Abstract
This paper surveys the research on the Tabu Search heuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes for a fleet of vehicles from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. In addition to describing basic features of each method, experimental results for Solomon’s benchmark test problems are presented and analyzed.
Similar content being viewed by others
References
Bachem A., Hochstättler W. and Malich M. (1996). The Simulated Trading Heuristic for Solving Vehicle Routing Problems.Discrete Applied Mathematics 65, 47–72.
Badeau P., Gendreau M., Guertin F., Potvin J.-Y. and Taillard E. (1997). A Parallel Tabu Search Heuristic for the Vehicle Routing Problem with Time Windows.Transportation Research C 5, 109–122.
Beasley J.E. (1990). A Lagrangian Heuristic for Set Covering Problems.Naval Research Logistics 37, 151–164.
Berger J., Barkaoui M. and Bräysy O. (2001). A Route-directed Hybrid Genetic Approach for the Vehicle Routing Problem with Time Windows. Working Paper, Defence Research Establishment Valcartier, Canada.
Bracca J., Bramel J. and Simchi-Levi D. (1994). A Computerized Approach to the New York City School Bus Routing Problem.IEE Transactions 29, 693–702.
Brandão J. (1999). Metaheuristic for the Vehicle Routing Problem with Time Windows. In: Voss S., Martello S., Osman I.H. and Roucairol C. (eds.),Metaheuristics Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, 19–36.
Bräysy O. (2001a). Local Search and Variable Neighborhood Search Algorithms for the Vehicle Routing Problem with Time Windows. Ph.D. Thesis, University of Vaasa, Finland.
Bräysy O. (2001b). A Reactive Variable Neighbourhood Search for the Vehicle Routing Problem with Time Windows.INFORMS Journal on Computing (to appear).
Bräysy O. and Gendreau M. (2001a). Route Construction and Local Search Algorithms for the Vehicle Routing Problem with Time Windows. Internal Report STF42 A01024, SINTEF Applied Mathematics, Department of Optimization, Norway.
Bräysy O. and Gendreau M. (2001b). Genetic Algorithms for the Vehicle Routing Problem with Time Windows. Internal Report STF42 A01021, SINTEF Applied Mathematics, Department of Optimization, Norway.
Bräysy O., Gendreau M., Hasle G. and Løkketangen A. (2002). A Survey of Rich Vehicle Routing Models and Heuristic Solution Techniques. Working Paper, SINTEF Applied Mathematics, Department of Optimization, Norway.
Campbell A., Clarke L. and Savelsbergh M. (2001). Inventory Routing in Practice. In: Toth P. and Vigo D. (eds.),The Vehicle Routing Problem. SIAM, 309–330.
Carlton W.B. (1995). A Tabu Search Approach to the General Vehicle Routing Problem. Ph.D. Thesis, University of Texas, Austin, U.S.A.
Chiang W.C. and Russell R.A. (1997). A Reactive Tabu Search Metaheuristic for the Vehicle Routing Problem with Time Windows.INFORMS Journal on Computing 9, 417–430.
Clarke G. and Wright J.W. (1964). Scheduling of Vehicles from a Central Depot to a Number of Delivery Points.Operations Research 12, 568–581.
Cook W. and Rich J.L. (1999). A Parallel Cutting-Plane Algorithm for the Vehicle Routing Problems with Time Windows. Working Paper, Department of Computational and Applied Mathematics, Rice University, Houston.
Cordeau J.F., Desaulniers G., Desrosiers J., Solomon M.M. and Soumis F. (2001a). The VRP with Time Windows. In: Toth P. and Vigo D. (eds.),The Vehicle Routing Problem. SIAM, 157–193.
Cordeau J.-F., Laporte G. and Mercier A. (2001b). A Unified Tabu Search Heuristic for Vehicle Routing Problems with Time Windows.Journal of the Operational Research Society 52, 928–936.
Crainic T.G. and Laporte G. (1997). Planning Models for Freight Transportation.European Journal of Operational Research 97, 409–438.
De Backer B. and Furnon V. (1997). Meta-heuristics in Constraint Programming Experiments with Tabu Search on the Vehicle Routing Problem. Second International Conference on Metaheuristics (MIC’97), Sophia Antipolis, France.
De Backer B., Furnon V., Kilby P., Prosser P. and Shaw P. (2000). Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics.Journal of Heuristics 6, 501–523.
Desrochers M., Lenstra J.K., Savelsbergh M.W.P. and Soumis F. (1988). Vehicle Routing with Time Windows: Optimization and Approximation. In: Golden B. and Assad A. (eds.),Vehicle Routing: Methods and Studies. Elsevier Science Publishers, 65–84.
