This paper introduces MnMOMFO, a novel multi-objective variant of the moth-flame optimization (MFO) algorithm that incorporates arithmetic and geometric mean concepts to enhance performance. The algorithm uses non-dominated sorting (NDS) and crowding distance (CD) strategies to achieve a well-distributed Pareto optimal front. The effectiveness of MnMOMFO is evaluated on three phases: (1) four ZDT multi-objective optimization problems using four performance metrics; (2) 24 complex multi-objective IEEE CEC 2020 test suits using two metrics; and (3) five real-world engineering problems. The results show that MnMOMFO outperforms several other algorithms, achieving more than 95% superior results on multi-objective ZDT benchmark problems, IEEE CEC 2020 test functions, and real-life issues. The experimental outcomes confirm MnMOMFO's superiority, establishing it as a robust and efficient algorithm for multi-objective optimization challenges with broad applicability to real-world engineering problems. Multi-objective optimization (MOO) is a powerful method for solving problems with competing objectives. The objective functions in a multi-objective problem often contradict one another, and there is often no way to find a single solution that optimizes every possible goal. Instead, decision-makers aim to find a solution that is Pareto optimal, meaning it cannot be improved in one objective without worsening another. The Pareto set is the set of all Pareto optimal solutions. Nature-based metaheuristic algorithms have been widely used to solve complex optimization problems. These include genetic algorithms (GA), ant colony optimization (ACO), differential evolution (DE), bacterial foraging algorithm (BFA), shuffled frog leaping (SFL), particle swarm optimization (PSO), and others. Since 2005, many new algorithms have been developed, including the artificial bee colony (ABC), biogeography-based optimization (BBO), gravitational search algorithm (GSA), grey wolf optimization (GWO), moth flame optimization (MFO), and others. Many of these algorithms have been improved and hybridized to enhance their performance and convergence to global optima. The MFO is a powerful algorithm based on the moths' transverse orientation technique developed by Mirjalili in 2015. It has been used for various practical issues, including parameter estimation of solar modules, flexible operation modeling, intelligent route planning of multiple UAVs, deep learning, machine scheduling problems, and neural networks. New population-based optimization methods have been proposed to improve the performance of MFO.This paper introduces MnMOMFO, a novel multi-objective variant of the moth-flame optimization (MFO) algorithm that incorporates arithmetic and geometric mean concepts to enhance performance. The algorithm uses non-dominated sorting (NDS) and crowding distance (CD) strategies to achieve a well-distributed Pareto optimal front. The effectiveness of MnMOMFO is evaluated on three phases: (1) four ZDT multi-objective optimization problems using four performance metrics; (2) 24 complex multi-objective IEEE CEC 2020 test suits using two metrics; and (3) five real-world engineering problems. The results show that MnMOMFO outperforms several other algorithms, achieving more than 95% superior results on multi-objective ZDT benchmark problems, IEEE CEC 2020 test functions, and real-life issues. The experimental outcomes confirm MnMOMFO's superiority, establishing it as a robust and efficient algorithm for multi-objective optimization challenges with broad applicability to real-world engineering problems. Multi-objective optimization (MOO) is a powerful method for solving problems with competing objectives. The objective functions in a multi-objective problem often contradict one another, and there is often no way to find a single solution that optimizes every possible goal. Instead, decision-makers aim to find a solution that is Pareto optimal, meaning it cannot be improved in one objective without worsening another. The Pareto set is the set of all Pareto optimal solutions. Nature-based metaheuristic algorithms have been widely used to solve complex optimization problems. These include genetic algorithms (GA), ant colony optimization (ACO), differential evolution (DE), bacterial foraging algorithm (BFA), shuffled frog leaping (SFL), particle swarm optimization (PSO), and others. Since 2005, many new algorithms have been developed, including the artificial bee colony (ABC), biogeography-based optimization (BBO), gravitational search algorithm (GSA), grey wolf optimization (GWO), moth flame optimization (MFO), and others. Many of these algorithms have been improved and hybridized to enhance their performance and convergence to global optima. The MFO is a powerful algorithm based on the moths' transverse orientation technique developed by Mirjalili in 2015. It has been used for various practical issues, including parameter estimation of solar modules, flexible operation modeling, intelligent route planning of multiple UAVs, deep learning, machine scheduling problems, and neural networks. New population-based optimization methods have been proposed to improve the performance of MFO.