Node-ejection chains for the vehicle routing problem: Sequential and parallel algorithms

We present a Tabu search algorithm for the vehicle routing problem under capacity and distance restrictions. The neighborhood search is based on compound moves generated by a node-ejection chain process. During the course of the algorithm, two types of neighborhood structures are used and crossing infeasible solutions is allowed. Then, a parallel version of the algorithm which exploits the moves’ characteristics is described. Parallel processing is used to explore the solution space more extensively and to accelerate the search process. Tests are carried out on a SUNSparc workstation and the parallel algorithm uses a network of four of these machines. Numerical tests indicate that the sequential version of the algorithm is highly competitive with the best existing heuristics and that the parallel algorithm outperforms all of these algorithms.

[1]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[2]  Fred Glover.  New Ejection Chain and Alternating Path Methods for Traveling Salesman Problems , 1992, Computer Science and Operations Research.

[3]  Jeffrey L. Rummel,et al.  A Subpath Ejection Method for the Vehicle Routing Problem , 1998 .

[4]  F. Glover,et al.  Tabu search and ejection chains—application to a node weighted version of the cardinality-constrained TSP , 1997 .

[5]  Jadranka Skorin-Kapov,et al.  Massively parallel tabu search for the quadratic assignment problem , 1993, Ann. Oper. Res..

[6]  F. Glover.  Tabu Search Fundamentals and Uses , 1995 .

[7]  Fred W. Glover,et al.  Tabu Thresholding: Improved Search by Nonmonotonic Trajectories , 1995, INFORMS J. Comput..

[8]  César Rego,et al.  Relaxed tours and path ejections for the traveling salesman problem , 1998, Eur. J. Oper. Res..

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

[10]  Bruce L. Golden,et al.  A Lagrangean relaxation heuristic for vehicle routing , 1984 .

[11]  Erwin Pesch,et al.  Fast Clustering Algorithms , 1994, INFORMS J. Comput..

[12]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[13]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

[14]  F. Glover,et al.  In Modern Heuristic Techniques for Combinatorial Problems , 1993 .

[15]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[16]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[17]  James P. Kelly,et al.  A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem , 1996, Transp. Sci..

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

[19]  Paulo Morelato França,et al.  VEHICLE ROUTING PROBLEMS VIA TABU SEARCH METAHEURISTIC , 1991 .

[20]  Pierre Hansen,et al.  Variable Neighborhood Decomposition Search , 1998, J. Heuristics.

[21]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

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

[23]  Michel Gendreau,et al.  TOWARDS A TAXONOMY OF PARALLEL TABU SEARCH ALGORITHMS. , 1993 .

[24]  Gilbert Laporte,et al.  Routing problems: A bibliography , 1995, Ann. Oper. Res..

[25]  Fred W. Glover,et al.  Ejection Chains, Reference Structures and Alternating Path Methods for Traveling Salesman Problems , 1996, Discret. Appl. Math..

[26]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[27]  R. H. Mole,et al.  A Sequential Route-building Algorithm Employing a Generalised Savings Criterion , 1976 .

[28]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[29]  Billy E. Gillett,et al.  A Heuristic Algorithm for the Vehicle-Dispatch Problem , 1974, Oper. Res..

[30]  Fred Glover,et al.  Tabu Search and Adaptive Memory Programming — Advances, Applications and Challenges , 1997 .

[31]  J. P. Kelly,et al.  Tabu search for the multilevel generalized assignment problem , 1995 .

[32]  Gilbert Laporte,et al.  An Improved Petal Heuristic for the Vehicle Routeing Problem , 1996 .

[33]  Bezalel Gavish,et al.  Parallel Savings Based Heuristics for the Delivery Problem , 1991, Oper. Res..

[34]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

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

[36]  Michel Gendreau,et al.  TABU SEARCH HEURISTIC FOR THE VEHICLE ROUTING PROBLEM WITH STOCHASTIC DEMANDS AND CUSTOMERS - REVISED EDITION , 1995 .

[37]  Nicos Christofides,et al.  A new exact algorithm for the vehicle routing problem based onq-paths andk-shortest paths relaxations , 1995, Ann. Oper. Res..

[38]  Fred Glover,et al.  Efficient facility layout planning in a maximally planar graph model , 1999 .

[39]  Farid Harche,et al.  A generalized exchange heuristic for the capacitated vehicle routing problem , 1994 .