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A maximum mean discrepancy indicator-based evolutionary algorithm for solving dynamic multi-objective optimization problems with undetectable changes
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DOI：10.1016/j.swevo.2026.102530.png)
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Abstract
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Most existing research on dynamic multi-objective optimization problems assumes that environmental changes can be detected. However, in real-world applications, many environmental changes are undetectable, posing significant challenges to traditional dynamic multi-objective evolutionary algorithms. The key issue is how to improve population diversity without sacrificing convergence. To address the challenge, a maximum mean discrepancy indicator-based evolutionary algorithm (MMDEA) is proposed. First, an MMD indicator-based front evolution assessment strategy is designed to monitor the state of the evolutionary process. Based on the ability of MMD to effectively measure the distance between distributions, we employ it to identify the evolutionary state of the population. By calculating the MMD indicator value between the current and previous approximated optimal fronts, the population state can be classified as either a convergence state or a diversity state. When the population is in the convergence state, a convergence enhancement strategy is employed that guides the evolution of non-dominated solutions based on the deviation between them and their nearest dominated solutions. When the population is in the diversity state, a diversity enhancement strategy is proposed that guides the evolution of dominated solutions based on the deviation between non-dominated solutions and their nearest dominated solutions. Experimental results have been presented for various dynamic multi-objective optimization problems, compared with several state-of-the-art algorithms. The comprehensive results demonstrate that the proposed algorithm is highly effective and superior in solving these problems, with undetectable changes.
Keywords:
Maximum mean discrepancy
Evolutionary algorithm
Dynamic multi-objective optimization problems
Undetectable changes
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