Enhanced versions of the shuffled shepherd optimization algorithm for the optimal design of skeletal structures

This paper consists of two main parts. The first part is devoted to developing a parameter-free variant of the shuffled shepherd optimization algorithm (SSOA), named as a parameter-free shuffled shepherd optimization algorithm (PF-SSOA). Next, a set-theoretical multi-phase framework is proposed for the population-based metaheuristic algorithms. The proposed framework's main idea is based on dividing the population of candidate solutions into some number of well-arranged sub-populations. The number of sub-populations gradually changes during the optimization process. The framework is applied to the PF-SSOA, leading to a set-theoretical multiphase variant of PF-SSOA named STMP-SSOA. The STMP-SSOA stands for a set-theoretical multi-phase shuffled shepherd optimization algorithm. Some skeletal structures are optimized to verify the validity and efficiency of the proposed algorithms. The optimization problems include two truss size optimization problems with multiple frequency constraints and two planar frame structures with strength and displacement constraints. The results indicate that the developed algorithms perform better than the standard version of the SSOA, especially in terms of robustness and convergence characteristics.