Integer and combinatorial optimization
Integer and combinatorial optimization
A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
Discrete Mathematics
Software—Practice & Experience - Special issue on discrete algorithm engineering
Branch-and-cut algorithms for the capacitated VRP
The vehicle routing problem
The vehicle routing problem
2-Path Cuts for the Vehicle Routing Problem with Time Windows
Transportation Science
Formulations and exact algorithms for the vehicle routing problem with time windows
Computers and Operations Research
The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches
Computational Optimization and Applications
Computers and Industrial Engineering
A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows
Computers and Operations Research
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This paper considers the vehicle routing problem with time windows, where the service of each customer must start within a specified time interval. We consider the Lagrangian relaxation of the constraint set requiring that each customer must be served by exactly one vehicle yielding a constrained shortest path subproblem. We present a stabilized cutting-plane algorithm within the framework of linear programming for solving the associated Lagrangian dual problem. This algorithm creates easier constrained shortest path subproblems because less negative cycles are introduced and it leads to faster multiplier convergence due to a stabilization of the dual variables. We have embedded the stabilized cutting-plane algorithm in a branch-and-bound search and introduce strong valid inequalities at the master problem level by Lagrangian relaxation. The result is a Lagrangian branch-and-cut-and-price (LBCP) algorithm for the VRPTW. Making use of this acceleration strategy at the master problem level gives a significant speed-up compared to algorithms in the literature based on traditional column generation. We have solved two test problems introduced in 2001 by Gehring and Homberger with 400 and 1000 customers respectively, which to date are the largest problems ever solved to optimality. We have implemented the LBCP algorithm using the ABACUS open-source framework for solving mixed-integer linear-programs by branch, cut, and price.