In order to address the issues of poor solution accuracy, convergence, and local optimality often observed in the firefly algorithm when solving multi-objective optimization problems, this study proposes a multi-objective firefly algorithm with dynamic reflection guidance and bi-dimensional variation (MOFA-DGM). MOFA-DGM incorporates Tent mapping during the population initialization stage to ensure uniform coverage of the entire feasible domain, thus improving the quality of the initial population. During the firefly position updating stage, a dynamic reflection guidance model is introduced, which uses both the elite solution and the current optimal solution from the external archive, along with an enhanced simplex method, to calculate the reflection solution that guides the movement of the fireflies. This approach enhances the convergence of the algorithm. Additionally, a two-dimensional variation mechanism is proposed to help the population escape local optima and prevent the formation of firefly clusters during late iterations, thereby enhancing the exploration capability of the algorithm. Experimental results comparing MOFA-DGM with recent multi-objective evolutionary algorithms demonstrate that MOFA-DGM effectively improves solution accuracy, enhances algorithm convergence, and improves the algorithm’s ability to search for optimal solutions compared to the other algorithms.

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Multi-objective Firefly Algorithm with Dynamic Reflection Guidance and Bi-dimensional Variants

  • Zhi-Yang Zeng,
  • Shui-Ping Kang,
  • Jia-Zhen Hou,
  • Xiu-Mei Tian

摘要

In order to address the issues of poor solution accuracy, convergence, and local optimality often observed in the firefly algorithm when solving multi-objective optimization problems, this study proposes a multi-objective firefly algorithm with dynamic reflection guidance and bi-dimensional variation (MOFA-DGM). MOFA-DGM incorporates Tent mapping during the population initialization stage to ensure uniform coverage of the entire feasible domain, thus improving the quality of the initial population. During the firefly position updating stage, a dynamic reflection guidance model is introduced, which uses both the elite solution and the current optimal solution from the external archive, along with an enhanced simplex method, to calculate the reflection solution that guides the movement of the fireflies. This approach enhances the convergence of the algorithm. Additionally, a two-dimensional variation mechanism is proposed to help the population escape local optima and prevent the formation of firefly clusters during late iterations, thereby enhancing the exploration capability of the algorithm. Experimental results comparing MOFA-DGM with recent multi-objective evolutionary algorithms demonstrate that MOFA-DGM effectively improves solution accuracy, enhances algorithm convergence, and improves the algorithm’s ability to search for optimal solutions compared to the other algorithms.