Studying complex nonlinear systems of equations by modified beluga whale optimization algorithm with analysis

This work aims to solve systems of nonlinear equations (SNLEs) by one of the swarm-based metaheuristic algorithms, beluga whale optimization algorithm (BWOA). BWOA has a slow rate of convergence and a propensity to become trapped in local optima. This paper suggests an amended BWOA (ABWOA), to enhance the BWOA's performance. ABWOA is a modification for the BWOA using a novel balance factor and a non-linear adaptive parameter. The benefits of the ABWOA are balance between exploration and exploitation, increase the probability of whale falling which helps to avoid falling into the local optimum, and improve the algorithm's local exploitation efficiency. To assess ABWOA's performance, computational experiments are conducted using 39 benchmark functions and seven benchmark systems of nonlinear equations with different dimensions. The results of the suggested algorithm are compared with those of many algorithms including the original BWOA to highlight the importance of the modifications made to ABWOA. To demonstrate the significance of the changes made in ABWOA, the results of the recommended algorithm are contrasted with those of the original BWOA; where ABWOA's average improvement rate was roughly 52.4, demonstrating that it is very successful at resolving SNLEs. Statistical analysis using Wilcoxon test between ABWOA and the other comparison methods reveals that and that the positive ranks (P-R) are significantly better than the negative ranks (N-R) in all benchmark problems and nonlinear equation systems. Compared with other algorithms, ABWOA has strong competitiveness and can better improve the efficiency of BWOA according to the experimental results and analysis.