2012 ). The training goal of nursing postgraduates is gradually expanding from academic master to professional master. The curriculum mainly includes classroom teaching and clinical practice. The classroom teaching contents include public courses (political theory, foreign languages, etc.), professional basic courses (advanced health assessment, pharmacotherapy, pathophysiology, evidence-based nursing, medical statistics or clinical epidemiology), specialized courses (advanced nursing practice theory) and Academic activities . The goal of nursing doctoral training is to cultivate high-level nursing research talents, focusing on the cultivation of scientific research ability rather than clinical practice ability. The curriculum includes ideology and politics, basic theory, research methods, specialized courses, development frontier, scientific writing, etc (Luo et al., 2018 ). There are some problems in the training mode and curriculum, such as theory and practice are out of touch, traditional lecture-based classroom teaching makes students passively accept knowledge, students attach importance to theory over practice, knowledge input to ability output, professional study to humanities knowledge. Nursing students receive no theoretical and/or practical training in problem solving before entering the clinical setting, so there is not a starting point for these nurses to clinical dilemmas in their professional life.

With the development of medicine, people pay more attention to health and have higher requirements for nursing service ability (Yang, Ning, et al., 2018). The National Nursing Development Plan (National Development and Reform Commission, 2017 ) points out that it is necessary to strengthen the construction of nurse teams, establish nurse training mechanisms and improve the professional quality and service ability of nurses. However, in the face of increasingly complex and changeable clinical environment, nurses are still lacking in problem-solving thinking and ability, and often fall into the dilemma of problem solving (Li et al., 2020 ).

Typical decision theory approaches to the identification of problem solving in nursing have viewed the process as a series of decision formulations that include: decisions about what observations should be made in the patient situation; decisions about deriving meaning from the data observed (clinical inferences); and decisions regarding the selection of action to be taken that will be of optimal benefit to the patient (McGuire, 1985 ). Information processing theory describes problem solving as an interaction between the information processing system (the problem-solver) and a task environment, which can be analysed as two simultaneously occurring sub-processes of “understanding” and “search” (VanLehn, 1989 ). Individuals collect the stimulus that poses the problem in the understanding process, forming the internal representation of the problem, transforming the problem stimulus into the initial information needed in the search process, and then producing mental information structures for the understanding of the problem, which making individuals distinguish the nature of the problem and clarify the goal of the problem. The mental information structures drive the search process that enables the individual to find or calculate the solution to the problem. This process starts with the nurse identifying the clinical problem and continues until the decision is made to resolve the problem (Taylor, 2000 ). Clinical problem solving requires nurses to have a variety of cognitive strategies, which involves nurses’ knowledge, experience, and memory process. Nurses must recognize the current problem and use all available knowledge and experience to transform the problem into their internal problem representation, and then set goals and search for strategies that can achieve the goal (Mayer & Wittrock, 1992 ). In today’s complex clinical environment, nurses need to be able to solve problems accurately, thoroughly, and quickly. Nurses who can solve problems efficiently have fewer medical errors (Babaei et al., 2018 ), and the level of nursing skills and empathy are higher (Ay et al., 2020 ; Bayindir Çevik & Olgun, 2015 ). To cultivate nurses’ problem solving thinking and ability, it is necessary to better understand the influencing factors of problem solving dilemma. However, these cannot be obtained by observing nurses’ behaviour in their work, and cannot be obtained through quantitative research either. Exploring the thinking process involved in nurses’ work through qualitative interviews is an effective way to understand the influencing factors of nurses’ problem solving. Given this, this study used qualitative research methods to deeply analyse the influencing factors of clinical front-line nurses’ problem solving dilemma, to provide a basis for making relevant strategies to cultivate nurses’ thinking and ability of problem solving.

Study design

A qualitative study based on in-depth interviews was conducted to obtain influencing factors of nurses’ problem-solving dilemma.

Settings and participants

Purposive sampling combined with a maximum variation strategy was used to identify and select information-rich participants related to the research phenomenon. Maximum variation was achieved in terms of participants’ gender, education level, professional title, marital status, seniority, and administrative office, respectively. The study was conducted between August 2020 to December 2020 in a tertiary hospital in Shanghai, China. The inclusion criteria were a nurse practicing certificate of the People’s Republic of China and within the valid registration period; having been engaged in clinical nursing work for at least 1 year and still engaged in clinical nursing work; clear language expression, able to clearly describe the solution and feelings of clinical problem solving; informed consent to this study and voluntary participation. The exclusion criterion were on leave during the study period (personal leave, maternity leave, sick leave, etc.); out for further study or came to the hospital for further study; confirmed or suspected mental illness and psychotropic medicine users. Purposive sampling continued until thematic saturation was reached during data analysis.

