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    Area of Science:

    • Optimization
    • Computer Science
    • Operations Research

    Background:

    • Permutation-based multiobjective combinatorial optimization problems (MOCOPs) present unique challenges due to their complex search space structures.
    • Existing methods may not fully exploit the inherent properties of permutation-based MOCOPs, such as their permutation tree-shaped search space.

    Purpose of the Study:

    • To propose a generic and effective multiobjective set-based particle swarm optimization methodology based on decomposition (MS-PSO/D) tailored for permutation-based MOCOPs.
    • To develop a method that leverages the permutation tree structure for efficient and feasible solution generation.

    Main Methods:

    • MS-PSO/D utilizes an element-based representation and a constructive approach to generate solutions step-by-step, respecting the permutation tree structure.
    • A decomposition strategy converts the multiobjective problem into single-objective subproblems using weight vectors.
    • Problem-specific heuristic information is integrated into the constructive approach, and a diversity control mechanism is included.

    Main Results:

    • Extensive experiments were conducted on the multiobjective traveling salesman problem (MOTSP) and the multiobjective project scheduling problem (MOPSP).
    • The proposed MS-PSO/D methodology demonstrated promising performance on these benchmark problems.
    • The element-based representation and constructive approach effectively generated feasible solutions within the permutation-tree-shaped search space.

    Conclusions:

    • MS-PSO/D is a promising generic methodology for addressing permutation-based MOCOPs.
    • The integration of decomposition, element-based representation, and constructive heuristics offers an effective approach to multiobjective optimization in this domain.
    • The method's flexibility in diversity control further enhances its applicability to various permutation-based MOCOPs.