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Journal of Heuristics

, Volume 11, Issue 4, pp 267–306 | Cite as

Local Search for Vehicle Routing and Scheduling Problems: Review and Conceptual Integration

  • Birger Funke
  • Tore Grünert
  • Stefan Irnich
Article

Abstract

Local search and local search-based metaheuristics are currently the only available methods for obtaining good solutions to large vehicle routing and scheduling problems. In this paper we provide a review of both classical and modern local search neighborhoods for this class of problems. The intention of this paper is not only to give an overview but to classify and analyze the structure of different neighborhoods. The analysis is based on a formal representation of VRSP solutions given by a unifying giant-tour model. We describe neighborhoods implicitly by a set of transformations called moves and show how moves can be decomposed further into partial moves. The search method has to compose these partial moves into a complete move in an efficient way. The goal is to find a local best neighbor and to reach a local optimum as quickly as possible. This can be achieved by search methods, which do not scan all neighbor solutions explicitly. Our analysis shows how the properties of the partial moves and the constraints of the VRSP influences the choice of an appropriate search technique.

Keywords

local search search techniques vehicle routing and scheduling 

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References

  1. Aarts, E. and J. Lenstra. (1997). Local Search in Combinatorial Optimization. Wiley, Chichester.Google Scholar
  2. Ahuja, R., N. Boland, and I. Dumitrescu. (2001a). “Exact and Heuristic Algorithms for the Subset Disjoint Minimum Cost Cycle Problem.” Technical report, MIT, Boston.Google Scholar
  3. Ahuja, R., O. Ergun, J. Orlin, and A. Punnen. (1999). “A Survey of Very Large-Scale Neighborhood Search Techniques.” Technical report, Department of Industrial & Systems Engineering, University of Florida, Gainesville, FL 32611.Google Scholar
  4. Ahuja, R., J. Orlin, and D. Sharma. (2001b). “Multi-Exchange Neighborhood Structures for the Capacitated Minimum Spanning Tree Problem.” Mathematical Programming, Series A 91(1), 71–97.Google Scholar
  5. Balas, E. and N. Simonetti. (2001). “Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study.” INFORMS Journal on Computing 13(1), 56–75.CrossRefGoogle Scholar
  6. Balas, E. (1999). “New Classes of Efficiently Solvable Generalized Traveling Salesman Problems.” Annals of Operations Research 86, 529–558.CrossRefGoogle Scholar
  7. Beasley, J. (1983). “Route First—Cluster Second Methods for Vehicle Routing. OMEGA International Journal of Management Science 11(4), 403–408.CrossRefGoogle Scholar
  8. Bentley, J. (1992). “Fast Algorithms for Geometric Traveling Salesman Problems.” Operations Research Society of America 4(4), 387–411.Google Scholar
  9. Bodin, L.D., B. Golden, A. Assad, and M. Ball. (1983). “Routing and Scheduling of Vehicles and Crews—The State of the Art.” Computers & Operations Research 10, 63–211.Google Scholar
  10. Bräysy, O. and M. Gendreau. (2005a). “Vehicle Routing with Time Windows, Part II: Metaheuristics.” Transportation Science 39(1), 119–139.CrossRefGoogle Scholar
  11. Bräysy, O. and M. Gendreau. (2005b). “Vehicle Routing with Time Windows, Part I: Route Construction and Local Search Algorithms.” Transportation Science 39(1), 104–118.CrossRefGoogle Scholar
