MOSRS: An engineering multi-objective optimization through Einsteinian concept

Abstract

Multi-objective optimization stands at the intersection of mathematics, engineering, and decision-making, and metaheuristics offer a promising avenue for tackling such challenges. The literature shows they are the best, and there is space for new algorithms to deliver Pareto Fronts (PFs) with more convergence and coverage at lower computational costs. This paper presents the Multi-objective Special Relativity Search (MOSRS) for the first time. It relies on principles inspired by the theory of special relativity physics, which iteratively refines solutions toward optimality and self-adapts its parameters using these laws. Unlike most algorithms in the literature today, the user sets only the number of iterations and particles (or population). To test the performance, MOSRS is applied to the most challenging test functions set (CEC 2009) and 21 real and constrained world problems, being compared with a total of eleven metaheuristics: NSGA-II, NSGA-III, MOEA/D, MOPSO, MOGWO, ARMOEA, TiGE2, CCMO, ToP, and AnD. Inverted Generational Distance, Spacing, Maximum Spread, and Hypervolume are used to identify the best algorithm. MOSRS was robust in finding the best PF in most studied problems. The source codes of the MOSRS algorithm are publicly available at https://nimakhodadadi.com/algorithms-%2B-codes.