Multi-objective Mantis Search Algorithm (MOMSA): A novel approach for engineering design problems and validation

This paper proposes a new Multi-Objective Mantis Search Algorithm (MOMSA) to handle complex optimization problems, including real-world engineering optimization problems. The Mantis Search Algorithm (MSA) is a recently reported nature-inspired metaheuristic algorithm, and it has been inspired by the unique hunting behavior and sexual cannibalism of praying mantises. The proposed MOMSA algorithm employs the same underlying MSA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto-optimal solutions. In addition, MOMSA employs the crowding distance mechanism to enhance the coverage of optimal solutions across all objectives. To validate its performance, we conduct 29 case studies, encompassing twenty multi-objective benchmark problems (ZDT, DTLZ, and CEC 2009) and nine engineering design problems. Furthermore, MOMSA is applied to the IEEE-30 bus system, addressing both single- and multi-objective optimal power flow problems across eight distinct cases. Results are compared with some state-of-the-art approaches using various performance metrics such as GD, MS, IGD, and HV. The findings demonstrate MOMSA's ability to effectively balance convergence, diversity, and uniformity, providing valuable insights for decision-makers addressing complex problems. The source code of MOMSA is publicly accessible at https://www.mathworks.com/matlabcentral/fileexchange/159623-momsa-multi-objective-mantis-search-algorithm.