Hybrid PSO-GA Metaheuristic Optimization for Comprehensive Student Performance Enhancement

Pitchika P N G PhaniKumar; Junali Jasmine Jena; Sagiraju Srinadhraju; Sudhirvarma Sagiraju

doi:10.12688/f1000research.171008.1

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Research Article

Hybrid PSO-GA Metaheuristic Optimization for Comprehensive Student Performance Enhancement

[version 1; peer review: awaiting peer review]

Pitchika P N G PhaniKumar¹, Junali Jasmine Jena¹, Sagiraju Srinadhraju², Sudhirvarma Sagiraju²

PUBLISHED 01 Dec 2025

Author details Author details

¹ School of Computer Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India
² Department of Computer Science & Engineering, Raghu Engineering College, Visakhapatnam, Andhra Pradesh, India

Pitchika P N G PhaniKumar
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Software, Visualization, Writing – Original Draft Preparation

Junali Jasmine Jena
Roles: Conceptualization, Funding Acquisition, Methodology, Project Administration, Resources, Supervision, Validation, Writing – Review & Editing

Sagiraju Srinadhraju
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Validation, Visualization, Writing – Original Draft Preparation

Sudhirvarma Sagiraju
Roles: Conceptualization, Formal Analysis, Methodology, Resources, Validation, Writing – Original Draft Preparation

OPEN PEER REVIEW

REVIEWER STATUS AWAITING PEER REVIEW

This article is included in the Artificial Intelligence and Machine Learning gateway.

Abstract

Students aim for well-rounded performance, and higher education institutions strive to support them. While written tests assess academic achievement, they do not fully capture skills like critical thinking, creativity, public speaking, and physical fitness. The proposed paper suggests a holistic optimization model involving a Hybrid PSO-GA (Particle Swarm Optimization - Genetic Algorithm) metaheuristic algorithm that would generate a more holistic student assessment platform that constitutes a fitness function that would evaluate students not only on exams but also on academic, co-curricular and extracurricular facets. The model formulates a constrained optimization problem where cognitive effort allocation is optimized under individual workload limits derived from factors such as cognitive capacity, time availability, fatigue, and task complexity. Proposed model evaluated in C++ and analyzed statistically in Python across three setups with population sizes of 25, 50, and 100, and up to 200 iterations. A previous survey-based study was considered in formulating datasets, and normalized cognitive workload scores were applied to five categories of tasks. The hybrid algorithm outperformed standalone Genetic Algorithm and Particle Swarm Optimization methods, achieving the highest mean fitness of 1.273 and the lowest standard deviation of 0.004. Statistical significance was confirmed using the Friedman and Nemenyi tests with p-values less than 0.0001, demonstrating the robustness and superior convergence of the hybrid model. The proposed approach provides a computationally intelligent and statistically robust framework for holistic student performance assessment, with implications for adaptive academic workload management and policy-driven educational enhancement.

Keywords

student performance, survey, optimization, metaheuristic, hybrid

Corresponding author: Junali Jasmine Jena

Competing interests: No competing interests were disclosed.

Grant information: The authors acknowledge that this publication received partial funding support from Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar, India.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2025 P N G PhaniKumar P 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 work is properly cited.

How to cite: P N G PhaniKumar P, Jena JJ, Srinadhraju S and Sagiraju S. Hybrid PSO-GA Metaheuristic Optimization for Comprehensive Student Performance Enhancement [version 1; peer review: awaiting peer review]. F1000Research 2025, 14:1344 (https://doi.org/10.12688/f1000research.171008.1) First published: 01 Dec 2025, 14:1344 (https://doi.org/10.12688/f1000research.171008.1) Latest published: 01 Dec 2025, 14:1344 (https://doi.org/10.12688/f1000research.171008.1)

1. Introduction

Education is widely recognized as a fundamental human right essential for personal and national development. Over the years, education systems have faced numerous challenges and changes in their approaches. Today, institutions are increasingly focused on retaining students and providing engaging, effective teaching. However, assessing students’ abilities in various areas remains a challenge, as many institutions still heavily rely on written exams for evaluation. This narrow focus can overlook important skills, leaving students unprepared in areas beyond academics. A potential solution is to adopt smarter, data-driven methods for evaluating students’ strengths and weaknesses. This would enable faster and more personalized assessments through computational intelligence.

Constrained optimization problems often transform subjective human judgments into structured mathematical models. Classic NP-hard problems (Karp, 1972), such as the Traveling Salesman Problem (TSP) (Sharma, 2024), optimize routing for scheduling and deliveries, while the Knapsack Problem (He et al., 2024) determines optimal selections under constraints. Boolean satisfiability (SAT) (Boulebnane & Montanaro, 2024) deals with binary variable conditions, and MAX-SAT (Das et al., 2025) focuses on maximizing satisfied clauses. These mathematical frameworks enable the systematic evaluation of subjective tasks, such as student assessments, for objective decision-making.

Metaheuristic algorithms are powerful optimization techniques inspired by natural processes, designed to efficiently tackle complex problems where traditional methods are inadequate. They balance exploration and exploitation to achieve near-optimal solutions. For instance, the Genetic Algorithm (Tang et al., 1996) simulates natural selection, while Particle Swarm Optimization (Kennedy & Eberhart, 1995) models collective behaviour. Teaching-Learning-Based Optimization (TLBO) (Rao et al., 2012) is based on the teacher-student knowledge transfer mechanism, Ant Colony Optimization (Dorigo et al., 1996) replicates how ants use pheromone trails to find optimal paths, and Light Spectrum Optimization (Abdel-Basset et al., 2022) is inspired by light dispersion. Due to their adaptability and effectiveness, these methods are widely applied across various domains.

The structure of the paper is as follows: Introduction section and Literature Review section examines prior research on the topic, providing a critical evaluation of different perspectives while highlighting their strengths and limitations. Problem Definition section establishes the problem framework and presents a mathematical formulation, including an objective function, a constraint equation, and equations for evaluating effectiveness and stress levels. Datasets section details the datasets compiled from various studies and survey papers. Hybrid PSO-GA approach section introduces a novel metaheuristic algorithm designed to address the problem. In Results and Discussion section, multiple simulations are conducted to assess the algorithm’s performance in terms of optimization accuracy and computational efficiency, with results ranked using standard statistical techniques. Finally, Conclusion summarizes the key contributions and outlines potential directions for future research.

2. Literature review

This section will review several recent papers published addressing the student evaluation and prediction problem through the application of computational intelligence.

