An arithmetic and geometric mean-based multi-objective moth-flame optimization algorithm

Expanding the capacity of optimization algorithms for simultaneous optimization of multiple competing objectives is a crucial aspect of research. This study presents MnMOMFO, a novel non-dominated sorting (NDS) and crowding distance (CD)-based multi-objective variant of the moth-flame optimization (MFO) algorithm for multi-objective optimization problems. The algorithm incorporates arithmetic and geometric mean concepts to address MFO’s limitations and to improve its performance. Subsequently, we extend this enhanced MFO into a multi-objective variant, leveraging NDS and CD strategies to achieve a well-distributed Pareto optimal front. The effectiveness of the proposed MnMOMFO algorithm is rigorously evaluated across three distinct phases. In the initial phase, we scrutinize its performance on four ZDT multi-objective optimization problems, employing four performance metrics—general distance, inverted general distance, spacing, and spread metric. Comparative analyses with select competitive multi-objective optimization algorithms comprehensively understand MnMOMFO’s efficacy. Secondly, 24 complex multi-objective IEEE CEC 2020 test suits are considered on two performance metrics. Namely, Pareto sets proximity and the inverted generational distance in decision space. In the third phase, five real-world engineering problems are considered to measure the problem-solving ability of the MnMOMFO algorithm. The results from the experiments indicated that the MnMOMFO was the best candidate algorithm, achieving more than 95% superior results for multi-objective ZDT benchmark problems, IEEE CEC 2020 test functions, and real-life issues in contrast to several other algorithms. The experimental outcomes substantiate MnMOMFO’s superiority, establishing it as a robust and efficient algorithm for multi-objective optimization challenges with broad applicability to real-world engineering problems.