  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
optimal values of niching parameters for different optimization problems, and
how to jump out of the local optima efficiently. These two difficulties limited
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. In 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. In the other hand, WSA-IC enables
the identification of extreme point during iterations relying on two new
parameters (i.e., stability threshold Ts and fitness threshold Tf), to jump out
of the located extreme point. 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 five additional
classical multimodal functions with high dimensions. The experimental results
demonstrate that WSA-IC statistically outperforms other niching metaheuristic
algorithms on most test functions.
