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

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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.

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References

  • Aarts, E. and J. Lenstra. (1997). Local Search in Combinatorial Optimization. Wiley, Chichester.

  • Ahuja, R., N. Boland, and I. Dumitrescu. (2001a). “Exact and Heuristic Algorithms for the Subset Disjoint Minimum Cost Cycle Problem.” Technical report, MIT, Boston.

  • 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.

  • 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 

  • 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.

    Article  Google Scholar 

  • Balas, E. (1999). “New Classes of Efficiently Solvable Generalized Traveling Salesman Problems.” Annals of Operations Research 86, 529–558.

    Article  Google Scholar 

  • Beasley, J. (1983). “Route First—Cluster Second Methods for Vehicle Routing. OMEGA International Journal of Management Science 11(4), 403–408.

    Article  Google Scholar 

  • Bentley, J. (1992). “Fast Algorithms for Geometric Traveling Salesman Problems.” Operations Research Society of America 4(4), 387–411.

    Google Scholar 

  • 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 

  • Bräysy, O. and M. Gendreau. (2005a). “Vehicle Routing with Time Windows, Part II: Metaheuristics.” Transportation Science 39(1), 119–139.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Christofides, N. and S. Eilon. (1969). “An Algorithm for the Vehicle-Dispatching Problem.” Operational Research Quarterly 20(3), 309–318.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Cordone, R. and R. Wolfer Calvo. (2001). “A Heuristic for the Vehicle Routing Problem with Time Windows.” Journal of Heuristics 7, 107–129.

    Article  Google Scholar 

  • Cornuéjols, G., D. Naddef, and W. Pulleyblank. (1983). “Halin Graphs and the Traveling Salesman Problem.” Mathematical Programming 26, 287–294.

    Google Scholar 

  • Croes, G. (1958). “A Method for Solving Traveling-Salesman Problems.” Operations Research 6, 791–812.

    Google Scholar 

  • 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.

  • 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 

  • Desaulniers, G. and D. Villeneuve. (2000). “The Shortest Path Problem with Time Windows and Linear Waiting Costs.” Transportation Science 34(3), 312–319.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

  • Funke, B., T. Grünert, and S. Irnich. (2004). “A Note on Single Alternating Cycle Neighborhoods for the TSP.” Journal of Heuristics (to appear).

  • 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.

  • 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.

  • 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 

  • Gendreau, M., A. Hertz, and G. Laporte (1992). “New Insertion and Postoptimization Procedures for the Traveling Salesman Problem.” Operations Research 40(6), 1086–1094.

    MathSciNet  Google Scholar 

  • Gilmore, P., E. Lawler, and D. Shmoys. (1985). “Well-Solved Special Cases.” In Lawler et al., (eds.), (1985), chapter 4. pp. 87–143.

  • Glover, F. and M. Laguna. (1997). Tabu Search. Dortrecht: Kluwer.

    Google Scholar 

  • 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.

  • 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.

  • 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.

  • Glover, F. (1996a). “Ejection Chains, Reference Structures and Alternating Path Structures for Traveling Salesman Problems.” Discrete Applied Mathematics 65, 223–253.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gutin, G. and A. Punnen (eds.). (2002). The Traveling Salesman Problem and Its Variations, Vol. 12 of Combinatorial Optimization. Dordrecht: Kluwer.

    Google Scholar 

  • 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.

  • Irnich, S., B. Funke, and T. Grünert. (2004). “Sequential Search and Its Aplication to Vehicle-Routing Problems.” Computers & Operations Research (to appear).

  • 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 

  • Kernighan, B. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.” Bell Syst. Tech. J. 49, 291–307.

    Google Scholar 

  • 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 

  • 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 

  • Lin, S. and B. Kernighan. (1973). “An Effective Heuristic Algorithm for the Traveling-Salesman Problem.” Operations Research 21, 498–516.

    Google Scholar 

  • Lin, S. (1965). “Computer Solutions of the Traveling Salesman Problem.” Bell System Technical Journal 44, 2245–2269.

    Google Scholar 

  • Magos, D. and T. Miliotis. (1994). “An Algorithm for the Planar Three-Index Assignment Problem.” European Journal of Operational Research 77(1), 141–153.

    Article  Google Scholar 

  • 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.

  • Osman, I. (1993). “Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problem.” Annals of Operations Research 41, 421–451.

    Article  Google Scholar 

  • 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 

  • Prins, C. (2003). “A Simple and Effective Evolutionary Algorithm for the Vehicle Routing Problem.” Computers & Operations Research 1–18 (to appear).

  • 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 

  • Rego, C. (1998). “A Subpath Ejection Method for the Vehicle Routing Problem.” Management Science 44(10), 1447–1459.

    Google Scholar 

  • Russell, R. (1995). “Hybrid Heuristics for the Vehicle Routing Problem with Time Windows.” Transportation Science 29(2), 156–166.

    Google Scholar 

  • Russell, R. and D. Gribbin. (1991). “A Multiphase Approach to the Period Routing Problem.” Networks 21, 747–765.

    Google Scholar 

  • Savelsbergh, M. and M. Sol. (1985). “The General Pickup and Delivery Problem.” Transportation Science 29(1), 17–29.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Taillard, É. (1993). “Parallel Iterative Search Methods for Vehicle Routing Problems.” Networks 23, 661–676.

    Google Scholar 

  • Thompson, P. and H. Psaraftis. (1993). “Cyclic Transfer Algorithms for Multivehicle Routing and Scheduling Problems.” Operations Research 41(5), 935–946.

    MathSciNet  Google Scholar 

  • 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 

  • 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.

  • 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.

  • 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 

  • 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 

  • Walshaw, C. (2002). “A Multilevel Approach to the Travelling Salesman Problem.” Operations Research 50(5), 862–877.

    Article  Google Scholar 

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Authors and Affiliations

  1. GTS Systems and Consulting GmbH, Herzogenrath, Germany

    Birger Funke & Tore Grünert

  2. Deutsche Post Lehrstuhl für Optimierung von Distributionsnetzwerken, RWTH Aachen University, Aachen, Germany

    Stefan Irnich

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  1. Birger Funke
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  2. Tore Grünert
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  3. Stefan Irnich
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Correspondence to Birger Funke.

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Funke, B., Grünert, T. & Irnich, S. Local Search for Vehicle Routing and Scheduling Problems: Review and Conceptual Integration. J Heuristics 11, 267–306 (2005). https://doi.org/10.1007/s10732-005-1997-2

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