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    A new local regularity model (LRM) enhances multimodal multiobjective optimization by improving solution distribution. This method prevents the loss of local optimal solutions, boosting decision space diversity.

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    Area of Science:

    • Optimization algorithms
    • Computational intelligence
    • Decision science

    Background:

    • Multimodal multiobjective optimization (MMO) seeks diverse acceptable decisions (ADs), including global optimal solutions (GOS) and local optimal solutions (LOSs).
    • Existing methods struggle with LOS discrimination due to solution distribution sensitivity, risking diversity loss.
    • The distribution of candidate solutions critically impacts the identification and preservation of LOSs.

    Purpose of the Study:

    • To introduce a novel Local Regularity Model (LRM) method for enhancing multimodal multiobjective optimization.
    • To improve the distribution of candidate solutions in the decision space, thereby preserving local optimal solutions.
    • To enhance the diversity and quality of acceptable decisions in multimodal optimization problems.

    Main Methods:

    • Developed a Hierarchical Principal Component Analysis (HPCA) to extract principal components from nondominated sets.
    • Constructed the LRM by segmenting distribution features using candidate solutions for manifold estimation.
    • Implemented a self-organization strategy for improved local fitting and a probability reproduction strategy for population reconstruction.

    Main Results:

    • The proposed LRM method effectively improves the distribution of candidate solutions.
    • The HPCA and self-organization strategy contribute to accurate manifold estimation of acceptable decisions.
    • Population reconstruction using LRM enhances the density and spread of solutions in the decision space.

    Conclusions:

    • The Local Regularity Model (LRM) method significantly improves multimodal multiobjective optimization by addressing solution distribution challenges.
    • The proposed approach effectively preserves local optimal solutions, leading to more diverse and reliable outcomes.
    • Integration into existing multimodal optimization algorithms demonstrates the method's practical effectiveness and potential for broader application.