This paper introduces a novel multi-objective variant of the moth-flame optimization (MFO) algorithm, named MnMOMFO, which incorporates arithmetic and geometric mean concepts to enhance its performance. The algorithm leverages non-dominated sorting (NDS) and crowding distance (CD) strategies to achieve a well-distributed Pareto optimal front. The effectiveness of MnMOMFO is evaluated through three phases: (1) solving four ZDT multi-objective optimization problems using four performance metrics, (2) testing 24 IEEE CEC 2020 test functions on Pareto sets proximity and inverted generational distance, and (3) applying it to five real-world engineering problems. The results show that MnMOMFO outperforms several other algorithms, achieving over 95% superior results in all three phases, making it a robust and efficient solution for multi-objective optimization challenges.This paper introduces a novel multi-objective variant of the moth-flame optimization (MFO) algorithm, named MnMOMFO, which incorporates arithmetic and geometric mean concepts to enhance its performance. The algorithm leverages non-dominated sorting (NDS) and crowding distance (CD) strategies to achieve a well-distributed Pareto optimal front. The effectiveness of MnMOMFO is evaluated through three phases: (1) solving four ZDT multi-objective optimization problems using four performance metrics, (2) testing 24 IEEE CEC 2020 test functions on Pareto sets proximity and inverted generational distance, and (3) applying it to five real-world engineering problems. The results show that MnMOMFO outperforms several other algorithms, achieving over 95% superior results in all three phases, making it a robust and efficient solution for multi-objective optimization challenges.