  12. Burke, E., P. Cowling, and R. Keuthen. (2001). “Effective Local and Guided Variable Neighbourhood Search Methods for the Asymmetric Travelling Salesman Problem.” In E. Boers, J. Gottlieb, P. Lanzi, R. Smith, S. Cagnoni, E. Hart, G. Raidl, and H. Tijink, (eds.), Applications of Evolutionary Computing, Springer Verlag, Berlin, pp. 203–212.Google Scholar
  13. Carlier, J. and P. Villon. (1990). “A New Heuristic for the Traveling Salesman Problem.” RAIRO—Recherche opérationelle/Operations Research 24(3), 245–253.Google Scholar
  14. Christofides, N. and S. Eilon. (1969). “An Algorithm for the Vehicle-Dispatching Problem.” Operational Research Quarterly 20(3), 309–318.Google Scholar
  15. Congram, R., C. Potts, and S. van de Velde. (2002). “An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Sceduling Problem.” INFORMS Journal on Computing 14(1), 52–67.CrossRefMathSciNetGoogle Scholar
  16. Cordeau, J., G. Desaulniers, J. Desrosiers, M. Solomon, and F. Soumis. (2002a). “VRP with Time Windows.” In Toth and Vigo (eds.), (2002c), chapter 7, pp. 155–194.Google Scholar
  17. Cordeau, J., M. Gendreau, G. Laporte, J. Potvin, and F. Semet. (2002b). “A Guide to Vehicle Routing Heuristics.” Journal of the Operational Research Society 53, 512–522.CrossRefGoogle Scholar
  18. Cordone, R. and R. Wolfer Calvo. (2001). “A Heuristic for the Vehicle Routing Problem with Time Windows.” Journal of Heuristics 7, 107–129.CrossRefGoogle Scholar
  19. Cornuéjols, G., D. Naddef, and W. Pulleyblank. (1983). “Halin Graphs and the Traveling Salesman Problem.” Mathematical Programming 26, 287–294.Google Scholar
  20. Croes, G. (1958). “A Method for Solving Traveling-Salesman Problems.” Operations Research 6, 791–812.Google Scholar
  21. Desaulniers, G., J. Desrosiers, A. Erdmann, M. Solomon, and F. Soumis. (2002). “VRP with Pickup and Delivery.” In Toth and Vigo (eds.), (2002c) chapter 9, pp. 225–242.Google Scholar
  22. Desaulniers, G., J. Desrosiers, I. Ioachim, M. Solomon, F. Soumis, and D. Villeneuve. (1998). “A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems.” In T. Crainic and G. Laporte (eds.), Fleet Management and Logistics, chapter 3. Boston, Dordrecht, London: Kluwer Academic Publisher, pp. 57–93.Google Scholar
  23. Desaulniers, G. and D. Villeneuve. (2000). “The Shortest Path Problem with Time Windows and Linear Waiting Costs.” Transportation Science 34(3), 312–319.CrossRefGoogle Scholar
  24. Desrosiers, J., Y. Dumas, M. Solomon, and F. Soumis. (1995). “Time Constrained Routing and Scheduling.” In M. Ball, T. Magnanti, C. Monma, and G. Nemhauser (eds.), Handbooks in Operations Research and Management Science, Vol. 8, Network Routing, chapter 2. Amsterdam: Elsevier, pp. 35–139.Google Scholar
  25. De#x0311;neko, V. and Woeginger, G. (2000). “A Study of Exponential Neighborhoods for the Travelling Salesman Problem and for the Quadratic Assignment Problem.” Mathematical Programming 87(3), 519–542.CrossRefGoogle Scholar
  26. Ergun, O., J. Orlin, and A. Steele-Feldman. (2002). “Creating Very Large Scale Neighborhoods Out of Smaller Ones by Compounding Moves: A Study on the Vehicle Routing Problem.” Technical report, Department of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA.Google Scholar
  27. Funke, B., T. Grünert, and S. Irnich. (2004). “A Note on Single Alternating Cycle Neighborhoods for the TSP.” Journal of Heuristics (to appear).Google Scholar
  28. Funke, B. (2003). “Effiziente Lokale Suche für Vehicle Routing und Scheduling Probleme mit Ressourcenbeschränkungen.” PhD thesis, Fakultät für Wirtschaftswissenschaften, RWTH Aachen, Templergraben 64, 52062 Aachen.Google Scholar
  29. Gambardella, L., É. Taillard, and G. Agazzi. (1999). “MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows.” In D. Corne, M. Dorigo, and F. Glover (eds.), New Ideas in Optimization, chapter 5. London: McGraw-Hill, pp. 63–76.Google Scholar