To begin with, Lakshmi et al. (Miranda Lakshmi et al., 2013) conducted a study that explored the use of genetic algorithms as an effective method for analyzing complex educational data (Batool et al., 2023). By applying principles of natural evolution, their model identified significant factors affecting student performance through a quantitative evaluation of various academic metrics, such as theoretical, mathematical, and practical scores. This approach not only assisted educational institutions in improving teaching quality by analyzing student marks but also served as a valuable tool for classifying and examining performance determinants throughout the academic year. The findings indicated that even minor adjustments to the genetic algorithm’s parameters could yield significant insights into key performance indicators. Ultimately, the model provided students with a self-assessment mechanism to better understand their academic standing and identify areas for improvement, underscoring the effectiveness of genetic algorithms in predicting student performance and enhancing educational development across various contexts.

Another similar study, done by Hamsa et al. (Hamsa et al., 2016) developed a hybrid model that combines decision tree algorithms with a fuzzy genetic algorithm to predict student academic performance (Yağcı, 2022) in bachelor’s and master’s programs. By analyzing various parameters such as internal marks, sessional scores, and admission scores, the model evaluates each student’s subject-specific outcomes and provides educators with a valuable tool to promote academic success (Jin, 2023). The decision tree (“Predictive Analytics in Business Analytics,” 2022) component effectively identifies at-risk students, enabling instructors to offer additional support to improve final exam results, while the fuzzy genetic algorithm classifies more students as passing by accommodating borderline cases, reassuring them and allowing for indirect monitoring of their progress. This balanced approach fosters a supportive learning environment (Niu et al., 2022) and helps high-performing students attract early recruitment from reputable companies, ultimately benefiting both the students and the institution’s reputation.

Gomede et al. (Gomede et al., 2018) developed a computational intelligence model (Ikegwu et al., 2024) to improve education quality and support decision-making, particularly in regions with limited access to quality education (Timotheou et al., 2023). Using data science and mining techniques (Shu & Ye, 2023), the model generated personalized knowledge profiles, helping teachers monitor key performance indicators (KPIs) (Joppen et al., 2019) and make informed decisions. Based on real K–9 student data from a private school in Brazil, it utilized graph-based visualization, recommendation systems, and random forest algorithms for classification (Shaik & Srinivasan, 2019) and prediction (Schonlau & Zou, 2020). This approach enabled performance forecasting, identified key links, and provided tailored recommendations to enhance learning outcomes. Operating within a PDCA (Plan, Do, Check, Act) cycle, the model improved prediction accuracy and aligned indicators with educational system goals.

Furthermore, in a paper by Taylan et al. (Taylan et al., 2017), the authors analyzed learning objectives for graduate and program-level industrial engineering students by developing the “house of cognitive learning,” which emphasizes cognitive depth, outcome components, and conceptual understanding. To address challenges in assessment and measurement, they proposed a “learning index” derived using an integrated integer programming model. This index was refined through statistical methods and quality control charts to provide a comprehensive and longitudinal view of student progress (Ifenthaler & Yau, 2020b, 2020a). Their findings underscored the importance of clearly defined learning objectives and shared instructor-student expectations in driving effective curriculum outcomes (Ifenthaler et al., 2019). The study reinforced the growing role of data-driven course design in enhancing learning impact, while also promoting self-directed learning and personalized feedback mechanisms to foster continuous student engagement and responsibility.

Agaarna et al. (Michael & Amenawon, 2015) analyzed factors influencing academic performance in world-class universities using a linear programming model (Mayer, 2022). Key elements included entry points, student-to-staff ratio, library spending, accommodation quality, teaching assessments, research ratings, and international student presence. Using the simplex method (Huiberts et al., 2022) and MAPLE14 software, the model standardized these factors to assess their significance. Results showed teaching assessment as the most critical factor, followed by entry points. The study underscored the importance of high teaching quality, library engagement, and proper admission criteria. A comprehensive understanding of these variables was found to be essential for optimizing student outcomes in higher education.

3. Problem definition

We consider a set of task categories indexed by i ∊ {1,2, …, n}, each associated with a cognitive load value c_i. The objective is to optimize the allocation of effort x_i to maximize the total cognitive benefit, formulated as:

(1)

max \sum_{i = 1}^{n} x_{i} . c_{i}

Subject to the following constraint:

(2)

\sum_{i = 1}^{n} x_{i} \leq λ \sum_{i = 1}^{n} c_{i}

where λ represents an individual’s personalized cognitive load limit. This parameter is determined based on multiple factors to ensure a balanced cognitive workload. Specifically, λ is a function of:

• Cognitive Capacity (Baseline) Assessed through historical academic performance or aptitude scores.
• Time Availability Measured in terms of structured task hours available per day.
• Fatigue & Stress Levels Evaluated through self-reported metrics, including stress surveys, sleep quality, and mental fatigue levels.
• Task Complexity & Adaptability Determined via problem-solving assessments reflecting adaptability to cognitive challenges.

For this study, we focus on task categories that have quantifiable cognitive workload based on survey-derived satisfaction metrics. These categories are:

• Academic Performance
Mapped to: Memory & Learning, Analytical & Problem-Solving
• Assignments & Projects
Mapped to: Memory & Learning, Analytical & Problem-Solving
• Co-curricular & Extra-curricular Engagement
Mapped to: Social & Communication, Multitasking
• Clubs & Societies
Mapped to: Social & Communication
• Sports & Cultural Participation
Mapped to: Physical & Sensorimotor, Social & Communication

These categories were selected based on strong representation in the dataset and clear association with distinct cognitive domains, enabling an evidence-based approach to modeling student workload and performance.

4. Materials and methods

4.1 Datasets

Cognitive load value (c_i):

The dataset utilized in this study was extracted from Table 2, Table 3, and Table 4 of a survey-based study conducted by Yangdon et al. (Karma et al., 2021). The mean satisfaction scores for each category, based on Likert-scale responses, were normalized using Equation 3 to map the values onto a scale from 0 to 1. Here, M denotes the average satisfaction rating for a given category. To represent cognitive workload instead of satisfaction, the normalized values were inverted by subtracting them from 1.

(3)

C_{i} = 1 - \frac{M - 1}{4}

Five academic task categories were considered in this study, denoted as C₁ to C₅. C₁ corresponds to Academic Performance, while C₂ represents Assignments & Projects. Co-curricular & Extra-curricular Engagement is categorized under C₃, whereas C₄ refers to Clubs & Societies. Finally, C₅ is assigned to Sports & Cultural Participation. Each task category is mapped to one or more cognitive domains, forming the basis for workload estimation and cognitive effort distribution in this study.

The values taken from the survey paper are shown in Table 1 and the resulting workload scores are summarized in Table 2.

Table 1. Mapped academic task categories with associated cognitive domains, source reference, and computed workload values.

