A novel transcendental metaphor metaheuristic algorithm based on power method.

This paper proposes a novel metaheuristic algorithm-the Power Method Algorithm (PMA), which is inspired by the power iteration method to solve complex optimization problems. PMA simulates the process of computing dominant eigenvalues and eigenvectors, incorporating strategies such as stochastic angle generation and adjustment factors, effectively addressing eigenvalue problems in large sparse matrices. The algorithm is rigorously evaluated on 49 benchmark functions from the CEC 2017 and CEC 2022 test suites. Quantitative analysis reveals that PMA surpasses nine state-of-the-art metaheuristic algorithms and performs better, with average Friedman rankings of 3, 2.71, and 2.69 for 30, 50, and 100 dimensions, respectively. Statistical tests including the Wilcoxon rank-sum and Friedman test further confirm the robustness and reliability. Additionally, PMA demonstrates exceptional performance in solving eight real-world engineering optimization problems, consistently delivering optimal solutions. Experimental results show that PMA achieves an effective balance between exploration and exploitation, effectively avoiding local optima while maintaining high convergence efficiency. Therefore, PMA demonstrates notable competitiveness and practical value in interdisciplinary complex optimization tasks.