  30. Gendreau, M., A. Hertz, G. Laporte, and M. Stan. (1998). “A Generalized Insertion Heuristics for the Traveling Salesman Problem with Time Windows.” Operations Research 43(3), 330–335.Google Scholar
  31. Gendreau, M., A. Hertz, and G. Laporte (1992). “New Insertion and Postoptimization Procedures for the Traveling Salesman Problem.” Operations Research 40(6), 1086–1094.MathSciNetGoogle Scholar
  32. Gilmore, P., E. Lawler, and D. Shmoys. (1985). “Well-Solved Special Cases.” In Lawler et al., (eds.), (1985), chapter 4. pp. 87–143.Google Scholar
  33. Glover, F. and M. Laguna. (1997). Tabu Search. Dortrecht: Kluwer.Google Scholar
  34. Glover, F. and A. Punnen. (1994). “The Traveling Salesman Problem: Linear Time Heuristics with Exponential Combinatorial Leverage.” Technical report, US West Chair in Systems Science, University of Colorado, Boulder, School of Business, Campus Box 419, Boulder, CO, 80309.Google Scholar
  35. Glover, F. (1991). “Multilevel Tabu Search and Embedded Search Neighborhoods for the Travling Salesman Problem.” Technical report, US West Chair in Systems Science, University of Colorado, Boulder, School of Business, Campus Box 419, Boulder, CO, 80309.Google Scholar
  36. Glover, F. (1992). “New Ejection Chain and Alternating Path Methods for Traveling Salesman Problems.” In O. Balci, R. Sharda, and S. Zenios (eds.), Computer Science and Operations Research—New Developments in their Interfaces. Pergamon Press, pp. 491–508.Google Scholar
  37. Glover, F. (1996a). “Ejection Chains, Reference Structures and Alternating Path Structures for Traveling Salesman Problems.” Discrete Applied Mathematics 65, 223–253.CrossRefGoogle Scholar
  38. Glover, F. (1996b).“Finding a Best Traveling Salesman 4-opt Move in the Same Time as a Best 2-opt Move.” Journal of Heuristics 2, 169–179.CrossRefGoogle Scholar
  39. Gutin, G. and A. Punnen (eds.). (2002). The Traveling Salesman Problem and Its Variations, Vol. 12 of Combinatorial Optimization. Dordrecht: Kluwer.Google Scholar
  40. Irnich, S. and G. Desaulniers. (2004). “Shortest Path Problems with Resource Constraints.” Technical Report G-2004-11, Les Cahiers du GERAD, HEC Montréal, Montréal, Quebec, Canada.Google Scholar
  41. Irnich, S., B. Funke, and T. Grünert. (2004). “Sequential Search and Its Aplication to Vehicle-Routing Problems.” Computers & Operations Research (to appear).Google Scholar
  42. Johnson, D. and L. McGeoch. (1997). “The Traveling Salesman Problem: A Case Study in Local Optimization.” In E. Aarts and J. Lenstra (eds.), Local Search in Combinatorial Optimization, chapter 8. Chichester: Wiley, pp. 215–310.Google Scholar
  43. Kernighan, B. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.” Bell Syst. Tech. J. 49, 291–307.Google Scholar
  44. Kindervater, G. and M. Savelsbergh. (1997). “Vehicle Routing: Handling Edge Exchanges.” In E. Aarts and J. Lenstra (eds.), Local Search in Combinatorial Optimization, chapter 10. Chichester: Wiley, pp. 337–360.Google Scholar
  45. Lawler, E., J. Lenstra, A. Rinnooy Kan, and D. Shmoys, (eds.). (1985). “The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization.” Wiley-Interscience Series in Discrete Mathematics. Chichester: Wiley.Google Scholar
  46. Lin, S. and B. Kernighan. (1973). “An Effective Heuristic Algorithm for the Traveling-Salesman Problem.” Operations Research 21, 498–516.Google Scholar
  47. Lin, S. (1965). “Computer Solutions of the Traveling Salesman Problem.” Bell System Technical Journal 44, 2245–2269.Google Scholar
