Most real-world optimization problems often come with multiple global optima or local optima. Therefore, increasing niching metaheuristic algorithms, which devote to finding multiple optima in a single run, are developed to solve these multimodal optimization problems. However, there are two difficulties urgently to be solved for most existing niching metaheuristic algorithms: how to set the niching parameter valules for different optimization problems, and how to jump out of the local optima efficiently. These two difficulties limit their practicality largely. Based on Whale Swarm Algorithm (WSA) we proposed previously, this paper presents a new multimodal optimizer named WSA with Iterative Counter (WSA-IC) to address these two difficulties. On the one hand, WSA-IC improves the iteration rule of the original WSA for multimodal optimization, which removes the need of specifying different values of attenuation coefficient for different problems to form multiple subpopulations, without introducing any niching parameter. On the other hand, WSA-IC enables the identification of extreme points during the iterations relying on two new parameters (i.e., stability threshold T s and fitness threshold T f ), to jump out of the located extreme points. Moreover, the convergence of WSA-IC is proved. Finally, the proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and on five additional high-dimensional multimodal functions. The experimental results demonstrate that WSA-IC statistically outperforms other niching metaheuristic algorithms on most test functions.Keywords Whale swarm algorithm · multimodal optimization · metaheuristic algorithm · niching · extreme point 1 IntroductionMost of the real-world optimization problems are multimodal [1-8], i.e., their objective functions have multiple global optima or local optima. If applying traditional numerical
Hydraulic actuator becomes an increasingly concerned driver for human-like robots. However, its dynamic performance under the control should be still further improved because hydraulic system is a typical nonlinearity system. Interval type-2 fuzzy logic controller is an advanced control method featured with high performance to deal with uncertain and nonlinear dynamics, so designing an interval type-2 fuzzy logic controller for the control of hydraulic is a feasible method. In this article, an improved drone squadron optimization-based approach is proposed to optimize interval type-2 fuzzy logic controller parameters. To verify the feasibility and priority of improved drone squadron optimization, a comparison on three different typical plants including proportional-derivative (PD) system, proportional-integral (PI) system, and PI nonlinear system between improved drone squadron optimization and other meta-heuristic algorithms is carried out. Simulation results demonstrate that improved drone squadron optimization not only gets an appropriate interval type-2 fuzzy logic controller for system control but also outperforms other popular algorithms in accuracy of performance.
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