A memetic animal migration optimizer for multimodal optimization

Abstract

Unimodal optimization algorithms can find only one global optimum solution, while multimodal ones have the ability to detect all/most existing local/global optima in the problem space. Many practical scientific and engineering optimization problems have multiple optima to be located. There are a considerable number of optimization approaches in the literature to address the unimodal problems. Although multimodal optimization methods have not been studied as much as the unimodal ones, they have attracted an enormous amount of attention recently. However, most of them suffer from a common niching parameter problem. The main difficulty faced by existing approaches is determining the proper niching radius. Determining the appropriate radius of the niche requires prior knowledge of the problem space. This paper proposes a novel multimodal optimization scheme that does not face the dilemma of having prior knowledge of the problem space as it does not require the niching parameter to be determined in advance. This scheme is the extended version of the unimodal animal migration optimization (AMO) algorithm that has the capability of taking advantage of finding multiple solutions. Like other multimodal optimization approaches, the proposed MAMO requires specific modifications to make it possible to locate multiple optima. The local neighborhood policy is modified to adapt the multimodal search by utilizing Coulomb's law. Also, Coulomb's law is also applied to decide the movement direction of the individuals. Hence, instead of moving an individual toward the two randomly chosen individuals, it moves toward the near and good enough two neighborhoods. Additionally, a further local search step is performed to improve the exploitation. To investigate the performance of the MAMO, the comparisons are conducted with five existing multi-modal optimization algorithms on nine benchmarks of the CEC 2013 competition. The experimental results reveal that the MAMO performs success in locating all or most of the local/global optima and outperforms other compared methods. Note that the source codes of the proposed MAMO algorithm are publicly available at www.taymaz.dev .