Desrosiers J., Dumas Y., Solomon M.M. and Soumis F. (1995). Time Constrained Routing and Scheduling. In: Ball M.O., Magnanti T.L., Monma C.L. and Nemhauser G.L. (eds.),Handbooks in Operations Research and Management Science 8: Network Routing. Elsevier Science Publishers, 35–139.
Dongarra J. (1998). Performance of Various Computers Using Standard Linear Equations Software. Report CS-89-85, Department of Computer Science, University of Tennessee, U.S.A.
Duhamel C., Potvin J.-Y. and Rousseau J.-M. (1997). A Tabu Search Heuristic for the Vehicle Routing Problem with Backhauls and Time Windows.Transportation Science 31, 49–59.
Gambardella L.M., Taillard E. and Agazzi G. (1999). MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows. In: Corne D., Dorigo M. and Glover F. (eds.),New Ideas in Optimization. McGraw-Hill, 63–76.
García B.-L., Potvin J.-Y. and Rousseau J.-M. (1994). A Parallel Implementation of the Tabu Search Heuristic for Vehicle Routing Problems with Time Window Constraints.Computers and Operations Research 21, 1025–1033.
Gehring H. and Homberger J. (1999). A Parallel Hybrid Evolutionary Metaheuristic for the Vehicle Routing Problem with Time Windows. In: Miettinen K., Mäkelä M. and Toivanen J. (eds.),Proceedings of EUROGEN99 — Short Course on Evolutionary Algorithms in Engineering and Computer Science, Reports of the Department of Mathematical Information Technology, Series A. Collections, No. A 2/1999. Universityof Jyväskylä 57–64.
Gehring H. and Homberger J. (2001). Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows.Asia-Pacific Journal of Operational Research 18, 35–47.
Gendreau M., Hertz A. and Laporte G. (1992). A New Insertion and Postoptimization Procedure for the Traveling Salesman Problem.Operations Research 40, 1086–1093.
Gendreau M., Hertz A., Laporte G. and Stan M. (1998). A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows.Operations Research 46, 330–335.
Glover F. (1986). Future Paths for Integer Programming and Links to Artificial Intelligence.Computers and Operations Research 13, 533–549.
Glover F. (1989). Tabu Search Ű Part I.Journal on Computing 1, 190–206.
Glover F. (1990). Tabu Search Ű Part II.Journal on Computing 2, 4–32.
Glover F. (1991). Multilevel Tabu Search and Embedded Search Neighborhoods for the Traveling Salesman Problem. Working Paper, College of Business and Administration, University of Colorado, U.S.A.
Glover F. (1992). New Ejection Chain and Alternating Path Methods for Traveling Salesman Problems. In: Balci O., Sharda R. and Zenios S. (eds.),Computer Science and Operations Research: New Developments in Their Interfaces. Pergamon Press, 449–509.
Glover F. and Laguna M. (1997).Tabu Search. Kluwer Academic Publishers.
Golden B.L. and Assad A.A. (1986). Perspectives on Vehicle Routing: Exciting New Developments.Operations Research 34, 803–809.
Golden B.L. and Wasil E.A. (1987). Computerized Vehicle Routing in the Soft Drink Industry.Operations Research 35, 6–17.
Golden B.L. and Assad A.A. (1988).Vehicle Routing: Methods and Studies. Elsevier Science Publishers.
Golden B.L., Assad A.A. and Wasil E.A. (2001). Routing Vehicles in the Real World: Applications in the Solid Waste, Beverage, Food, Dairy and Newspaper Industries. In: Toth P. and Vigo D. (eds.),The Vehicle Routing Problem. SIAM, 245–286.
Halse K. (1992). Modeling and Solving Complex Vehicle Routing Problems. Ph.D. Thesis, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark.
Hertz A., Taillard E. and De Werra D. (1997). Tabu Search. In: Aarts E. and Lenstra J.K. (eds.),Local Search in Combinatorial Optimization. John Wiley, 121–136.
Holland J.H. (1975).Adaptation in Natural and Artificial Systems. University of Michigan Press.
Homberger J. and Gehring H. (1999). Two Evolutionary Meta-heuristics for the Vehicle Routing Problem with Time Windows.INFOR 37, 297–318.
King G.F. and Mast C.F. (1997). Excess Travel: Causes, Extent and Consequences.Transportation Research Record 1111, 126–134.
Lambert V., Laporte G. and Louveaux F. (1993). Designing Collection Routes through Bank Branches.Computers and Operations Research 20, 783–791.
Larsen J. (1999). Parallelization of the Vehicle Routing Problem with Time Windows. Ph.D. Thesis, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark.
Lau H.C., Lim Y.F. and Liu Q. (2000). Diversification of Neighborhood via Constraint-Based Local Search and its Application to VRPTW. Working paper, School of Computing, National University of Singapore.
Li H., Lim A. and Huang J. (2001). Local Search with Annealing-like Restarts to Solve the VRPTW. Working paper, Department of Computer Science, National University of Singapore.
