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    Area of Science:

    • Computational Intelligence
    • Optimization Algorithms
    • Evolutionary Computation

    Background:

    • Multimodal optimization problems (MMOPs) necessitate algorithms capable of finding multiple solutions concurrently.
    • Existing evolutionary algorithms (EAs) often rely on niching techniques for MMOPs, but these methods typically involve sensitive parameters and complex population partitioning.
    • This poses a significant challenge for robust and efficient multimodal algorithm design.

    Purpose of the Study:

    • To propose a novel parameter-free niching method for evolutionary algorithms to address the challenges in solving MMOPs.
    • To develop a distributed differential evolution (DDE) algorithm integrated with adaptive estimation distribution (AED) for enhanced multimodal optimization.
    • To overcome the limitations of sensitive niching parameters and complex population partitioning in existing methods.

    Main Methods:

    • Introduced a parameter-free niching method based on adaptive estimation distribution (AED).
    • Developed a distributed differential evolution (DDE) algorithm, termed AED-DDE, where each individual self-determines its niche size.
    • Employed a master-slave multiniche distributed model for co-evolution and incorporated probabilistic local search (PLS) for solution refinement.

    Main Results:

    • The AED-DDE algorithm successfully avoids the difficulties associated with population partitioning and sensitive niching parameters.
    • The multiniche co-evolution mechanism enhances population diversity, leading to more comprehensive exploration of the search space and identification of global optima.
    • Comparative results demonstrate the superiority of AED-DDE over existing multimodal algorithms, including the CEC2015 competition winner.

    Conclusions:

    • AED-DDE offers a robust and effective approach for solving multimodal optimization problems.
    • The parameter-free niching strategy and distributed co-evolutionary framework significantly improve performance and simplify implementation.
    • This research provides a valuable advancement in the field of evolutionary computation for complex optimization tasks.