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  • 关于TSP问题的第三代LKH算法 PDF 下载

    关于TSP问题的第三代LKH算法 PDF 下载

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    1. Introduction
    The Lin-Kernighan-Helsgaun TSP solver, LKH [1, 2], is a state-of-the-art heuristic solver for the
    traveling salesman problem. LKH implements a powerful local search heuristic for the TSP based on
    the variable depth local search of Lin and Kernighan [3]. LKH has produced optimal solutions for all
    solved problems we have been able to obtain; including an 85,900-city instance (at the time of writ-
    ing, the largest nontrivial instance solved to optimality). Furthermore, the algorithm has improved
    the best known solutions for a series of large-scale instances with unknown optima, among these a
    1,904,711-city instance (World TSP).
    However, in many practical situations, the TSP has additional constraints such as limited resources,
    time windows and precedence constraints. Since the current version of LKH, LKH-2, is highly
    customized for the standard TSP and cannot accommodate constraints, its usage is extremely limited
    in these situations. Furthermore, solving problems that involve multiple traveling salesmen is not
    straightforward.
    This is the motivation for extending LKH-2 with facilities handling constraints and multiple traveling
    salesmen. The extension, named LKH-3, is currently able to solve the following problem types:
    2
    ACVRP: Asymmetric capacitated vehicle routing problem
    BWTSP: Black and white traveling salesman problem
    CCVRP: Cumulative capacitated vehicle routing problem
    CVRP: Capacitated vehicle routing problem
    CVRPTW: Capacitated vehicle routing problem with time windows
    DCVRP: Distance constrained capacitated vehicle routing problem
    1-PDTSP: One-commodity pickup-and-delivery traveling salesman problem
    m-PDTSP: Multi-commodity pickup-and-delivery traveling salesman problem
    m1-PDTSP: Multi-commodity one-to-one pickup-and-delivery traveling salesman problem
    MTRP: Multiple traveling repairman problem
    MTRPD: Multiple traveling repairman problem with distance constraints
    mTSP: Multiple traveling salesmen problem
    OVRP: Open vehicle routing problem
    PDPTW: Pickup-and-delivery problem with time windows
    PDTSP: Pickup-and-delivery traveling salesman problem
    PDTSPF: Pickup-and-delivery traveling salesman problem with FIFO loading
    PDTSPL: Pickup-and-delivery traveling salesman problem with LIFO loading
    RCTVRP: Risk-constrained cash-in-transit vehicle routing problem
    RCTVRPTW: Risk-constrained cash-in-transit vehicle routing with time windows
    SOP: Sequential ordering problem
    TRP: Traveling repairman problem
    TSPPD: Traveling salesman problem with pickups and deliveries
    TSPTW: Traveling salesman problem with time windows
    VRPB: Vehicle routing problem with backhauls
    VRPBTW: Vehicle routing problem with backhauls and time windows
    VRPMPD: Vehicle routing problem with mixed pickup and delivery
    VRPMPDTW: Vehicle routing problem with mixed pickup and delivery and time windows
    VRPSPD: Vehicle routing problem with simultaneous pickup and delivery
    VRPSPDTW: Vehicle routing problem with simultaneous pickup-delivery and time windows
    Extensive testing on benchmark instances from the literature has shown that LKH-3 is effective. Best
    known solutions are often obtained, and in some cases, new best solutions are found.
    The next sections describe the implementation of LKH-3.

     

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