A multipopulation cooperative coevolutionary whale optimization algorithm with a two-stage orthogonal learning mechanism

Abstract

This paper designed a multipopulation cooperative coevolutionary framework with a two-stage orthogonal learning (OL) mechanism for the whale optimization algorithm (MCCWOA) to improve the performance of the whale optimization algorithm (WOA). In the framework, a prediction model of the neighborhood structure is established by discovering the guidance information of the following iteration process in the objective space at the first-stage OL. In the second-stage OL, an auxiliary vector pool with various features in the decision space is introduced to guide the candidates falling in the stagnant status to conduct more valuable exploration. According to the domain knowledge of the candidates, the population is divided into the elite population, the intermediate population, and the inferior population. The information of the subpopulations has interacted with the corresponding historical populations in the evolution processes to enhance the ability of cooperative coevolution among individuals. A standard set of comprehensive benchmark cases and three engineering cases are utilized to verify the advantages of the proposed algorithm. The results of the statistical analysis, diversity analysis, and convergence analysis testified that the MCCWOA outperforms the 15 state-of-the-art algorithms regarding efficiency and significance.