Category	Cognitive domain(s)	Source Table/Section	Workload (0–1)
Academic Performance	Memory & Learning, Analytical & Problem-Solving	Table 4 (M = 3.42)	0.57
Assignments & Projects	Memory & Learning, Analytical & Problem-Solving	Table 4 (M = 2.83)	0.71
Co-curricular & Extra-curricular Engagement	Social & Communication, Multitasking	Table 2 (Recreation M = 3.08)	0.65
Clubs & Societies	Social & Communication	Table 3 (Tutor Support M = 3.16)	0.68
Sports & Cultural Participation	Physical & Sensorimotor, Social & Communication	Table 2 (Sports M = 3.25)	0.65

Table 2. Cognitive workload values (c_i) for each category (C₁ to C₅).

C₁	C₂	C₃	C₄	C₅
0.57	0.71	0.65	0.68	0.65

Personal cognitive limit (λ):

The personal cognitive limit λ was assumed to be influenced by four key factors: cognitive capacity, time availability, fatigue & stress levels, and task complexity & adaptability. These factors were represented as l_1, l_2, l₃, and l₄, respectively. Since precise values for these factors were unavailable, they were randomly chosen within a reasonable range for the scope of this study.

The cognitive limit λ was computed using the following equation:

(4)

λ = \sum α_{i} l_{i}

where α_i represents the weighting coefficients assigned to each factor which in this study is considered to be 0.25. For this study, 3 student’s data have been randomly generated as shown in Table 3 and will be used in experiments.

Table 3. Limit values of student S1, S2 and S3 generated at random.

Student	l₁	l₂	l₃	l₄
S1	0.36	0.73	0.45	0.71
S2	0.25	0.45	0.61	0.63
S3	0.23	0.32	0.12	0.87

4.2 Hybrid PSO-GA approach

The Hybrid PSO-GA algorithm synergizes the exploration capabilities of Genetic Algorithms (GA) with the exploitation strengths of Particle Swarm Optimization (PSO) to achieve more robust optimization. Each particle in the population acts as a self-contained agent that holds several key pieces of memory throughout the search process. These include its current position in the solution space, its velocity, its personal best position (the most optimal solution it has found so far), the fitness value of that best position, and crucially, the iteration index at which it achieved this personal best. This extra memory component allows the algorithm to keep track of stagnation at an individual level. The entire structure of a single particle in the whole population can be seen in Figure 1. A hyperparameter called the iteration threshold determines how long a particle can go without improving before triggering an alternative search behaviour.

Figure 1. Structure of a particle in Hybrid PSO-GA.

When a particle exceeds this stagnation threshold, it is subjected to Genetic Algorithm operations instead of standard PSO updates. Specifically, the particle is selected for crossover with another randomly chosen particle from the population. A subset of genes (position values) is swapped between the two using a defined crossover probability and window size. After crossover, each gene has a chance to undergo mutation, governed by a mutation probability. Once the new candidate solutions are formed, they are passed through a repair function r(x) to ensure that all variables remain within the problem’s constraints of [0,1], which basically is a slightly modified sigmoid function as shown in Equation 5. The fitness of these modified solutions is then evaluated. This GA-based route reinjects diversity into the population and allows the algorithm to escape local optima.

(5)

r (x) = \frac{1}{1 + e^{- (x - 0.5) . c}}

If a particle has not yet stagnated, it continues to evolve using the conventional PSO dynamics. The velocity is updated based on its inertia and the difference vectors between its current position and both its personal best and the global best found in the population, with some randomness injected to encourage exploration. The new position is computed, repaired if needed, and evaluated for fitness. If the new fitness surpasses its personal best, the personal best is updated along with the iteration in which the improvement occurred. Simultaneously, the global best is also updated whenever a particle exceeds the previous best. This hybrid framework ensures a balance between local refinement and global exploration, leading to higher resilience against premature convergence and better performance in complex, multimodal search landscapes.

The whole flowchart of the algorithm can be seen in Figure 2.

Figure 2. Flowchart displaying the functionality of Hybrid PSO-GA.

Algorithm 1. Hybrid PSO-GA Optimization (Condensed).

1: Init particle population: positions, velocities

2: Evaluate fitness, set personal and global bests

3: for each generation do

4: for each particle p do

5: if no improv. for p in threshold iterations then

6: Select particle q randomly

7: Crossover p and q with P_c

8: Mutate p’s genes with P_m

9: Repair invalid genes using r(x)

10: Evaluate fitness of p, q

11: else

12: Update p’s velocity and position (PSO)

13: Repair and evaluate fitness

14: end if

15: if fitness(p) > personal best then

16: Update personal best, note iteration

17: end if

18: if fitness(p) > global best then

19: Update global best

20: end if

21: end for

22: end for

5. Results and discussion

The simulations were implemented in C++ with GCC version 14.2.1, while Python 3.12 was employed for the statistical analysis of the results. The tests were conducted on a system with an Intel Core i7-1255U processor and 16GB of RAM, running Fedora Linux 40. The final fitness values were ranked using a standard ranking method, preserving the initial values for each algorithm to ensure a fair comparison. This approach allowed for an objective assessment of each algorithm’s performance, providing a detailed overview of their efficiency and convergence. Each sub-experiment was executed 50 times to ensure a statistically valid comparison between all the algorithms, resulting in a total of 3 × 3 × 50 = 450 simulation runs across all configurations.

5.1 Experiment set S-1

Experiment A (Population: 25, Iterations: 50):

The first experiment in Set S-1 evaluates algorithmic performance under a limited computational budget, using a population size of 25 and 50 iterations. The results show a clear advantage for the Hybrid PSO-GA algorithm over the standalone GA and PSO variants. It achieves the highest average fitness value of 1.254 and maintains the lowest standard deviation of 0.015, highlighting both its superior optimization capability and enhanced stability across five problem cases.

To validate these observations statistically, a non-parametric Friedman test was conducted. The test yielded a Chi-Square value of 75.9192 with a p-value of 0.0000, indicating that the observed performance differences among the three algorithms are statistically significant at the 95% confidence level (p < 0.05).

Subsequently, the Nemenyi posthoc test was applied to evaluate pairwise significance. The resulting p-values demonstrated that Hybrid PSO-GA significantly outperforms both GA and PSO individually, with p-values of 4.07 × 10⁻¹⁴ and 8.63 × 10⁻¹³ respectively. However, no significant difference was observed between GA and PSO (p = 0.9156). This highlights the strength of the hybrid strategy, especially in lower-resource environments. The Nemenyi matrix and the convergence trend are shown in Figures 3 and 4, respectively. Detailed fitness results are reported in Table 4.

Figure 3. Experiment S1-A Nemenyi test matrix.

Figure 4. Experiment S1-A convergence graph.

