Metaheuristic algorithms (MAs) are powerful tools for solving complex optimization problems across diverse domains. This comprehensive study analyzes 162 MAs through a unified multi-criteria taxonomy classifying algorithms by control parameters (parameter-free, low-parameter, high-parameter), inspiration sources (biological, physical, human-based), search space scope, and exploration–exploitation balance—alongside bibliometric assessment of publications from 2000 to 2024 (including articles, reviews, books, and conference papers). We evaluate the time complexity of 24 highly cited MAs and their real-world applications in engineering, healthcare, and energy systems. Results demonstrate that different MAs exhibit algorithmic simplicity, often requiring only a small number of control parameters, and are capable of efficient global search. Additionally, several algorithms demonstrate strong adaptability for hybridization with other techniques. However, certain methods are prone to premature convergence, primarily due to unbalanced exploration and exploitation dynamics. The proposed work also critically examines metaphor-inspired algorithms, whose contributions are critically evaluated in light of their conceptual complexity. The rise of such methods has led to redundancy and fragmentation in the field, as many reframe familiar optimization principles using superficial metaphors rather than advancing core algorithmic mechanisms. Bibliometric analysis reveals accelerated growth in MA research (64% journal articles, 31% conference papers, 3% from reviews, 1% from conference reviews, and 1% from book chapters). Similarly, in terms of classification, human-inspired methods constitute the largest category (45%), followed by evaluation-inspired (33%), swarm-inspired (14%), and game-inspired and physics-based algorithms (4%). This work consolidates two decades of advancements, identifies critical performance limitations, and provides practical guidelines for algorithm selection and hybridization to enhance optimization efficiency.

Engineering design optimization problems present significant challenges due to the complexity of objective functions, which often involve both continuous and discrete design variables, along with multiple constraints. GWO and PSO are well-known heuristic algorithms with efficient search ability and reasonable execution time. They are often used to solve complex optimization problems, but there are still problems such as premature convergence and limited global search efficiency. To overcome these limitations and enhance solution quality, this study proposes a novel Hybrid Grey Wolf-Particle Swarm Optimization (HGWPSO) algorithm. HGWPSO integrates the exploration ability of GWO with the rapid convergence and exploitation efficiency of PSO. The algorithm’s performance is first validated using CEC_2022 benchmark functions and then applied to eight complex engineering design problems, including pressure vessel design, compression spring design, three-bar truss design, gear train design, cantilever beam design, welded beam design, transmission line parameter estimation, and reactive power planning problem. The improvement in the average best optimal value varies across different cases, demonstrating the effectiveness of the proposed method. In Case 1, the improvement is 71.61%, while in Cases 2 and 4 obtained a 99% improvement. Case 3 shows an enhancement of 53.46%, and Case 5 reaches 71.92%, whereas Case 6 also obtained 99%. In Case 7, the improvement depends on the bundle configuration, with two-bundle conductors showing a 76.91% increase, three-bundle conductors achieving 43.94%, and four-bundle conductors reaching 46.57%. Finally, in Case 8, the improvement is 1.02%. The obtained results demonstrate that HGWPSO achieves better performance than other methods in terms of convergence rate, cost function minimization, and constraint handling. This study highlights the effectiveness of HGWPSO as a powerful tool for solving complex engineering design problems.

Nowadays, cluster analyses are widely used in mental health research to categorize student stress levels. However, conventional clustering methods experience challenges with large datasets and complex issues, such as converging to local optima and sensitivity to initial random states. To address these limitations, this research work introduces an Improved Grey Wolf Clustering Algorithm (iGWCA). This improved approach aims to adjust the convergence rate and mitigate the risk of being trapped in local optima. The iGWCA algorithm provides a balanced technique for exploration and exploitation phases, alongside a local search mechanism around the optimal solution. To assess its efficiency, the proposed algorithm is verified on two different datasets. The dataset-I comprises 1100 individuals obtained from the Kaggle database, while dataset-II is based on 824 individuals obtained from the Mendeley database. The results demonstrate the competence of iGWCA in classifying student stress levels. The algorithm outperforms other methods in terms of lower intra-cluster distances, obtaining a reduction rate of 1.48% compared to Grey Wolf Optimization (GWO), 8.69% compared to Mayfly Optimization (MOA), 8.45% compared to the Firefly Algorithm (FFO), 2.45% Particle Swarm Optimization (PSO), 3.65%, Hybrid Sine Cosine with Cuckoo search (HSCCS), 8.20%, Hybrid Firefly and Genetic Algorithm (FAGA) and 8.68% Gravitational Search Algorithm (GSA). This demonstrates the effectiveness of the proposed algorithm in minimizing intra-cluster distances, making it a better choice for student stress classification. This research contributes to the advancement of understanding and managing student well-being within academic communities by providing a robust tool for stress level classification.

Transmission line (TL) parameters, particularly capacitance, are important for ensuring the efficient and reliable operation of power systems. As power networks become increasingly complex, accurately determining TL parameters faces certain challenges, particularly capacitance, which involves overcoming computational challenges due to bundling configurations. The interconnected nature of modern TL and the use of advanced technologies further add to the complexity. Effective estimation requires advanced measurement techniques and sophisticated computational tools. Recently, optimization techniques have become widely used for TL parameter calculations. However, traditional methods struggle with challenges like limited exploration and slow convergence. To address these issues, this research introduces a hybrid algorithm called HGWPSO, which combines the Grey Wolf Optimizer (GWO) with Particle Swarm Optimization (PSO). The main objective is to enhance the exploitation ability of GWO with the exploration capability of PSO, maximizing the strengths of both variants. Initially, to verify the efficiency of HGWPSO, CEC_19 benchmark functions are utilized to evaluate its performance. Secondly, the main focus of this study is to calculate TL parameters such as capacitance considering two, three, and four-bundle conductors using the HGWPSO algorithm and comparing its performance with other optimization techniques. According to the obtained result, the average percentage reduction for HGWPSO is 0.15 % in test case 1, 4.85 % in test case 2, and 2.84 % in test case 3, compared to others. It shows that the HGWPSO has better performance than other methods regarding convergence speed, and ability to locate the global optimum. Finally, experimental analysis confirms the superiority of the HGWPSO in accurately estimating TL capacitance for different bundle conductor configurations, obtaining lower average values, and effectively addressing the characteristic complexities in the TL parameter.