Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems

We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of "related" customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems.

[1]  Éric D. Taillard,et al.  Parallel iterative search methods for vehicle routing problems , 1993, Networks.

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

[3]  Egon Balas,et al.  The Shifting Bottleneck Procedure for Job Shop Scheduling , 1988 .

[4]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[5]  François Laburthe,et al.  Solving Small TSPs with Constraints , 1997, ICLP.

[6]  P. A. Geelen,et al.  Dual Viewpoint Heuristics for Binary Constraint Satisfaction Problems , 1992, ECAI.

[7]  François Laburthe,et al.  Disjunctive Scheduling with Task Intervals , 1995 .

[8]  Toby Walsh,et al.  Interleaved and Discrepancy Based Search , 1998, ECAI.

[9]  Toby Walsh,et al.  From Approximate to Optimal Solutions: Constructing Pruning and Propagation Rules , 1997, IJCAI.

[10]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[11]  Matthew L. Ginsberg,et al.  Limited Discrepancy Search , 1995, IJCAI.

[12]  Toby Walsh,et al.  An Empirical Study of Dynamic Variable Ordering Heuristics for the Constraint Satisfaction Problem , 1996, CP.

[13]  Jean-Yves Potvin A GENETIC APPROACH TO THE VEHICLE ROUTING PROBLEM WITH TIME WINDOWS. , 1993 .

[14]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[15]  William J. Cook,et al.  A Computational Study of the Job-Shop Scheduling Problem , 1991, INFORMS Journal on Computing.

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

[17]  Martin W. P. Savelsbergh,et al.  The Vehicle Routing Problem with Time Windows: Minimizing Route Duration , 1992, INFORMS J. Comput..

[18]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[19]  Toby Walsh,et al.  The Constrainedness of Search , 1996, AAAI/IAAI, Vol. 1.

[20]  Michel Gendreau,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows , 1997, Transp. Sci..

[21]  Ibrahim H. Osman,et al.  Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problems with Time Windows , 1997 .

[22]  Michel Gendreau,et al.  GENIUS-CP: a Generic Single-Vehicle Routing Algorithm , 1997, CP.

[23]  Michel Gendreau,et al.  A View of Local Search in Constraint Programming , 1996, CP.