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    This study introduces a novel Niche Center Distinguishing-based Differential Evolution (NCD-DE) algorithm to solve multimodal optimization problems. NCD-DE effectively identifies multiple optimal solutions by treating niche center selection as an optimization problem.

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    Area of Science:

    • Computational Intelligence
    • Optimization Algorithms
    • Evolutionary Computation

    Background:

    • Real-world problems often require finding multiple optimal solutions simultaneously (multimodal optimization problems, MMOPs).
    • Existing niching techniques struggle with effectively distinguishing appropriate individuals as niche centers, hindering MMOP solution efficiency.
    • Balancing population diversity for locating global optima and refining accuracy for precise solutions is crucial for MMOP algorithms.

    Purpose of the Study:

    • To propose a novel Niche Center Distinguishing-based Differential Evolution (NCD-DE) algorithm to address the challenges in solving MMOPs.
    • To treat the Niche Center Distinguishing (NCD) problem as an optimization problem solvable by an internal genetic algorithm (GA).
    • To enhance the exploration and exploitation capabilities of the NCD-DE algorithm for improved MMOP performance.

    Main Methods:

    • Developed an NCD-DE algorithm where niches are formed using an internal GA to solve the NCD problem online.
    • Designed a fitness-entropy measurement objective function within the internal GA to evaluate the promise of niche center groups.
    • Introduced a niching and global cooperative mutation strategy utilizing both niche and population information for generating new individuals.

    Main Results:

    • The proposed NCD-DE algorithm demonstrated superior or competitive performance compared to state-of-the-art and recent algorithms.
    • Experimental results indicate significant improvements in both the accuracy and completeness of solutions found by NCD-DE.
    • The internal GA effectively optimizes niche center selection, contributing to the algorithm's overall efficiency in solving MMOPs.

    Conclusions:

    • The NCD-DE algorithm provides an effective approach to solving multimodal optimization problems by optimizing niche center identification.
    • The integration of an internal GA and a cooperative mutation strategy enhances the algorithm's ability to find diverse and accurate solutions.
    • NCD-DE represents a promising advancement in evolutionary computation for tackling complex real-world optimization challenges.