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    A new heuristic algorithm effectively solves the multidepot and periodic vehicle routing problem (MDPVRP). This approach balances exploration and exploitation, outperforming existing methods on benchmark tests.

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    Area of Science:

    • Operations Research
    • Computer Science

    Background:

    • The vehicle routing problem (VRP) is a significant combinatorial optimization challenge.
    • Existing VRP variants, such as the multidepot and periodic VRP (MDPVRP), present complex routing and scheduling demands.

    Purpose of the Study:

    • To introduce and solve a novel variant of the multidepot and periodic VRP (MDPVRP).
    • To develop a heuristic-initialized stochastic memetic algorithm capable of handling large-scale MDPVRP instances.

    Main Methods:

    • An intelligent initialization technique creating a diverse solution population through a mix of random and heuristic methods.
    • Stochastic learning using simulated annealing with random and heuristic operators to selectively improve solution quality.
    • A hybrid approach combining randomness and greedy strategies to maintain a balance between exploration and exploitation in the search space.

    Main Results:

    • The proposed algorithm demonstrated superior performance on benchmark MDPVRP problems compared to baseline algorithms.
    • Significant improvements were observed when compared to current state-of-the-art algorithms for the MDPVRP formulation.

    Conclusions:

    • The heuristic-initialized stochastic memetic algorithm is highly effective for solving the MDPVRP.
    • The algorithm's ability to balance exploration and exploitation leads to enhanced solution quality and performance gains.