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Most real-world optimization problems often come with multiple global optimaor local optima. Therefore, increasing niching metaheuristic algorithms, whichdevote to finding multiple optima in a single run, are developed to solve thesemultimodal optimization problems. However, there are two difficulties urgentlyto be solved for most existing niching metaheuristic algorithms: how to set theoptimal values of niching parameters for different optimization problems, andhow to jump out of the local optima efficiently. These two difficulties limitedtheir practicality largely. Based on Whale Swarm Algorithm (WSA) we proposedpreviously, this paper presents a new multimodal optimizer named WSA withIterative Counter (WSA-IC) to address these two difficulties. In the one hand,WSA-IC improves the iteration rule of the original WSA for multimodaloptimization, which removes the need of specifying different values ofattenuation coefficient for different problems to form multiple subpopulations,without introducing any niching parameter. In the other hand, WSA-IC enablesthe identification of extreme point during iterations relying on two newparameters (i.e., stability threshold Ts and fitness threshold Tf), to jump outof the located extreme point. Moreover, the convergence of WSA-IC is proved.Finally, the proposed WSA-IC is compared with several niching metaheuristicalgorithms on CEC2015 niching benchmark test functions and five additionalclassical multimodal functions with high dimensions. The experimental resultsdemonstrate that WSA-IC statistically outperforms other niching metaheuristicalgorithms on most test functions.

Whale swarm algorithm with the mechanism of identifying and escaping from extreme points for multimodal function optimization