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A dynamic multi-objective evolutionary algorithm with direction-guided and sensitive-dimension-based two evolution
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DOI：10.1016/j.eswa.2026.133667.png)
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Abstract
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In dynamic multi-objective optimization, environmental changes can rapidly invalidate converged solution sets. Therefore, achieving fast convergence recovery while maintaining solution-set distribution stability remains a key challenge. Existing methods often lack effective coordination between change response and subsequent optimization, which limits their recovery speed and long-term tracking stability. To address this issue, this paper proposes a dynamic multi-objective evolutionary algorithm with direction-guided hybrid response and sensitive-dimension-based two-stage evolution. First, a direction-guided hybrid response strategy is developed to improve post-change recovery. It estimates the population migration direction from the elite centroid and the population centroid, and then generates a response population through directional translation, change-intensity-related perturbation, and small-scale random reinitialization. The response population then provides the decision-space basis for sensitive-dimension identification. The identified dimensions further provide search guidance for the subsequent two-stage evolution. Second, a sensitive-dimension identification mechanism is constructed to locate decision variables that are more sensitive to environmental changes. Based on the dispersion characteristics of elite solutions in the decision space, the identified sensitive dimensions are used to guide a two-stage evolutionary process. Predictive search is performed on sensitive dimensions to accelerate Pareto-front tracking, while local refinement is conducted on relatively stable dimensions to improve solution-set distribution. Finally, a multi-source fusion elite recombination strategy is introduced to enhance the robustness of population updating. It removes duplicates and performs controlled replacement among the original population, two-stage candidate solutions, and elite information. Experimental results on FDA, DF, and JY benchmark problems under different change-frequency settings show that the proposed algorithm outperforms the competing algorithms on most test problems and remains competitive on the others. Further studies on aluminum electrolysis operating-parameter optimization and the dynamic multi-objective knapsack problem demonstrate its practical applicability in both continuous-and discrete-variable decision scenarios.
Keywords:
Dynamic multi-objective optimization
Direction-guided hybrid response
Sensitive-dimension identification
Two-stage evolution
Operating-parameter optimization of aluminum electrolysis
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