CPSOA: A hybrid metaheuristic for solving optimization problems – a case study on systems of nonlinear equations

Abstract

. Many scientific and engineering models require solving systems of nonlinear equations (SNLEs), and significant advances in these fields depend on solving such systems accurately and efficiently. Our research proposes a hybrid intelligent algorithm to tackle SNLEs. The chaotic particle swarm optimization algorithm (CPSOA) combines the particle swarm optimization algorithm (PSOA) with the chaotic search technique (CST). Its goal is to improve performance, increase solution diversity, accelerate convergence, avoid premature convergence to local optima, and optimize the search process. Reformulating SNLEs as an optimization problem is the initial step. Within the CPSOA framework, CST updates infeasible solutions while PSOA updates feasible ones. Since infeasible solutions are often located near the optimal solution, CPSOA optimizes them rather than dismissing them, thereby improving search efficiency and achieving an effective exploitation-exploration balance. Fifty benchmark functions were used to assess convergence speed and solution quality for the proposed algorithm. Four benchmark systems of nonlinear equations with different dimensions were also used to evaluate the accuracy, robustness, and stability of CPSOA. The study validated performance using the non-parametric Friedman and Wilcoxon tests. Experimental results show that CPSOA outperforms existing techniques in solving a wide range of optimization problems and systems of nonlinear equations.