Solving VRPTWs with Constraint Programming Based Column Generation

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.

[1]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[2]  Martin Desrochers,et al.  A Column Generation Algorithm for the Vehicle Routing Problem with Time Windows , 1992 .

[3]  Michel Gendreau,et al.  On the flexibility of constraint programming models: From single to multiple time windows for the traveling salesman problem , 1999, Eur. J. Oper. Res..

[4]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[5]  Meinolf Sellmann,et al.  Cost Based Filtering for the Constrained Knapsack Problem , 2002, Ann. Oper. Res..

[6]  Daniele Vigo,et al.  Solving TSP through the Integration of OR and CP Techniques , 1999, Electron. Notes Discret. Math..

[7]  E. Gaudin,et al.  Contribution de la programmation par contraintes au transport : definition et resolution d'un modele complexe de gestion de flotte , 1997 .

[8]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .

[9]  Niklas Kohl,et al.  An Optimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Lagrangian Relaxation , 1997, Oper. Res..

[10]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[11]  Marco A. Boschetti,et al.  A Set Partitioning Approach to the Crew Scheduling Problem , 1999, Oper. Res..

[12]  F. Maffioli,et al.  On prize-collecting tours and the asymmetric travelling salesman problem , 1995 .

[13]  Stefan E. Karisch,et al.  A Framework for Constraint Programming Based Column Generation , 1999, CP.

[14]  Meinolf Sellmann,et al.  Constraint Programming Based Column Generation with Knapsack Subproblems , 1999 .

[15]  Paolo Toth,et al.  Algorithms and codes for the assignment problem , 1988 .

[16]  Michel Gendreau,et al.  An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows , 1998, Transp. Sci..