A New Heuristic for the Traveling Salesman Problem with Time Windows
Transportation Science
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
A Hybrid Exact Algorithm for the TSPTW
INFORMS Journal on Computing
A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows
INFORMS Journal on Computing
Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows
Operations Research
Beam-ACO for the travelling salesman problem with time windows
Computers and Operations Research
New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem
Operations Research
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The traveling salesman problem with time windows (TSPTW) is the problem of finding in a weighted digraph a least-cost tour starting from a selected vertex, visiting each vertex of the graph exactly once according to a given time window, and returning to the starting vertex. This nP-hard problem arises in routing and scheduling applications. This paper introduces a new tour relaxation, called ngL-tour, to compute a valid lower bound on the TSPTW obtained as the cost of a near-optimal dual solution of a problem that seeks a minimum-weight convex combination of nonnecessarily elementary tours. This problem is solved by column generation. The optimal integer TSPTW solution is computed with a dynamic programming algorithm that uses bounding functions based on different tour relaxations and the dual solution obtained. An extensive computational analysis on basically all TSPTW instances (involving up to 233 vertices) from the literature is reported. The results show that the proposed algorithm solves all but one instance and outperforms all exact methods published in the literature so far.