  48. Magos, D. and T. Miliotis. (1994). “An Algorithm for the Planar Three-Index Assignment Problem.” European Journal of Operational Research 77(1), 141–153.CrossRefGoogle Scholar
  49. Or, I. (1976). “Traveling Salesman-Type Problems and their Relation to the Logistics of Regional Blood Banking.” PhD thesis, Department of Industrial Engineering and Management Sciences. Northwestern University, Evanston, IL.Google Scholar
  50. Osman, I. (1993). “Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problem.” Annals of Operations Research 41, 421–451.CrossRefGoogle Scholar
  51. Potvin, J., G. Lapalme, and J. Rousseau (1989). “A Generalized k-opt Exchange Procedure for the MTSP.” Information Systems and Operations Research 27(4), 474–481.Google Scholar
  52. Prins, C. (2003). “A Simple and Effective Evolutionary Algorithm for the Vehicle Routing Problem.” Computers & Operations Research 1–18 (to appear).Google Scholar
  53. Rego, C. and F. Glover. (2002). “Local Search and Metaheuristics.” In G. Gutin and A. Punnen (eds.), The Traveling Salesman Problem and Its Variations, volume 12 of Combinatorial Optimization, chapter 8. Dordrecht: Kluwer, pp. 309–368.Google Scholar
  54. Rego, C. (1998). “A Subpath Ejection Method for the Vehicle Routing Problem.” Management Science 44(10), 1447–1459.Google Scholar
  55. Russell, R. (1995). “Hybrid Heuristics for the Vehicle Routing Problem with Time Windows.” Transportation Science 29(2), 156–166.Google Scholar
  56. Russell, R. and D. Gribbin. (1991). “A Multiphase Approach to the Period Routing Problem.” Networks 21, 747–765.Google Scholar
  57. Savelsbergh, M. and M. Sol. (1985). “The General Pickup and Delivery Problem.” Transportation Science 29(1), 17–29.Google Scholar
  58. Schrimpf, G., J. Schneider, H. Stamm-Wilbrandt, and G. Dueck. (2000). “Record Breaking Optimization Results Using the Ruin and Recreate Principle.” Journal of Computational Physics 159, 139–171.CrossRefMathSciNetGoogle Scholar
  59. Taillard, É. (1993). “Parallel Iterative Search Methods for Vehicle Routing Problems.” Networks 23, 661–676.Google Scholar
  60. Thompson, P. and H. Psaraftis. (1993). “Cyclic Transfer Algorithms for Multivehicle Routing and Scheduling Problems.” Operations Research 41(5), 935–946.MathSciNetGoogle Scholar
  61. Toth, P. and D. Vigo. (1996). “Fast Local Search Algorithms for the Handicapped Persons Transportation Problem.” In I. Osman and J. Kelly (eds.), Meta-Heuristics: Theory & Application, chapter 41. Boston: Kluwer Academic, pp. 677–690.Google Scholar
  62. Toth, P. and D. Vigo. (2002a). “Branch-and-Bound Algorithms for the Capacitated VRP.” In Toth and Vigo (eds.), The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications (2002c), chapter 2, pp. 29–51.Google Scholar
  63. Toth, P. and D. Vigo. (2002b). “An Overview of Vehicle Routing Problems.” In Toth and Vigo (eds.), The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications (2002c), chapter 1, pp. 1–23.Google Scholar
  64. Toth, P. and D. Vigo (eds.). (2002c). The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications. Philadelphia: Society for Industrial and Applied Mathematics.Google Scholar
  65. Voß, S., S. Martello, I. Osman, and C. Roucairol. (1999). Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Boston: Kluwer Academic.Google Scholar
  66. Walshaw, C. (2002). “A Multilevel Approach to the Travelling Salesman Problem.” Operations Research 50(5), 862–877.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.GTS Systems and Consulting GmbHHerzogenrathGermany
  2. 2.Deutsche Post Lehrstuhl für Optimierung von DistributionsnetzwerkenRWTH Aachen UniversityAachenGermany

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