Data collection

Face-to-face, a semi-structured interview was used to collect information. All interviews were conducted in the lounge to ensure quiet and undisturbed by a female postgraduate nursing student with the guidance of her master tutor. Initially, an interview guide was developed based on literature review and expert consultation including about five predetermined questions: What thorny problems have you encountered in clinical work or have a great impact on you? How did you solve it? Why take such a solution? What is the biggest difficulty encountered in the process of problem solving? How does it affect you? How do you feel in the process of problem solving? Before the interview, the consent of the interviewee was obtained and then the researcher fully explains to the interviewees and starts with a friendly chat to allay the interviewees’ worries. During the interview, the researcher listened carefully and responded in time, always maintaining a neutral attitude, without any inducement or hint, if necessary, giving encouragement and praise to support the expression of the interviewees, and to record the interviewees’ facial expressions, physical movements and emotional responses in time. At the same time, a recording pen was used to ensure that the interview content was recorded accurately and without omission. The interview time for each person was 30 to 40 minutes.

Data analysis

After each interview, the researcher wrote an interview diary in time to reflect on the interview process and transcribed the interview content into words within 24 hours, then the researcher made a return visit by phone the next day to confirm that the information is correct. The seven-step method of Colaizzi’s phenomenological analysis method ( Table I ) was adopted to analyse the collected data(Colaizzi, 1978 ). Two researchers collated the original data, independently coded, summarized this information as themes, and organized a research group meeting once a week to discuss and reach a consensus.

7 steps of Colaizzi’s phenomenological analysis method.

Ethical considerations

This study was approved by the Ethics Committee of the Shanghai Pulmonary Hospital, Affiliated to Tongji University, project number: K16-252. Before the interview, the researcher explained the purpose and significance of the study to each interviewee in detail and obtained the informed consent of them on a voluntary basis and all of the interviewees signed informed consent forms. To protect the privacy of each interviewee, their names are replaced by numbers (e.g., N1, N2), and the original materials and transcribed text materials involved are kept by the first author himself, and all materials are destroyed after the completion of the study.

There was no new point of view when the 13th nurse was interviewed, and there was still no new point of view when one more nurse was interviewed, the interview was over, 14 nurses were interviewed. Three themes and seven subthemes were extracted. The characteristics of the participants ( N = 14) are provided in Table II .

Participant characteristics (N = 14).

Nurses’ own factors

Differences in knowledge structure and thinking.

Differences in the structure of prior knowledge and way of thinking will affect nurses’ processing of clinical data, thus affecting their clinical decision-making. The nurses made a wrong judgement of the condition because of the solidified thinking that postoperative nausea and vomiting symptoms were side effects of narcotic drugs and the lack of overall control and understanding of the patient’s condition.

There was a patient who came back after surgery with nausea and vomiting, the first thing that went through my mind, is the drug side effects, so I didn’t pay much attention, as is often the case, the most common cause of postoperative nausea and vomiting is anesthetic drug side effects, but later found to be cerebral infarction, this kind of situation I find it hard to recognize.

Differences in professional values

Professional values of nurses are accepted codes of conduct internalized by nursing professionals through training and learning (Pan, 2016 ). Negative professional values are easy to lead to problem solving dilemma. Some nurses think nursing is just a service.

The work is difficult to do, everything is the nurse’s fault, the nurse must apologize and put up with the patient’s scolding, nursing is a service industry, sometimes I am really wronged.” There are also nurses who believe that nursing work can reflect their personal value, and solving problems successfully will bring them a sense of achievement.

Although the nursing work is very intense, I live a full life every day. I feel a sense of accomplishment and pride that I can solve the problems of patients and discharge them smoothly through my work.

Poor strain capacity

Nursing work is patient-centred holistic nursing, the current clinical situation is complex and changeable, requiring nurses must have good strain capacity, and can “be anxious about what the patient needs, think what the patient thinks, and solve the patient’s difficulties.”

