A Comparative Study of Metaheuristic Optimization Algorithms on Distinct Benchmark Functions

Abstract

Metaheuristic optimization algorithms are widely applied to tackle optimization problems across various fields. Recently, these algorithms have gained prominence over traditional deterministic methods for solving complex optimization issues. However, no single technique is universally effective for all types of optimization challenges. As a result, researchers have focused on enhancing existing metaheuristic methods or creating new ones. Numerous nature-inspired meta-heuristic algorithms have emerged to address complex optimization problems. This study evaluates and compares the performance of four algorithms, Particle Swarm Optimization (PSO), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Salp Swarm Algorithm (SSA) on five benchmark functions, including both unimodal and multimodal types. Experimental results demonstrate that GWO consistently outperforms the other algorithms in terms of solution quality and convergence speed. GWO achieved the lowest average error across all five benchmark functions and demonstrated the fastest convergence overall, reaching near-optimal solutions in under 150 iterations for most cases and as few as 66 iterations on the simplest function. DE ranked second, while PSO and SSA trailed behind. Statistical analysis using the Wilcoxon signed-rank test confirmed that GWO's superiority is statistically significant (p < 0.05) when compared to all other algorithms, even after applying Holm-Bonferroni correction.