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    Area of Science:

    • Computational intelligence
    • Optimization algorithms
    • Evolutionary computation

    Background:

    • Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a popular framework for evolutionary multiobjective optimization.
    • MOEA/D decomposes problems into subproblems, with agents collaboratively solving them.
    • Current MOEA/D selection focuses on convergence and diversity, but requires improvement.

    Purpose of the Study:

    • To propose a novel selection method for MOEA/D that balances convergence and diversity.
    • To address the dual requirements of MOEA/D agents: convergence to the efficient front and distinction among solutions.
    • To introduce a method for defining and utilizing mutual preferences between subproblems and solutions.

    Main Methods:

    • Defining mutual preferences between subproblems and solutions to guide agent selection.
    • Developing an interrelationship between subproblems and solutions based on these mutual preferences.
    • Using this interrelationship to select elite solutions for the next generation of parents.

    Main Results:

    • The proposed selection operator effectively balances convergence and diversity in the search process.
    • Comprehensive experiments on complex multiobjective optimization problems (MOPs) demonstrate the algorithm's efficacy.
    • The algorithm shows competitive performance compared to existing methods on MOP test instances.

    Conclusions:

    • The proposed method effectively enhances the performance of MOEA/D by considering mutual preferences.
    • This approach offers a promising direction for improving evolutionary multiobjective optimization.
    • The algorithm is effective and competitive for solving MOPs with complex Pareto sets.