Chapter 9 - An enhanced whale optimization algorithm using the Nelder-Mead algorithm and logistic chaotic map

Abstract

Metaheuristic algorithms are nature-inspired approaches for global optimization. They provide near-optimal solutions in a reasonable amount of time, unlike gradient-based algorithms, which are computationally intractable and greedy. We introduce a novel hybrid metaheuristic optimizer for global optimization. We combine the Nelder-Mead and the whale optimization algorithms. First, we apply the Nelder-Mead algorithm to restrict the area of the search space, minimize the search effort, and avoid stagnating in local optimums. Then, we use the linear chaotic map to control the decrementation of the values of vector a→ in the basic whale optimization algorithm. We employ the CEC 2021 benchmark test suite to evaluate the performance of the proposed hybrid optimizer. In addition, we compare our work to the original whale optimization algorithm and the chaotic whale optimization algorithm. Finally, we use the Friedman and Wilcoxon statistical tests to analyze the comparative study. The proposed algorithm shows efficient performance by comparing the considered metaheuristic algorithms.