Spherical search algorithm with memory-guided population stage-wise control for bound-constrained global optimization problems

The recently proposed Spherical Search (SS) algorithm replaces the traditional square search pattern with a spherical boundary to provide position-diverse solutions. The algorithm balances its exploration and exploitation performance by utilizing 2 exploration and exploitation sub-populations of equal size. SS has been proven to be highly competitive. However, we observed that when it is used to solve a variety of problems as well as during different searching stages, the fixed sub-population size limits its adaptability and flexibility for achieving continuous exploitation–exploration balance. The balance potential of two operators with distinct characteristics is underdeveloped. As a result, SS and its advanced variants are prone to still easily falling into local optima and lacks certain performance advantages over peer algorithms. In this paper, we further develop SS and propose a memory-guided population stage-wise control strategy based SS, called SSM. By our proposed memory-guided stage-wise evaluation mechanism, SS evaluates the exploitation–exploration balance extent in real time and thus adaptively optimizes and predicts better resource allocation ratio values between its 2 sub-populations and thus achieves significant performance advantages over peer algorithms. The experiments are conducted on 120 benchmark functions and 22 real-world problems, and the results show that SSM significantly outperforms other 13 state-of-the-art evolutionary algorithms. Additionally, we conduct analyses based on method characteristics, convergence process, solution quality robustness testing, population diversity, exploitation and exploration balance, and computational complexity.