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    This study introduces a novel multistage differential evolution (DE) algorithm that adapts strategies to evolutionary stages. The approach improves performance by dynamically selecting strategies based on underestimation error, outperforming existing DE variants.

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    Area of Science:

    • Optimization Algorithms
    • Computational Intelligence
    • Evolutionary Computation

    Background:

    • Single strategies in differential evolution (DE) may not be optimal across all evolutionary stages.
    • Determining the appropriate evolutionary stage for strategy adaptation is challenging.

    Purpose of the Study:

    • To propose an abstract convex underestimation-assisted multistage DE algorithm.
    • To dynamically adapt DE strategies based on estimated evolutionary stages.

    Main Methods:

    • Dividing the evolutionary process into three stages based on the variation of average underestimation error (UE).
    • Calculating underestimation using supporting vectors of neighboring individuals.
    • Employing a pool of candidate strategies for each stage and automatically selecting one per generation.
    • Introducing a centroid-based strategy for balancing diversity and convergence in the second stage.

    Main Results:

    • The proposed multistage DE algorithm demonstrated superior performance on benchmark test functions (CEC 2013, CEC 2014).
    • Experimental results show significant improvements over several advanced DE variants and non-DE approaches.

    Conclusions:

    • The abstract convex underestimation-assisted multistage DE effectively adapts strategies to different evolutionary phases.
    • This dynamic strategy selection enhances the overall performance of differential evolution algorithms.