Table 4. Fitness values for experiment A (S-1).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.071	0.678	0.341	0.457	0.251	1.217	0.025	3
PSO	0.046	0.649	0.369	0.488	0.246	1.219	0.023	2
Hybrid PSO-GA	0.013	0.914	0.136	0.605	0.150	1.254	0.015	1

Experiment B (Population: 50, Iterations: 100):

In the second experiment, the population and iteration counts were doubled to examine scalability and robustness in a more resource-rich environment. With a population of 50 and 100 iterations, the Hybrid PSO-GA continued to outperform the standalone GA and PSO, achieving the highest mean fitness of 1.265 and the lowest standard deviation of 0.009, further reinforcing its robustness.

The Friedman test for this setup produced a Chi-Square value of 81.5758 and a p-value of 0.0000, indicating statistically significant differences in algorithm performance. The Nemenyi test showed that Hybrid PSO-GA significantly surpassed GA (p = 2.88 × 10⁻¹³) and PSO (p = 5.66 × 10⁻¹¹), while the difference between GA and PSO remained statistically insignificant (p = 0.6079).

These results demonstrate the hybrid algorithm’s consistent advantage, even when more iterations and population diversity are available. The Nemenyi significance matrix and the convergence curve are shown in Figures 5 and 6, while the numeric results are reported in Table 5.

Figure 5. Experiment S1-B Nemenyi test matrix.

Figure 6. Experiment S1-B convergence graph.

Table 5. Fitness values for experiment B (S-1).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.021	0.885	0.218	0.570	0.113	1.243	0.016	3
PSO	0.005	0.910	0.218	0.551	0.133	1.251	0.013	2
Hybrid PSO-GA	0.006	0.929	0.029	0.785	0.076	1.265	0.009	1

Experiment C (Population: 100, Iterations: 200):

The third and final experiment in Set S-1 investigates performance under the maximum resource allocation—100 individuals over 200 iterations. Once again, Hybrid PSO-GA achieved the best fitness results, with a mean of 1.273 and a remarkably low standard deviation of 0.004. This emphasizes the algorithm’s convergence efficiency and reliability under extended search conditions.

The Friedman test produced a Chi-Square value of 85.2400 and a p-value of 0.0000, confirming the significance of the observed differences. The Nemenyi test revealed that Hybrid PSO-GA significantly outperforms GA (p = 6.43 × 10⁻¹²) and PSO (p = 2.74 × 10⁻¹⁰), while GA vs PSO remained statistically non-significant (p = 0.4863).

Figures 7 and 8 display the statistical and convergence analyses. Table 6 presents the corresponding quantitative results.

Figure 7. Experiment S1-C Nemenyi test matrix.

Figure 8. Experiment S1-C convergence graph.

Table 6. Fitness values for experiment C (S-1).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.009	0.925	0.111	0.755	0.018	1.259	0.013	3
PSO	0.002	0.928	0.005	0.859	0.035	1.270	0.005	2
Hybrid PSO-GA	0.003	0.981	0.007	0.832	0.008	1.273	0.004	1

Summary of experiment set S-1:

Across all three configurations in Experiment Set S-1, the Hybrid PSO-GA consistently outperforms both GA and PSO in terms of mean fitness and stability (as measured by standard deviation). Table 7 summarizes the average ranks, with Hybrid PSO-GA maintaining a perfect harmonic rank of 1.0 across all experiments.

Table 7. Rank summary for experiment set S-1.

Algorithm	A Rank	B Rank	C Rank	Harmonic Mean Rank
GA	3	3	3	3.00
PSO	2	2	2	2.00
Hybrid PSO-GA	1	1	1	1.00

5.2 Experiment set S-2

Experiment A (Population: 25, Iterations: 50):

The first experiment in Set S-2 assesses algorithmic efficiency under constrained computational conditions, using a small population of 25 over 50 iterations. The Hybrid PSO-GA again demonstrates superior performance, yielding the highest average fitness of 1.074 and the lowest standard deviation of 0.019. This suggests a strong capability for both exploration and exploitation even with limited resources.

The Friedman test reported a Chi-Square value of 79.8071 and a p-value of 0.0000, affirming statistically significant differences between the three algorithms. The Nemenyi posthoc analysis further validated these differences, with Hybrid PSO-GA showing significant superiority over GA (p = 1.11 × 10⁻¹⁶) and PSO (p = 1.73 × 10⁻¹⁰). However, the difference between GA and PSO was not statistically significant (p = 0.1386).

Figures 9 and 10 present the Nemenyi matrix and the convergence trend respectively. The corresponding fitness values are listed in Table 8.

Figure 9. Experiment S2-A Nemenyi test matrix.

Figure 10. Experiment S2-A convergence graph.

Table 8. Fitness values for experiment A (S-2).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.107	0.545	0.268	0.389	0.204	1.019	0.045	3
PSO	0.037	0.547	0.291	0.324	0.339	1.039	0.027	2
Hybrid PSO-GA	0.013	0.782	0.148	0.428	0.190	1.074	0.019	1

Experiment B (Population: 50, Iterations: 100):

The second experiment expands the search horizon with a population of 50 and 100 iterations. Hybrid PSO-GA maintained its lead with a mean fitness of 1.089 and a minimal standard deviation of 0.011. These results further indicate its ability to adapt and scale effectively with larger computational budgets.

The Friedman test yielded a Chi-Square value of 77.5600 and a p-value of 0.0000, confirming statistically significant performance variation. The Nemenyi posthoc analysis confirmed that Hybrid PSO-GA significantly outperformed GA (p = 3.33 × 10⁻¹⁶) and PSO (p = 6.25 × 10⁻¹¹), while the GA-PSO comparison remained statistically non-significant (p = 0.2456).

Figures 11 and 12 illustrate the significance matrix and convergence behavior. Table 9 details the numerical results.

Figure 11. Experiment S2-B Nemenyi test matrix.

Figure 12. Experiment S2-B convergence graph.

Table 9. Fitness values for experiment B (S-2).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.050	0.826	0.231	0.295	0.150	1.064	0.020	3
PSO	0.015	0.856	0.174	0.354	0.159	1.074	0.016	2
Hybrid PSO-GA	0.008	0.910	0.074	0.476	0.102	1.089	0.011	1

Experiment C (Population: 100, Iterations: 200):

The final experiment in Set S-2 evaluates algorithmic performance under the highest computational allowance: 100 individuals across 200 iterations. Here, Hybrid PSO-GA again achieved the top performance, reporting a mean fitness of 1.098 and an impressively low standard deviation of 0.005, reflecting highly stable convergence.

