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    Area of Science:

    • Optimization
    • Computational Science
    • Operations Research

    Background:

    • Combinatorial multiobjective optimization problems (CMOPs) are prevalent in real-world applications.
    • Classical Pareto local search (PLS) struggles with computational and space complexity for problems with more than two objectives.
    • Existing PLS methods are often inefficient due to retaining all nondominated solutions.

    Purpose of the Study:

    • To develop an efficient PLS method for CMOPs with multiple objectives.
    • To reduce the computational and space complexity of PLS.
    • To improve the distribution of Pareto front approximations.

    Main Methods:

    • Proposed grid weighted sum dominance (gws-dominance) by combining Pareto dominance and weighted sum (WS) in a grid system.
    • Integrated gws-dominance into PLS for efficient local search.
    • Maintained at most one representative solution per grid to reduce complexity.

    Main Results:

    • The proposed grid weighted sum PLS significantly outperforms classical PLS and other decomposition-based and grid-based algorithms.
    • The method demonstrates effectiveness and efficiency on benchmark CMOPs, including many-objective problems.
    • Achieved more widely and uniformly distributed Pareto front approximations.

    Conclusions:

    • The grid weighted sum PLS offers a significant improvement for solving CMOPs, especially those with multiple objectives.
    • This approach effectively addresses the limitations of classical PLS regarding computational cost and scalability.
    • The method is suitable for both multiobjective and many-objective optimization challenges.