Lund K., Madsen O.B.G. and Rygaard J.M. (1996). Vehicle Routing Problems with Varying Degree of Dynamism. Technical Report, IMM, The department of Mathematical Modelling, Technical University of Denmark.
Mechti R., Poujade S., Roucairol C. and Lemarié B. (2001). Global and Local Moves in Tabu Search: A Real-Life Mail Collecting Application. Manuscript, PriSM laboratory, University of Versailles, France.
Metropolis W., Rosenbluth A., Rosenbluth M., Teller A. and Teller E. (1953). Equation of the State Calculations by Fast Computing Machines.Journal of Chemical Physics 21, 1087–1092.
Mladenovic N. and Hansen P. (1997). Variable Neighborhood Search.Computers and Operations Research 24, 1097–1100.
Nanry W.P. and Barnes J.W. (2000). Solving the Pickup and Delivery Problem with Time Windows Using Reactive Tabu Search.Transportation Research B 34, 107–121.
Or I. (1976). Traveling Salesman-Type Combinatorial Problems and Their Relation to the Logistics of Regional Blood Banking. Ph.D. Thesis, Northwestern University, Evanston, Illinois.
Osman I.H. (1993). Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problems.Annals of Operations Research 41, 421–452.
Potvin J.-Y. and Rousseau J.-M. (1993). A Parallel Route Building Algorithm for the Vehicle Routing and Scheduling Problem with Time Windows.European Journal of Operational Research 66, 331–340.
Potvin J.-Y. and Rousseau J.-M. (1995). An Exchange Heuristic for Routing Problems with Time Windows.Journal of the Operational Research Society 46, 1433–1446.
Potvin J.-Y., Kervahut T., Garcia B.L. and Rousseau J.-M. (1996). The Vehicle Routing Problem with Time Windows Part I: Tabu Search.INFORMS Journal on Computing 8, 157–164.
Rochat Y. and Taillard E. (1995). Probabilistic Diversification and Intensification in Local Search for Vehicle Routing.Journal of Heuristics 1, 147–167.
Russell R.A. (1995). Hybrid Heuristics for the Vehicle Routing Problem with Time Windows.Transportation Science 29, 156–166.
Savelsbergh, M.W.P. (1992). The Vehicle Routing Problem with Time Windows: Minimizing Route Duration.Journal on Computing 4, 146–154.
Schulze J. and Fahle T. (1999). A Parallel Algorithm for the Vehicle Routing Problem with Time Window Constraints.Annals of Operations Research 86, 585–607.
Shaw P. (1998). Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems. In: Maher M. and Puget J.-F. (eds.),Principles and Practice of Constraint Programming — CP98, Lecture Notes in Computer Science. Springer-Verlag, 417–431.
Sigurd M., Pisinger D. and Sig M. (2000). The Pickup and Delivery Problem with Time Windows and Precedences. Technical Report TR-00/08, Department of Computer Science, University of Copenhagen, Denmark.
Solomon M.M. (1987). Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints.Operations Research 35, 254–265.
Solomon M.M. and Desrosiers J. (1988). Time Window Constrained Routing and Scheduling Problems.Transportation Science 22, 1–13.
Taillard E., Badeau P., Gendreau M., Guertin F. and Potvin J.-Y. (1997). A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows.Transportation Science 31, 170–186.
Tan K.C., Lee L.H. and Zhu K.Q. (2000). Heuristic Methods for Vehicle Routing Problem with Time Windows.Proceedings of the 6th International Symposium on Artificial Intelligence and Mathematics. Ft. Lauderdale, Florida.
Thangiah S., Osman I.H. and Sun T. (1994). Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problems with Time Windows. Working Paper UKC/IMS/OR94/4, Institute of Mathematics and Statistics, University of Kent, Canterbury.
Vaidyanathan B.S., Matson J.O., Miller D.M. and Matson J.E. (1999). A Capacitated Vehicle Routing Problem for Just-In-Time Delivery.IEE Transactions 31, 1083–1092.
Voudouris C. (1997). Guided Local Search for Combinatorial Problems. Ph.D. Thesis, Department of Computer Science, University of Essex, Colchester, UK.
Wee Kit H., Chin J. and Lim A. (2001). A Hybrid Search Algorithm for the Vehicle Routing Problem with Time Windows.International Journal on Artificial Intelligence Tools (to appear).
Author information
Authors and Affiliations
Additional information
This work was partially supported by the Emil Aaltonen Foundation, Liikesivistysrahasto Foundation, the Canadian Natural Science and Engineering Research Council and the TOP program funded by the Research Council of Norway. This support is gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Bräysy, O., Gendreau, M. Tabu Search heuristics for the Vehicle Routing Problem with Time Windows. Top 10, 211–237 (2002). https://doi.org/10.1007/BF02579017
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02579017