The Friedman test indicated a Chi-Square value of 89.4400 with a p-value of 0.0000, highlighting statistically significant differences. The Nemenyi test showed Hybrid PSO-GA to be significantly better than both GA (p = 0.0000) and PSO (p = 6.42 × 10⁻⁸). Even the GA vs PSO comparison reached significance (p = 4.25 × 10⁻⁴), suggesting improved resolution of differences at higher resources.

Figures 13 and 14 depict the statistical and convergence visuals, and the fitness scores are shown in Table 10.

Figure 13. Experiment S2-C Nemenyi test matrix.

Figure 14. Experiment S2-C convergence graph.

Table 10. Fitness values for experiment C (S-2).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.030	0.838	0.146	0.483	0.069	1.080	0.012	3
PSO	0.001	0.928	0.040	0.529	0.074	1.093	0.006	2
Hybrid PSO-GA	0.005	0.980	0.048	0.525	0.017	1.098	0.005	1

Summary of experiment set S-2:

Across the entire Experiment Set S-2, the Hybrid PSO-GA consistently demonstrated the highest average fitness and the lowest standard deviation, confirming both its optimization strength and reliability under varying resource conditions. Table 11 presents the rank summary, where the hybrid method once again maintained an optimal harmonic mean rank of 1.0.

Table 11. Rank summary for experiment set S-2.

Algorithm	A Rank	B Rank	C Rank	Harmonic Mean Rank
GA	3	3	3	3.00
PSO	2	2	2	2.00
Hybrid PSO-GA	1	1	1	1.00

5.3 Experiment set S-3

Experiment A (Population: 25, Iterations: 50):

Experiment 3-A evaluates algorithmic efficiency in low-resource conditions, using a population size of 25 and 50 iterations. Hybrid PSO-GA again demonstrated superior optimization, achieving the highest mean fitness value of 0.863 with the lowest standard deviation of 0.014, indicating stable and effective performance under constraints.

The Friedman test reported a Chi-Square value of 77.6382 and a p-value of 0.0000, confirming statistically significant performance differences. The Nemenyi posthoc test established that Hybrid PSO-GA significantly outperformed GA (p = 5.55 × 10⁻¹⁶) and PSO (p = 4.44 × 10⁻¹¹), while GA and PSO showed no statistically significant difference (p = 0.2909).

Figures 15 and 16 show the significance heatmap and the convergence graph respectively. Detailed fitness values are provided in Table 12.

Figure 15. Experiment S3-A Nemenyi test matrix.

Figure 16. Experiment S3-A convergence graph.

Table 12. Fitness values for experiment A (S-3).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.039	0.618	0.224	0.210	0.093	0.810	0.034	3
PSO	0.029	0.446	0.190	0.374	0.177	0.826	0.023	2
Hybrid PSO-GA	0.034	0.881	0.110	0.154	0.064	0.863	0.014	1

Experiment B (Population: 50, Iterations: 100):

In Experiment 3-B, the population size and iterations were doubled, increasing the search horizon. Hybrid PSO-GA remained the top performer, achieving a mean fitness of 0.874 and a standard deviation of 0.008, indicating reliable convergence with higher resource allocation.

The Friedman test produced a Chi-Square value of 79.8400 and a p-value of 0.0000, revealing statistically significant differences among the algorithms. According to the Nemenyi posthoc analysis, Hybrid PSO-GA significantly outperformed GA (p = 0.0000) and PSO (p = 4.66 × 10⁻¹⁰), while GA and PSO remained statistically similar (p = 0.0712).

Figures 17 and 18 depict the statistical and convergence results. Corresponding numerical results are shown in Table 13.

Figure 17. Experiment S3-B Nemenyi test matrix.

Figure 18. Experiment S3-B Convergence Graph.

Table 13. Fitness values for experiment B (S-3).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.021	0.753	0.116	0.269	0.053	0.839	0.028	3
PSO	0.007	0.816	0.078	0.262	0.075	0.861	0.012	2
Hybrid PSO-GA	0.005	0.960	0.042	0.183	0.058	0.874	0.008	1

Experiment C (Population: 100, Iterations: 200):

The final experiment in Set S-3 tests scalability under maximum computational allowance. Hybrid PSO-GA once again led with a mean fitness of 0.880 and a very low standard deviation of 0.003, reflecting strong optimization capabilities and stability at scale.

The Friedman test yielded a Chi-Square value of 91.0000 with a p-value of 0.0000, confirming significance. The Nemenyi test validated Hybrid PSO-GA’s advantage over both GA (p = 0.0000) and PSO (p = 1.14×10⁻⁷). Interestingly, even GA and PSO showed significant differences in this configuration (p = 1.87 × 10⁻⁴).

Figures 19 and 20 show the test results, with the raw performance scores summarized in Table 14.

Figure 19. Experiment S3-C Nemenyi test matrix.

Figure 20. Experiment S3-C convergence graph.

Table 14. Fitness values for experiment C (S-3).

Algorithm	C1	C2	C3	C4	C5	Mean	Standard deviation	Rank
GA	0.015	0.937	0.097	0.143	0.041	0.861	0.017	3
PSO	0.001	0.949	0.061	0.191	0.049	0.875	0.006	2
Hybrid PSO-GA	0.004	0.998	0.016	0.219	0.014	0.880	0.003	1

Summary of experiment set S-3:

Throughout Experiment Set S-3, Hybrid PSO-GA outperformed both GA and PSO in all configurations, maintaining the highest mean fitness and lowest variance. The harmonic mean rank across the experiments as shown in Table 15 further emphasizes its consistent superiority.

Table 15. Rank Summary for experiment Set S-3.

Algorithm	A Rank	B Rank	C Rank	Harmonic Mean Rank
GA	3	3	3	3.00
PSO	2	2	2	2.00
Hybrid PSO-GA	1	1	1	1.00

6. Conclusion

This paper explores the use of metaheuristic algorithms for constrained decision-making, focusing on student performance optimization. Six key areas are identified for student workload optimization: Cognitive Capacity, Time Availability, Fatigue & Stress Levels and Task Complexity & Adaptability. These adaptable areas provide a flexible framework for optimization across various contexts.

A Hybrid PSO-GA (Particle Swarm Optimization - Genetic Algorithm) approach was employed to balance effort allocation among these areas. Multiple metaheuristic algorithms were tested and compared, with final results presented as the harmonic mean of multiple simulation runs to ensure reliability.