All patients are self-centered, and they don’t care whether you (the nurse) are busy or not. For example, once I gave oral medicine to a patient, a patient in the same ward was in a hurry and asked me to help him call his son. I was busy handing out the medicine and did not help. As a result, the patient was very dissatisfied and complained to the head nurse.

The 20-bed patient went through the discharge formalities but was still lying in the hospital bed. when the new patient arrived and she didn’t leave, I went to urge her to leave the hospital, she suddenly got angry and scolded me, I don’t know what to do.

Improper nursing management

Low sense of organizational support.

Organizational support is an important resource for clinical nurses in the process of problem solving (Poghosyan et al., 2020 ). Low sense of organizational support will hinder nurses’ problem solving.

The style of leadership and the atmosphere of the department are very important. in a department I rotated before, the leader was too strict to listen to your explanation, and the atmosphere of the department was not good. I couldn’t find help when I encountered problems. When I have a conflict with a patient, the leader will only criticize me, which makes me feel helpless.

Sometimes there will be a conflict with patients due to the bed turnover problem, and the patient will not listen to your explanation and turn around to complain, the nurse will be responsible for such things. In severe cases, even violent incidents will be encountered and the personal safety can not be guaranteed.

Insufficient allocation of manpower

Although the total number of nurses has increased substantially, there is still a shortage of human resources under the rapidly increasing workload (Guo et al., 2021 ).

When I was on the night shift and I encountered the critical moment of rescuing patients, I had to call an anesthesiologist, a doctor on duty, a nurse on duty simultaneously, an observation of the patient’s condition to prevent accidents was needed, I also have to race against time to give the patient ECG monitoring and oxygen inhalation. When the doctor came, he also criticized me that the first-aid equipment was not in place (crying).

According to the normal nurse-patient ratio, each nurse takes care of eight patients, and now there are not only eight patients, but also with extra beds and a fast turnover, and sometimes a nurse is responsible for more than 12 patients

Patient factors

The concept of emphasizing medicine and neglecting to nurse.

There is a deviation in society’s cognition of the profession of nurses, which believes that nurses are the “legs” of doctors, and nurses’ work is to help doctors run errands, give injections and give fluids. This concept not only leads to nurses’ lack of due respect, but also hinders nurses’ professional identity, and has a great negative impact on nurses’ problem-solving (Gao et al., 2015 ).

The patient did not dare to tell the doctor something he was not satisfied with, but complained directly to the nurse. For example, if the patient did not want to do some tests, he would scold the nurse. The nurse explained to him that he would not listen. But when the doctor came, he smiled and refused to admit that he cursed nurses, and he would frame the nurse. 90% of the patients would be willing to listen to the doctor.

Sometimes the patient says he was not feeling well, and I know the patient’s condition. I will give her some reasonable explanations, but the patient does not accept it. She is satisfied only when the doctor come to see her. In the final analysis, the patient just don’t believe us. No matter how much I explain to her, it is not as effective as the doctor’s glance at her.

Individual differences of patients

There are differences in patients’ personality characteristics, cultural background, views on nurses and state of an illness, these individual differences are also the reasons for nurses’ problem-solving dilemma (Chan et al., 2018 ).

Some cancer patients are in a period of anger, and it is very difficult to communicate with him. When I see him angry and lose his temper, I will not talk to him and just leave.”

Patients have different cultural levels and different social backgrounds. Sometimes I can’t talk too deeply. If patients are a little more educated, it will be easier for us to communicate with them, and some patients can’t understand anything we say.”

Multiple factors affecting clinical nurses’ problem-solving dilemma

The reasons for nurses’ failure in problem solving are mainly in the process of understanding the problem, the search process driven by the psychological information structure, and the problem or loss of balance in the process of implementing the plan. In the process, the three factors of nurses, management and patients all played an important role. Nurses’ knowledge structure and thinking loopholes led to the deviation of nurses’ internal representation of the problem (Jonassen, 2005 ). Poor professional values and low sense of organizational support can lead to nurses’ negative orientation and attitude towards problems (Poghosyan et al., 2020 ; X. Wang et al., 2018 ). The manpower allocation of nurses, patients’ emphasis on medical treatment over nursing care, and individual differences mainly increase the complexity and difficulty of nurses’ problem-solving task environment as external factors. The three factors work together on the problem-solving of clinical nurses, which leads to the dilemma of problem-solving.

