Journal Article10.1023/B:ANOR.0000032576.73681.29
Solving VRPTWs with Constraint Programming Based Column Generation
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TL;DR: This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming.
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Abstract: Constraint programming based column generation is a hybrid optimization framework recently proposed (Junker et al., 1999) that uses constraint programming to solve column generation subproblems. In the past, this framework has been used to solve scheduling problems where the associated graph is naturally acyclic and has done so very efficiently. This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming. We also introduce new redundant constraints which can be useful in the general framework. The experimental results are comparable to those of the similar method in the literature (Desrochers, Desrosiers, and Solomon, 1992) but the proposed method yields a much more flexible approach.
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Citations
•Book
Handbook of Constraint Programming
Francesca Rossi,Peter van Beek,Toby Walsh +2 more
- 01 Jan 2006
TL;DR: Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.
Shortest Path Problems with Resource Constraints
Stefan Irnich,Guy Desaulniers +1 more
- 01 Jan 2005
TL;DR: In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants.
742
Vehicle Routing Problem with Time Windows
Brian Kallehauge,Jesper Larsen,Oli B.G. Madsen,Marius M. Solomon +3 more
- 01 Jan 2005
TL;DR: This chapter discusses the Vehicle Routing Problem with Time Windows in terms of its mathematical modeling, its structure and decomposition alternatives, and describes generalizations of the problem.
The Vehicle Routing Problem with Time Windows
Guy Desaulniers,Oli B.G. Madsen,Stefan Ropke +2 more
- 01 Jan 2014
307
Exact Branch-Price-and-Cut Algorithms for Vehicle Routing
TL;DR: The leading exact algorithms for solving many classes of VRPs are branch-price-and-cut algorithms, which provide simple and scalable solutions to vehicle routing problems.
223
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A new optimization algorithm for the vehicle routing problem with time windows
TL;DR: This paper presents a new optimization algorithm capable of optimally solving 100-customer problems of the vehicle routing problem with time windows VRPTW and indicates that this algorithm proved to be successful on a variety of practical sized benchmark VRPTw test problems.
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A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows
Martin Desrochers,Jacques Desrosiers,Marius M. Solomon +2 more
- 01 Jun 1990
TL;DR: In this paper, the authors present an LP relaxation of the set partitioning formulation of the VRPTW problem, which is solved by column generation, where feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming.
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•Proceedings Article
A filtering algorithm for constraints of difference in CSPs
Jean-Charles Régin
- 01 Aug 1994
TL;DR: A new filtering algorithm is presented that achieves the generalized arc-consistency condition for these non-binary constraints and has been successfully used in the system RESYN, to solve the subgraph isomorphism problem.
An Optimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Lagrangian Relaxation
Niklas Kohl,Oli B.G. Madsen +1 more
TL;DR: In this article, a new optimization method for the vehicle routing problem with time windows (VRPTW) is presented, which is based on a Lagrangian relaxation of the constraint set requiring that each customer must be serviced.
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