Introduction

Achieving the optimal state is one of the most fundamental issues in the universe. Due to the limited resources accessible to humans, optimization has become a vital matter and its application range is increasing day by day. Mathematics, computer science, civil engineering, industries, mechanics, and economics discuss only a part of these important applications (Kaveh in Advances in meta-heuristic algorithms for optimal design of structures, 2021). In this type of critical issues, the goal is to obtain the best decision state among several different states. Today, meta-heuristic algorithms can be considered one of the most important methods for solving optimization problems. In order to optimize structural skeletons that include non-linear and non-convex modes and are often associated with several local optima, meta-heuristic algorithms face problems that cause stagnation in the optimization process. One of the most important of them is premature convergence and falling into the trap of local optima.