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.

扩展优化算法同时优化多个竞争目标的能力是研究的一个重要方面。本研究提出了 MnMOMFO，一种新颖的非支配排序 (NDS) 和基于拥挤距离 (CD) 的飞蛾火焰优化 (MFO) 算法的多目标变体，用于解决多目标优化问题。该算法结合了算术平均和几何平均概念来解决 MFO 的局限性并提高其性能。随后，我们将这种增强的 MFO 扩展为多目标变体，利用 NDS 和 CD 策略来实现分布均匀的 Pareto 最优前沿。所提出的 MnMOMFO 算法的有效性在三个不同的阶段进行了严格评估。在初始阶段，我们使用四个性能指标（一般距离、倒置一般距离、间距和扩展指标）检查其在四个 ZDT 多目标优化问题上的性能。与选定的竞争性多目标优化算法进行比较分析，全面了解 MnMOMFO 的功效。其次，在两个性能指标上考虑了 24 个复杂的多目标 IEEE CEC 2020 测试套件。即帕累托在决策空间中设定邻近度和倒代距离。在第三阶段，考虑五个现实世界的工程问题来衡量MnMOMFO算法解决问题的能力。实验结果表明，MnMOMFO 是最佳候选算法，与其他几种算法相比，在多目标 ZDT 基准问题、IEEE CEC 2020 测试函数和现实问题上取得了 95% 以上的优异结果。实验结果证实了 MnMOMFO 的优越性，将其确立为一种稳健且高效的算法，可应对多目标优化挑战，并广泛适用于现实世界的工程问题。