A Comprehensive Comparative Analysis of Metaheuristic Algorithms Rooted in Mathematical Principles

In recent years, there has been a burgeoning development of swarm intelligence-based metaheuristic algorithms, with those integrating mathematical principles and stochastic search strategies particularly capturing attention. These algorithms, through their unique mechanisms, effectively reconcile the contradiction between exploration and exploitation in traditional single/multi-population evolutionary algorithms, paving new avenues for individual optimization. To aid in future algorithm selection and application, this paper systematically evaluates the performance of eight recently developed math-inspired metaheuristic algorithms on the CEC 2022 benchmark suite, which encompasses complex problems of 20 dimensions. The robustness of the assessment results was ensured through the implementation of Wilcoxon rank-sum tests and Friedman rank tests. The experimental data reveal that, under 20 dimensions, the Geometric Mean Optimizer (GMO) algorithm demonstrated the most outstanding performance in addressing the 12 tests of CEC 2022, with the Gradient-Based Optimizer (GBO) and Exponential Distribution Optimizer (EDO) algorithms following closely, forming a competitive tier. While the Runge-Kutta Optimizer (RUN), PID-based Search Algorithm (PSA), Sine Cosine Optimizer (SCHO), Newton-Raphson-Based Optimizer (NRBO), and Arithmetic Optimization Algorithm (AOA) each have their distinctive features, they overall rank slightly lower, with their own applicable scenarios and limitations.