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    Area of Science:

    • Optimization Algorithms
    • Computational Intelligence
    • Evolutionary Computation

    Background:

    • Many-objective optimization problems (MaOPs) involve more than three objectives.
    • Decomposition methods, using reference vectors, are common for MaOPs.
    • Uniform reference vectors perform well on regular Pareto optimal fronts (POFs) but struggle with irregular POFs.

    Purpose of the Study:

    • To develop a generalized adaptive evolutionary algorithm for MaOPs.
    • To achieve competitive performance on both regular and irregular POFs.
    • To address limitations of fixed and purely adaptive reference vector strategies.

    Main Methods:

    • A decomposition-based evolutionary algorithm with adaptive reference vectors is proposed.
    • The algorithm starts with uniform reference vectors and learns over a period.
    • Reference directions are dynamically inserted/deleted, with original directions becoming active/inactive.

    Main Results:

    • The proposed approach demonstrates competence across a range of problems with up to 15 objectives.
    • It shows improved performance on both regular and irregular POFs compared to state-of-the-art methods.
    • Numerical experiments validate the algorithm's effectiveness.

    Conclusions:

    • The generalized adaptive reference vector approach enhances evolutionary algorithms for MaOPs.
    • It offers a robust solution for problems with diverse Pareto optimal front geometries.
    • This method provides a significant advancement in solving complex optimization challenges.