The statistical analysis in this study was conducted across three experimental sets (S-1, S-2, and S-3), each executed under three configurations with varying population sizes (25, 50, 100) and iteration counts (50, 100, 200). Each set compared the performance of Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and the proposed Hybrid PSO-GA. The evaluation metrics included mean fitness value, standard deviation, and algorithmic rank, while statistical significance was assessed using the Friedman test and Nemenyi posthoc test. In all experiments, the Hybrid PSO-GA consistently achieved the highest mean fitness and the lowest standard deviation, maintaining a harmonic mean rank of 1.0 throughout. In Experiment Set S-1, the hybrid algorithm attained a peak mean fitness of 1.273 with a standard deviation of 0.004. Similar patterns were observed in Sets S-2 and S-3, where the maximum fitness values reached 1.098 and 0.880, respectively. The Friedman test results indicated statistically significant differences in performance (p-value = 0.0000) across all configurations. The Nemenyi test further confirmed that the Hybrid PSO-GA significantly outperformed both GA and PSO. At the same time, the performance gap between GA and PSO remained statistically insignificant in most cases, except under maximum computational resources. These findings collectively demonstrated the hybrid algorithm’s robustness, scalability, and superior optimization performance across various student workload evaluation scenarios.

Future research should focus on empirical validation with diverse datasets, refining weight calibration, and comparing traditional assessment models. Enhancing computational efficiency through selective optimization and parameter tuning could improve scalability. Additionally, integrating machine learning for automated calibration and analyzing longitudinal data may further refine dynamic constraints. Cross-domain applications in employee assessment and personalized healthcare could extend this framework’s utility.

Ethical considerations

This research was conducted in accordance with the highest standards of academic integrity and ethical responsibility. The study utilized only anonymized secondary data, with no direct involvement of human participants. As such, issues of informed consent or potential risk to individuals do not arise, and formal ethical approval was not required.

All datasets were handled responsibly, ensuring confidentiality, fairness, and compliance with institutional and international research ethics guidelines. The reporting of this study maintains transparency, accuracy, and integrity, in line with best practices for responsible research conduct.

The authors declare adherence to ethical guidelines for responsible research conduct, including avoidance of plagiarism, proper attribution of intellectual property, and accurate reporting of results.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article and have also been uploaded to the Figshare data repository.

• Student Cognitive Workload Dataset:
This dataset contains the cognitive load capacities of students and is available at DOI: https://doi.org/10.6084/m9.figshare.30172204.v2 (PhaniKumar et al., 2025a).
• Students’ Maximum Cognitive Capacity Dataset:
This dataset contains the maximum cognitive capacities of three students, which were generated randomly for this study, and is available at DOI: https://doi.org/10.6084/m9.figshare.30172207.v2 (PhaniKumar et al., 2025b).

Data are available under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

References

Abdel-Basset M, Mohamed R, Sallam KM, et al.: Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. Mathematics. 2022; 10(19): 3466. Publisher Full Text
Batool S, Rashid J, Nisar MW, et al.: Educational data mining to predict students’ academic performance: A survey study. Educ. Inf. Technol. 2023; 28(1): 905–971. Publisher Full Text
Boulebnane S, Montanaro A: Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization Algorithm. PRX Quantum. 2024; 5(3): 030348. Publisher Full Text
Das RP, Paul A, Jena JJ, et al.: Hybrid Binary SGO-GA for solving MAX-SAT problem. Procedia Computer Science. 2025; 252: 944–953. Publisher Full Text
Dorigo M, Maniezzo V, Colorni A: Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B Cybern. 1996; 26(1): 29–41. PubMed Abstract | Publisher Full Text
Gomede E, Gaffo F, Briganó G, et al.: Application of Computational Intelligence to Improve Education in Smart Cities. Sensors. 2018; 18(1): 267. PubMed Abstract | Publisher Full Text | Free Full Text
Hamsa H, Indiradevi S, Kizhakkethottam JJ: Student Academic Performance Prediction Model Using Decision Tree and Fuzzy Genetic Algorithm. Procedia Technology. 2016; 25: 326–332. Publisher Full Text
He Y, Wang J, Liu X, et al.: Modeling and solving of knapsack problem with setup based on evolutionary algorithm. Math. Comput. Simul. 2024; 219: 378–403. Publisher Full Text
Huiberts S, Lee YT, Zhang X: Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method (Version 2). arXiv. 2022. Publisher Full Text
Ifenthaler D, Mah D-K, Yau JY-K: Utilising Learning Analytics for Study Success: Reflections on Current Empirical Findings.Ifenthaler D, Mah D-K, Yau JY-K, editors. Utilizing Learning Analytics to Support Study Success. Springer International Publishing; 2019; pp. 27–36. Publisher Full Text
Ifenthaler D, Yau JY-K: Reflections on Different Learning Analytics Indicators for Supporting Study Success. International Journal of Learning Analytics and Artificial Intelligence for Education (iJAI). 2020a; 2(2): 4. Publisher Full Text
Ifenthaler D, Yau JY-K: Utilising learning analytics to support study success in higher education: A systematic review. Educ. Technol. Res. Dev. 2020b; 68(4): 1961–1990. Publisher Full Text
Ikegwu AC, Nweke HF, Anikwe CV: Recent trends in computational intelligence for educational big data analysis. Iran J. Comput. Sci. 2024; 7(1): 103–129. Publisher Full Text
Jin X: Predicting academic success: Machine learning analysis of student, parental, and school efforts. Asia Pac. Educ. Rev. 2023. Publisher Full Text
Joppen R, Enzberg SV, Gundlach J, et al.: Key performance indicators in the production of the future. Procedia CIRP. 2019; 81: 759–764. Publisher Full Text
Karma Y, Kezang S, Pema C, et al.: Well-being and academic workload: Perceptions of Science and technology students. Educ. Res. Rev. 2021; 16(11): 418–427. Publisher Full Text
Karp RM: Reducibility among Combinatorial Problems.Miller RE, Thatcher JW, Bohlinger JD, editors. Complexity of Computer Computations. Springer US; 1972; pp. 85–103. Publisher Full Text
Kennedy J, Eberhart R: Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks. 1995; 4: 1942–1948. Publisher Full Text
Mayer J: Stochastic Linear Programming Algorithms: A Comparison Based on a Model Management System. Routledge; 1st ed. 2022. Publisher Full Text
Michael A, Amenawon E: OPTIMIZATION OF STUDENT’S ACADEMIC PERFORMANCE IN A WORLD-CLASS UNIVERSITY USING OPERATIONAL RESEARCH TECHNIQUE. International Journal of Mathematics and Computer Applications Research. 2015; 5(1): 43–50.
Miranda Lakshmi T, Martin A, Prasanna Venkatesan V: An Analysis of Students Performance Using Genetic Algorithm. Journal of Computer Sciences and Applications. 2013; 1(4): 75–79. Publisher Full Text
Niu W, Cheng L, Duan D, et al.: Impact of Perceived Supportive Learning Environment on Mathematical Achievement: The Mediating Roles of Autonomous Self-Regulation and Creative Thinking. Front. Psychol. 2022; 12: 781594. PubMed Abstract | Publisher Full Text | Free Full Text
PhaniKumar PPNG, Jena JJ, Srinadhraju S, et al.: Cognitive_workload.csv (p. 68 Bytes). [Dataset]. figshare. 2025a. Publisher Full Text
PhaniKumar PPNG, Jena JJ, Srinadhraju S, et al.: Student_info.csv (p. 89 Bytes). [Dataset]. figshare. 2025b. Publisher Full Text
Predictive Analytics in Business Analytics: Decision Tree. Advances in Decision Sciences. 2022; 26(1): 1–30. Publisher Full Text
Rao RV, Savsani VJ, Vakharia DP: Teaching–Learning-Based Optimization: An optimization method for continuous non-linear large scale problems. Inf. Sci. 2012; 183(1): 1–15. Publisher Full Text
Schonlau M, Zou RY: The random forest algorithm for statistical learning. The Stata Journal: Promoting Communications on Statistics and Stata. 2020; 20(1): 3–29. Publisher Full Text
Shaik AB, Srinivasan S: A Brief Survey on Random Forest Ensembles in Classification Model. Bhattacharyya S, Hassanien AE, Gupta D, et al., editors. International Conference on Innovative Computing and Communications. Singapore: Springer; 2019; Vol. 56. : pp. 253–260. Publisher Full Text
Sharma MK: Modified genetic algorithm with novel crossover and mutation operator for travelling salesman problem. Sigma Journal of Engineering and Natural Sciences – Sigma Mühendislik ve Fen Bilimleri Dergisi. 2024; 1876–1883. Publisher Full Text
Shu X, Ye Y: Knowledge Discovery: Methods from data mining and machine learning. Soc. Sci. Res. 2023; 110: 102817. Publisher Full Text
Tang KS, Man KF, Kwong S, et al.: Genetic algorithms and their applications. IEEE Signal Process. Mag. 1996; 13(6): 22–37. Publisher Full Text
Taylan O, Rizwan A, Parsaei H: Optimization of engineering student learning and assessment by cognitive methods. Engineering Education Letters. 2017; 2017(1). Publisher Full Text
Timotheou S, Miliou O, Dimitriadis Y, et al.: Impacts of digital technologies on education and factors influencing schools’ digital capacity and transformation: A literature review. Educ. Inf. Technol. 2023; 28(6): 6695–6726. PubMed Abstract | Publisher Full Text | Free Full Text
Yağcı M: Educational data mining: Prediction of students’ academic performance using machine learning algorithms. Smart Learning Environments. 2022; 9(1): 11. Publisher Full Text

