Hybrid Mutation Mechanism-Based Moth–Flame Optimization with Improved Flame Update Mechanism for Multi-Objective Engineering Problems

Due to the complexity of multi-objective engineering problems, solutions obtained by many algorithms often exhibit poor distribution, and the algorithms tend to fall into local optima. To effectively alleviate these issues, an improved multi-objective moth–flame optimization algorithm (IETMFO) is proposed in this paper, with three core novelties: A hybrid mutation mechanism (integrating two mutation techniques) is first used to generate a new population, and then an indicator-based selection mechanism is adopted to produce a high-quality initial population, enhancing solution distribution. Enhanced Brownian motion is introduced as a local search strategy to reduce the risk of falling into local optima. An improved flame update mechanism is incorporated to maintain flame diversity, boosting the algorithm’s adaptability. The IETMFO is tested on 49 benchmark functions and 6 constrained engineering problems, and then compared with seven well-known algorithms (including NSGA-II, MOEA/D, and traditional MFO). The experimental results show the following: in benchmark function tests, IETMFO reduces the IGD value by an average of 32.7% and increases the HV value by an average of 28.5% compared with NSGA-II; on ZDT series functions, it outperforms the seven contrast algorithms in solution distribution uniformity; in the six engineering problems, its optimal solution proportion reaches 66.7%, and the risk of falling into local optima is reduced by 41.2%. These results demonstrate that the IETMFO achieves competitive performance in addressing multi-objective engineering problems.