Nelder-Mead Enhanced Gazelle Optimizer for Solving Complex Optimization Problems

This paper presents the improved gazelle optimization algorithm, which is a new approach in the field of metaheuristic optimization algorithms inspired by nature. By hybridizing the classical gazelle optimization algorithm with the Nelder-Mead simplex method, the improved gazelle optimization algorithm was developed. The proposed IGOA algorithm aims to combine GOA's global search capability with NM's local healing power to provide a more balanced and effective optimization of optimization problems. The performance of the algorithm was evaluated by 30 independent runs on the CEC2017 benchmark functions. The statistical results obtained from the analyses of the mean, standard deviation, best and worst values and Wilcoxon signed ranks test show that IGOA exhibits a superior or competitive performance compared to other current optimization algorithms. Furthermore, the boxplot and convergence curves revealed that IGOA exhibited stable convergence behavior and had a low tendency to get stuck at local optimums. Big-O analysis, on the other hand, confirmed that the algorithm can scale efficiently even in high-dimensional problems. The results prove that the IGOA algorithm is a highly competitive, effective and generalizable tool in solving complex optimization problems.