Multi-Objective Stochastic Fractal Search: a powerful algorithm for solving complex multi-objective optimization problems

Stochastic Fractal Search (SFS) is a novel and powerful metaheuristic algorithm. This paper presents a Multi-Objective Stochastic Fractal Search (MOSFS) for the first time, to solve complex multi-objective optimization problems. The presented algorithm uses an external archive to collect efficient Pareto optimal solutions during the optimization process. Using dominance rules, leader selection and grid mechanisms, MOSFS precisely approximates the true Pareto optimal front. The MOSFS is implemented on nine multi-objective benchmark functions (CEC 2009) with multimodal, convex, discrete and non-convex optimal Pareto fronts. Performance of the proposed algorithm is compared to well-known algorithms. In addition, different performance measures are considered to evaluate the convergence and coverage abilities of the algorithms including Inverted Generational Distance, Maximum Spread and Spacing. Furthermore, statistical analyses are utilized to determine the superior algorithm. The results revealed that the MOSFS performs significantly better than other algorithms in both convergence and coverage and it is able to approximate true Pareto front precisely. In the end, MOSFS is implemented to solve a real-world engineering design problem called welded beam design problem and efficiency of the algorithm is compared to recently developed algorithms. The results of simulations and the Wilcoxon rank-sum test showed that the MOSFS is able to provide the most promising Pareto front for the problem considering various performance metrics at a 95% confidence level.