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Author details Author details

¹ School of Computer Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India
² Department of Computer Science & Engineering, Raghu Engineering College, Visakhapatnam, Andhra Pradesh, India

Pitchika P N G PhaniKumar
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Software, Visualization, Writing – Original Draft Preparation

Junali Jasmine Jena
Roles: Conceptualization, Funding Acquisition, Methodology, Project Administration, Resources, Supervision, Validation, Writing – Review & Editing

Sagiraju Srinadhraju
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Validation, Visualization, Writing – Original Draft Preparation

Sudhirvarma Sagiraju
Roles: Conceptualization, Formal Analysis, Methodology, Resources, Validation, Writing – Original Draft Preparation

Competing interests

No competing interests were disclosed.

Grant information

The authors acknowledge that this publication received partial funding support from Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar, India.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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[1] Abdel-Basset M, Mohamed R, Sallam KM, et al.: Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. Mathematics. 2022; 10(19): 3466. Publisher Full Text

[2] Batool S, Rashid J, Nisar MW, et al.: Educational data mining to predict students’ academic performance: A survey study. Educ. Inf. Technol. 2023; 28(1): 905–971. Publisher Full Text

[3] Boulebnane S, Montanaro A: Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization Algorithm. PRX Quantum. 2024; 5(3): 030348. Publisher Full Text

[4] Das RP, Paul A, Jena JJ, et al.: Hybrid Binary SGO-GA for solving MAX-SAT problem. Procedia Computer Science. 2025; 252: 944–953. Publisher Full Text

[5] Dorigo M, Maniezzo V, Colorni A: Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B Cybern. 1996; 26(1): 29–41. PubMed Abstract | Publisher Full Text

[6] Gomede E, Gaffo F, Briganó G, et al.: Application of Computational Intelligence to Improve Education in Smart Cities. Sensors. 2018; 18(1): 267. PubMed Abstract | Publisher Full Text | Free Full Text

[7] Hamsa H, Indiradevi S, Kizhakkethottam JJ: Student Academic Performance Prediction Model Using Decision Tree and Fuzzy Genetic Algorithm. Procedia Technology. 2016; 25: 326–332. Publisher Full Text

[8] He Y, Wang J, Liu X, et al.: Modeling and solving of knapsack problem with setup based on evolutionary algorithm. Math. Comput. Simul. 2024; 219: 378–403. Publisher Full Text

[9] Huiberts S, Lee YT, Zhang X: Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method (Version 2). arXiv. 2022. Publisher Full Text

[10] Ifenthaler D, Mah D-K, Yau JY-K: Utilising Learning Analytics for Study Success: Reflections on Current Empirical Findings.Ifenthaler D, Mah D-K, Yau JY-K, editors. Utilizing Learning Analytics to Support Study Success. Springer International Publishing; 2019; pp. 27–36. Publisher Full Text

[11] Ifenthaler D, Yau JY-K: Reflections on Different Learning Analytics Indicators for Supporting Study Success. International Journal of Learning Analytics and Artificial Intelligence for Education (iJAI). 2020a; 2(2): 4. Publisher Full Text

[12] Ifenthaler D, Yau JY-K: Utilising learning analytics to support study success in higher education: A systematic review. Educ. Technol. Res. Dev. 2020b; 68(4): 1961–1990. Publisher Full Text

[13] Ikegwu AC, Nweke HF, Anikwe CV: Recent trends in computational intelligence for educational big data analysis. Iran J. Comput. Sci. 2024; 7(1): 103–129. Publisher Full Text

[14] Jin X: Predicting academic success: Machine learning analysis of student, parental, and school efforts. Asia Pac. Educ. Rev. 2023. Publisher Full Text

[15] Joppen R, Enzberg SV, Gundlach J, et al.: Key performance indicators in the production of the future. Procedia CIRP. 2019; 81: 759–764. Publisher Full Text

[16] Karma Y, Kezang S, Pema C, et al.: Well-being and academic workload: Perceptions of Science and technology students. Educ. Res. Rev. 2021; 16(11): 418–427. Publisher Full Text

[17] Karp RM: Reducibility among Combinatorial Problems.Miller RE, Thatcher JW, Bohlinger JD, editors. Complexity of Computer Computations. Springer US; 1972; pp. 85–103. Publisher Full Text

[18] Kennedy J, Eberhart R: Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks. 1995; 4: 1942–1948. Publisher Full Text

[19] Mayer J: Stochastic Linear Programming Algorithms: A Comparison Based on a Model Management System. Routledge; 1st ed. 2022. Publisher Full Text

[20] Michael A, Amenawon E: OPTIMIZATION OF STUDENT’S ACADEMIC PERFORMANCE IN A WORLD-CLASS UNIVERSITY USING OPERATIONAL RESEARCH TECHNIQUE. International Journal of Mathematics and Computer Applications Research. 2015; 5(1): 43–50.

