Multi-Objective Majority–Minority Cellular Automata Algorithm for Global and Engineering Design Optimization

When dealing with complex models in real situations, many optimization problems require the use of more than one objective function to adequately represent the relevant characteristics of the system under consideration. Multi-objective optimization algorithms that can deal with several objective functions are necessary in order to obtain reasonable results within an adequate processing time. This paper presents the multi-objective version of a recent metaheuristic algorithm that optimizes a single objective function, known as the Majority–minority Cellular Automata Algorithm (MmCAA), inspired by cellular automata operations. The algorithm presented here is known as the Multi-objective Majority–minority Cellular Automata Algorithm (MOMmCAA). The MOMmCAA adds repository management and multi-objective search space density control to complement the performance of the MmCAA and make it capable of optimizing multi-objective problems. To evaluate the performance of the MOMmCAA, results on benchmark test sets (DTLZ, quadratic, and CEC-2020) and real-world engineering design problems were compared against other multi-objective algorithms recognized for their performance (MOLAPO, GS, MOPSO, NSGA-II, and MNMA). The results obtained in this work show that the MOMmCA achieves comparable performance with the other metaheuristic methods, demonstrating its competitiveness for use in multi-objective problems. The MOMmCAA was implemented in MATLAB and its source code can be consulted in GitHub.