Abstract
In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical k-opt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective function drives the search out of local optima. No parameter tuning is required and no random choice is made: these are the distinguishing features with respect to the recent literature. The algorithm has been tested on benchmark problems which prove it to be more effective than comparable algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baker, E.K. and J.R. Shaffer. (1986). “Solution Improvement Heuristic for the Vehicle Routing and Scheduling Problem with Time Window Constrainats.” American Journal of Mathematical and Managenent Sciences 6, 261–300.
Chiang, W.-C. and R. Russell. (1996). “Simulated Annealing Metaheuristics for the Vehicle Routing Problem with Time Windows.” Annals of Operations Research 63, 1–29.
Cordone, R. and R. Wolfler Calvo. (1996). “Note About Time Window Constraints in Routin Problems.” Internal Report 96-005, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano (Submitted).
Desrochers, M., J. Desrosiers, and M.M. Solomon. (1992). “A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows.” Operations Research 40(2), 342–354.
Desrosiers, J., Y. Dumas, M.M Solomon, and F. Soumis. (1995). “Time Constrained Routing and Scheduling.” In Handbooks in Operations Research and Management Science, Vol. 8: Network Routing, North-Holland, pp. 35–139.
Dongarra, J.J. (1998). “Performance of Various Computers Using Standard Linear Equations Software.” Report CS-89-85, Computer Science Departement, University of Tennesse.
Fisher, M.L. and R. Jaikumar. (1981). “A Generalized Assignment Heuristic for the Vehicle Routing Problem.” Networks 11, 109–124.
Fisher, M.L., K.O. Jornsten, and O.B.G. Madsen. (1997). “Vehicle Routing with TimeWindows–Two Optimization Algorithms.” Operations Research 45, 488–492.
Healy, P. and R. Moll. (1995). “A New Extension of Local Search Applied to the Dial-a-Ride Problem.” European Journal of Operational Research 83, 83–104.
Kindervater, G.A.P. and M.W.P. Savelsbergh. (1997). “ehicle Routing: Handling Edge Exchanges.” In Local Search in Combinatorial Optimization. Chichester: Wiley, pp. 337–360.
Kohl, N., J. Desrosiers, O.B.G. Madsen, M.M. Solomon, and F. Soumis. (1997). “K-path Cuts for the Vehicle Routing Problem with Time Windows.” Technical Report 1997-12, Department of Mathematical Modelling, The Technical University of Denmark.
Kohl, N. and O.B.G. Madsen. (1997). “An Optimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Lagrangean Relaxation.” Operations Research 45, 395–406.
Kolen, A.W.J., A.H.G. Rinnooy Kan, and H.W.J.M. Trienekens. (1997). “Vehicle Routing with Time Windows.” Operations Research 35, 266–273.
Kontoravdis, G. and J.F. Bard. (1995). “A GRASP for the Vehicle Routing Problem with Time Windows.” ORSA Journal on Computing 7, 10–23.
Lin, S. (1965). “Computer Solutions to the Travelling Salesman Problem.” Bell System Technical Journal 44, 2245–2269.
Lin, S. and B.W. Kernighan. (1973). “An Effective Heuristic Algorithm for the Travelling Salesman Problem.” Operations Research 21, 498–516.
Or, I. (1976). “Traveling Salesman Type Combinatorial Problems and Their Relation to the Logistics of Blood Banking.” Ph.D. thesis, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois.
Potvin, J.Y. and S. Bengio. (1996). “The Vehicle Routing Problem with TimeWindows—Part II: Genertic Search.” INFORMS Journal of Coputing 8, 165–172.
Potvin, J.Y., T. Kervahut, B.L. Garcia, and J.M. Rousseau. (1996).“The Vehicle Routing Problem with Time Windows—Part I: Tabu Search.” INFORMS Journal of Computing 8, 158–164.
Potvin, J.Y. and J.M. Rousseau. (1993). “A Parallel Route Building Algorithm for the Vehicle Routing and Scheduling Problem with Time Windows.” European Journal of Operational Research 66, 331–340.
Rochat, Y. and F. Semet. (1994). “A Tabu Search Approach for Delivering Pet Food and Flour in Switzerland.” Journal of Operational Research Society 45, 1233–1246.
Rochat, Y. and E.D. Taillard. (1995). “Probabilistic Diversification and Intensification in Local Search for Vehicle Routing.” Journal of Heuristics 1, 147–167.
Russell, R.A. (1977). “An Effective Heuristic for the m-Tour Travelling Salesman Problem with Some Side Conditions.” Operation Research 25, 517–524.
Russell, R.A. (1995). “Hybrid Heuristics for the Vehicle Routing Problems with TimeWindows.” Transportation Science 29, 156–166.
Savelsbergh, M.W.P. (1985). “Local Search in Routing Problems with Time Windows.” Annals of Operations Research 4, 285–305.
Solomon, M.M. (1987). “Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints.” Operations Research 35, 254–265.
Taillard, E.D., P. Badeau, M. Gendreau, F. Guertin, and J.Y. Potvin. (1997). “A Tabu Search Heuristic for the Vehicle Routing Problem with Time Windows.” Transportation Science 31, 170–186.
Thangiah, S.R., I.H. Osman, and T. Sun. (1994). “Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problem with Time Windows.” Technical Report 27, Computer Science Department, Slippery Rock University (Forthcoming in the Annals of OR Transportation, Laporte and Gendreau, eds.).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cordone, R., Calvo, R.W. A Heuristic for the Vehicle Routing Problem with Time Windows. Journal of Heuristics 7, 107–129 (2001). https://doi.org/10.1023/A:1011301019184
Issue Date:
DOI: https://doi.org/10.1023/A:1011301019184