Implementing situational simulation training to improve the comprehensive quality of nurses

At present, the overall quality and ability of nurses cannot meet the requirements of systematic, effective and rapid problem-solving. It is necessary to strengthen the construction of nurses to improve nurses’ problem-solving ability. Some studies have shown that situational simulation class can improve students’ knowledge, experience, psychological quality and other abilities (Mohammad, 2020 ). It is suggested that nursing educators should explore targeted situational simulation teaching and strengthen the relationship between classroom teaching and clinical practice through situational simulation, and to build a novel, perfect and clinical knowledge network for nurses. Secondly, emergency situational simulation teaching should be carried out to enable nurses to experience emergency situations from different angles, so as to improve their thinking, skills and timeliness in dealing with emergencies (Zhang et al., 2019 ). The content of professional values training should also be added to the situational simulation class in order to cultivate nurses’ positive, accessible and stable professional values and promote their positive orientation and attitude when facing problems (Skeriene, 2019 ).

Optimize nursing management and improve nurses’ working experience

Through interviews, it is found that nursing management factors have caused nurses’ problem-solving dilemma to a certain extent, which needs to be optimized according to the specific problems existing in nursing management to help nurses deal with the problems and solve the dilemma effectively. The total number of registered nurses in China exceeded 4.7 million in 2021, an increase of 1.46 million from 3.24 million in 2015, an increase of 45% (Deng et al., 2019 ]. However, there is still a large workload and underallocation of manpower, which may be due to the unreasonable distribution of human resources between time periods and departments. Hospitals and nursing managers can use the hospital information system to evaluate the nursing workload, and allocate nursing human resources reasonably according to the evaluation results (H. Yang et al., 2019 ), so as to avoid nurses falling into the dilemma of problem solving due to long-term overloaded work. In addition, it is necessary to create a harmonious departmental atmosphere for nurses, create a supportive departmental environment (Aghaei et al., 2020 ), and strictly ensure the safety of nurses’ practice and put an end to the occurrence of violence. Timely and strong organizational support can reduce the painful feelings of nurses caused by adverse events (Stone, 2020 ). and help them to solve problems actively.

Using new media to improve the image and credibility of nurses

There is a bias in social cognition of the profession of nurses, and some negative media reports mislead patients, resulting in social stereotypes of nurses (L. Q. Wang et al., 2021 ). It is necessary to make full use of new media to objectively introduce the nursing profession to the public, publicize outstanding nursing figures and typical deeds, make the public realize the important role of nurses in health care, and create an atmosphere of understanding and supporting nurses in the whole society to enhance the image and credibility of nurses and help nurses deal with problems and solve difficulties effectively (Falkenstrom, 2017 ).

Limitations and strengths of the study

The limitation is that the transferability of this study’s results may be limited as a result of including a small number of participants and the participants all worked in the same hospital in Shanghai. More participants in different cities and hospitals could have increased the variety of the descriptions and experiences. The strength is that the use of purposive sampling facilitated inclusion of participants from a range of demographic groups. The use of maximum variation strategy facilitated that the participants covered different gender, education level, professional title, marital status, seniority and department, which helped to increase the representativeness of sample.

Implications for practice

This study provides an in-depth exploration of the problem solving dilemmas of clinical nurses in China and provides valuable insights into the continuing education of nurses. These insights shine a light on areas that warrant further investigation and need to be improved in continuing education of nurses. It is of great significance to improve nurses’ problem-solving ability, improve nurses’ professional quality, effectively solve patients’ medical treatment and health problems, and improve patients’ experience of seeking medical treatment.

Through the semi-structured interview, it is found that the problem-solving dilemma of clinical nurses is affected by many factors. Nurses themselves should be confident, self-improvement, constantly learning and enterprising to improve their own ability, and be good at using new media to improve nurses’ image and credibility. Hospitals, nursing administrators and nursing educators should take corresponding measures to improve the knowledge structure of nurses, cultivate nurses’ positive professional values and adaptability, and give full organizational support to nurses. optimize the allocation of nursing human resources to provide a strong guarantee for nurses to deal with problems solving dilemma.

Biographies

Yu Mei Li : associate chief nurse, master degree, master supervisor, engaged in nursing of tumor patients.

Yifan Luo : nurse, master degree, engaged in clinical nursing.

Funding Statement

This work was supported by the Graduate Education Research and Reform Education Management program of Tongji University [2021YXGL09].

Disclosure statement

No potential conflict of interest was reported by the author(s).

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