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    Area of Science:

    • Operations Research
    • Combinatorial Optimization
    • Computer Science

    Background:

    • The Multiple Traveling Salesman Problem (MTSP) models scenarios with multiple agents visiting shared locations.
    • Existing MTSP models do not accommodate scenarios where agents have both exclusive and shared tasks.
    • This limitation hinders applications requiring differentiated task assignments.

    Purpose of the Study:

    • Introduce the Colored Traveling Salesman Problem (CTSP) to address MTSP limitations.
    • Define CTSP with exclusive (single-color) and shared (multi-color) city groups.
    • Establish CTSP as an NP-hard problem, with special cases including multi-depot MTSP.

    Main Methods:

    • Propose a Genetic Algorithm (GA) with dual-chromosome coding for CTSP.
    • Enhance the GA by integrating Greedy, Hill-Climbing (HC), and Simulated Annealing (SA) operations.
    • Analyze the solution space and compare algorithm performance through experimentation.

    Main Results:

    • Experimental results highlight the limitations of exact solution methods for CTSP.
    • Simulated Annealing GA (SAGA) demonstrates superior solution quality.
    • Hill-Climbing GA (HCGA) provides an effective balance between solution quality and computational time.

    Conclusions:

    • CTSP offers a more realistic model for complex routing problems with mixed task types.
    • SAGA is recommended for applications prioritizing solution optimality.
    • HCGA is suitable for scenarios requiring efficient computation without significant compromise on solution quality.