Metaheuristic search algorithms in frequency constrained truss problems: Four improved evolutionary algorithms, optimal solutions and stability analysis

Truss problems with frequency constraints (TPFCs) are among the most complex real-world engineering optimization problems in the literature due to the non-linearity of the objective and constraint functions and the geometric structure of the search spaces. These problems have many local solutions due to the irregular geometric structure of the search spaces. Therefore, it is a challenge for meta-heuristic search (MHS) algorithms to converge stably to the global optimum solution for TPFCs. To overcome this challenge, this paper presents four new algorithms with improved performance for the optimization of TPFCs. The methodology of the research and the contributions to the literature are as follows: (i) a TPFC benchmark suite consisting of five different problem types was presented, (ii) for each problem in the benchmark suite, 152 different MHS algorithms were tested and the ones with the best convergence performance were identified, (iii) the update mechanisms of these algorithms that perform competitively on TPFCs were redesigned using the Natural Survivor Method (NSM). Thus, four different MHS algorithms with improved performance were proposed for the optimization of TPFCs, (iv) the optimal solutions for TPFCs were presented, (v) the stability of the proposed algorithms for TPFCs was analyzed and the times and success rates of finding feasible solutions were presented. According to the results of the statistical analysis, the optimal and feasible solutions for the 10/37/52/72/200 bar truss problems were found by the NSM-MadDE, NSM-LSHADE-CnEpSin, NSM-LSHADE-SPACMA and NSM-BO algorithms introduced in this paper.