Performance Analysis of Grey Wolf Optimizer for Solving Nonlinear Systems with Complex Roots

Abstract

Nonlinear systems of equations consist of multiple equations that must be solved simultaneously, and analytical solutions are often difficult to obtain, particularly for complex cases. For this reason, numerical and metaheuristic approaches are frequently employed as practical alternatives. This study investigates the performance of the Grey Wolf Optimizer (GWO) in solving nonlinear systems involving both real and complex roots. The problem is reformulated as an optimization task by minimizing a modulus based objective function derived from the given system. The implementation is carried out in MATLAB using several test cases, and a parameter sensitivity analysis is conducted with respect to the number of search agents, search boundaries, and maximum iterations. To evaluate its performance, the results obtained using GWO are compared with those of the Particle Swarm Optimization (PSO) algorithm reported in previous studies. The findings indicate that GWO is able to produce stable solutions with objective function values close to zero across different cases. However, PSO tends to achieve higher accuracy and faster convergence in certain scenarios. Despite this, GWO demonstrates strong exploration capability, which contributes to its robustness and makes it a viable alternative for solving complex nonlinear systems.