[21] Miranda Lakshmi T, Martin A, Prasanna Venkatesan V: An Analysis of Students Performance Using Genetic Algorithm. Journal of Computer Sciences and Applications. 2013; 1(4): 75–79. Publisher Full Text

[22] Niu W, Cheng L, Duan D, et al.: Impact of Perceived Supportive Learning Environment on Mathematical Achievement: The Mediating Roles of Autonomous Self-Regulation and Creative Thinking. Front. Psychol. 2022; 12: 781594. PubMed Abstract | Publisher Full Text | Free Full Text

[23] PhaniKumar PPNG, Jena JJ, Srinadhraju S, et al.: Cognitive_workload.csv (p. 68 Bytes). [Dataset]. figshare. 2025a. Publisher Full Text

[24] PhaniKumar PPNG, Jena JJ, Srinadhraju S, et al.: Student_info.csv (p. 89 Bytes). [Dataset]. figshare. 2025b. Publisher Full Text

[25] Predictive Analytics in Business Analytics: Decision Tree. Advances in Decision Sciences. 2022; 26(1): 1–30. Publisher Full Text

[26] Rao RV, Savsani VJ, Vakharia DP: Teaching–Learning-Based Optimization: An optimization method for continuous non-linear large scale problems. Inf. Sci. 2012; 183(1): 1–15. Publisher Full Text

[27] Schonlau M, Zou RY: The random forest algorithm for statistical learning. The Stata Journal: Promoting Communications on Statistics and Stata. 2020; 20(1): 3–29. Publisher Full Text

[28] Shaik AB, Srinivasan S: A Brief Survey on Random Forest Ensembles in Classification Model. Bhattacharyya S, Hassanien AE, Gupta D, et al., editors. International Conference on Innovative Computing and Communications. Singapore: Springer; 2019; Vol. 56. : pp. 253–260. Publisher Full Text

[29] Sharma MK: Modified genetic algorithm with novel crossover and mutation operator for travelling salesman problem. Sigma Journal of Engineering and Natural Sciences – Sigma Mühendislik ve Fen Bilimleri Dergisi. 2024; 1876–1883. Publisher Full Text

[30] Shu X, Ye Y: Knowledge Discovery: Methods from data mining and machine learning. Soc. Sci. Res. 2023; 110: 102817. Publisher Full Text

[31] Tang KS, Man KF, Kwong S, et al.: Genetic algorithms and their applications. IEEE Signal Process. Mag. 1996; 13(6): 22–37. Publisher Full Text

[32] Taylan O, Rizwan A, Parsaei H: Optimization of engineering student learning and assessment by cognitive methods. Engineering Education Letters. 2017; 2017(1). Publisher Full Text

[33] Timotheou S, Miliou O, Dimitriadis Y, et al.: Impacts of digital technologies on education and factors influencing schools’ digital capacity and transformation: A literature review. Educ. Inf. Technol. 2023; 28(6): 6695–6726. PubMed Abstract | Publisher Full Text | Free Full Text

[34] Yağcı M: Educational data mining: Prediction of students’ academic performance using machine learning algorithms. Smart Learning Environments. 2022; 9(1): 11. Publisher Full Text

Hybrid PSO-GA Metaheuristic Optimization for Comprehensive Student Performance Enhancement

Abstract

Keywords

1. Introduction

2. Literature review

3. Problem definition

(1)

(2)

4. Materials and methods

4.1 Datasets

(3)

Table 1. Mapped academic task categories with associated cognitive domains, source reference, and computed workload values.

Table 2. Cognitive workload values (ci) for each category (C1 to C5).

(4)

Table 3. Limit values of student S1, S2 and S3 generated at random.

4.2 Hybrid PSO-GA approach

Figure 1. Structure of a particle in Hybrid PSO-GA.

(5)

Figure 2. Flowchart displaying the functionality of Hybrid PSO-GA.

Algorithm 1. Hybrid PSO-GA Optimization (Condensed).

5. Results and discussion

5.1 Experiment set S-1

Figure 3. Experiment S1-A Nemenyi test matrix.

Figure 4. Experiment S1-A convergence graph.

Table 4. Fitness values for experiment A (S-1).

Figure 5. Experiment S1-B Nemenyi test matrix.

Figure 6. Experiment S1-B convergence graph.

Table 5. Fitness values for experiment B (S-1).

Figure 7. Experiment S1-C Nemenyi test matrix.

Figure 8. Experiment S1-C convergence graph.

Table 6. Fitness values for experiment C (S-1).

Table 7. Rank summary for experiment set S-1.

5.2 Experiment set S-2

Figure 9. Experiment S2-A Nemenyi test matrix.

Figure 10. Experiment S2-A convergence graph.

Table 8. Fitness values for experiment A (S-2).

Figure 11. Experiment S2-B Nemenyi test matrix.

Figure 12. Experiment S2-B convergence graph.

Table 9. Fitness values for experiment B (S-2).

Figure 13. Experiment S2-C Nemenyi test matrix.

Figure 14. Experiment S2-C convergence graph.

Table 10. Fitness values for experiment C (S-2).

Table 11. Rank summary for experiment set S-2.

5.3 Experiment set S-3

Figure 15. Experiment S3-A Nemenyi test matrix.

Figure 16. Experiment S3-A convergence graph.

Table 12. Fitness values for experiment A (S-3).

Figure 17. Experiment S3-B Nemenyi test matrix.

Figure 18. Experiment S3-B Convergence Graph.

Table 13. Fitness values for experiment B (S-3).

Figure 19. Experiment S3-C Nemenyi test matrix.

Figure 20. Experiment S3-C convergence graph.

Table 14. Fitness values for experiment C (S-3).

Table 15. Rank Summary for experiment Set S-3.

6. Conclusion

Ethical considerations

Data availability

References

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Table 2. Cognitive workload values (c_i) for each category (C₁ to C₅).