Abstract
This paper discusses neighborhood search algorithms where the size of the neighborhood is “very large” with respect to the size of the input data. We concentrate on such a very large scale neighborhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts, swaps, and insertions. We present a systematic way of creating and searching CIM neighborhoods for routing problems with side constraints. For such problems, the exact search of the CIM neighborhood becomes NP-hard. We introduce a multi-label shortest path algorithm for searching these neighborhoods heuristically. Results of a computational study on the vehicle routing problem with capacity and distance restrictions shows that CIM algorithms are very competitive approaches for solving vehicle routing problems. Overall, the solutions generated by the CIM algorithm have the best performance among the current solution methodologies in terms of percentage deviation from the best-known solutions for large-scale capacitated VRP instances.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aarts, E. and J.K. Lenstra. (1997). Local Search in Combinatorial Optimization. New York: John Wiley & Sons.
Ahuja, R.K., Ö. Ergun, J.B. Orlin, and A.B. Punnen. (2002) “A Survey of Very Large-Scale Neighborhood Search Techniques.” Discrete Applied Mathematics 123, 75–102.
Ahuja, R.K., J.B. Orlin, and Thomas, L. Magnanti. (1993). Network Flows. NJ: Prentice-Hall.
Ahuja, R.K., J.B. Orlin, and D. Sharma. (2001). “Multi-Exchange Neighborhood Search Algorithms for The Capacitated Minimum Spanning Tree Problem.” Mathematical Programming 91, 71–97.
Christofides, N., A. Mingozzi, and P. Toth. (1979). “The Vehicle Routing Problem.” In N. Christofides, A. Mingozzi, P. Toth, and C. Sandi (eds.), Combinatorial Optimization. Chichester: Wiley.
Clarke, G. and J.W. Wright. (1964). “Scheduling of Vehicles From a Central Depot to a Number of Delivery Points.” Operations Research 12, 568–581.
Congram, R.K. (2000). “Pollynomially Searchable Exponential Neighborhoods for Sequencing Problems in Combinatorial Optimization.” Faculty of Mathematical Studies Thesis, University of Southampton.
Congram, R.K., C.N. Potts, and S.L. van de Velde. (2002). “An Iterated Dynasearch Algorithm for The Single Machine Total Weighted Tardiness Scheduling Problem.” INFORMS Journal on Computing 14, 52–67.
Deineko, V. and G.J. Woeginger. (2000). A Study of Exponential Neighborhoods for The Traveling Salesman Problem and The Quadratic Assignment Problem.” Mathematical Programming Series A 87, 519–542.
Desrochers, M. and F. Soumis. (1988). A Generalized Permanent Labeling Algorithm for the Shortest Path Problem With Time Windows.” INFOR 26, 191–212.
Dongarra, J. (2004). “Performance of Various Computers Using Standard Linear Equations Software.” University of Tennessee, Knoxville TN, 37996, Computer Science Technical Report Number CS-89 85. url:http://www.netlib.org/benchmark/performance.ps
Ergun, Ö. (2001). “New Neighborhood Search Algorithms Based on Exponentially Large Neighborhoods.” Operations Research Center Thesis, MIT.
Firla, R.T., B. Spille, and R. Weismantel. Personal Communication.
Fisher, M. (1995). “Vehicle Routing.” In M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (eds.), Network Routing, Handbooks in OR & MS Vol. 8. Amsterdam: Elsevier.
Gendreau, M., A. Hertz, and G. Laporte. (1994). “A Tabu Search Heuristic for the Vehicle Routing Problem.” Management Science 40, 1276–1290.
Gendreau, M., G. Laporte, and J.-Y. Potvin. (1997). “Vehicle Routing: Modern Heuristics.” In E. Aarts and J.K. Lenstra (eds.), Local Search in Combinatorial Optimization. New York: John Wiley & Sons, pp. 311–336.
Glover, F. (1996). “Ejection Chains, Reference Structures, and Alternating Path Algorithms for The Traveling Salesman Problem, Research Report, University of Colorado-Boulder, Graduate School of Business (1992).” A Short Version Appeared in Discrete Applied Mathematics 65, 223–253.
Glover, F. and M. Laguna. (1997). Tabu Search. Boston: Kluwer Academic Publisher.
Golden, B.L., E.A. Wasil, J.P. Kelly, and I-M. Chao. (1998). “Metaheuristics in Vehicle Routing.” In T.G Crainic, and C. Laporte (eds.), Fleet Management and Logistics. Boston: Kluwer Academic Publisher pp. 33–56.
Kirby, R.F. and R.B. Potts. (1969). “The Minimum Route Problem for Networks With Turn Penalties and Prohibitions.” Transportation Research 3, 397–408.
Laporte, G. and I.H. Osman. (1995). “Routing Problems: A Bibliography, in Freight Transportation.” In G. Laporte, and M. Gendreau (eds.), Annals of Operations Research Vol. 61, pp. 227–262
Liu, C.L. (1985). Elements of Discrete Mathematics. Singapore: McGraw-Hill.
Osman, I.H. (1993). “Metastrategy Simulated Annealing Search Algorithms for The Vehicle Routing Problem.” Annals of Operations Research 41, 421–451.
Potts, C.N. and S.L. van de Velde. (1995). “Dynasearch—Iterative Local Improvement by Dynamic Programming: Part I.” The Traveling Salesman Problem, Technical Report, University of Twente, The Netherlands.
Prins, C. (2004). “A Simple and Effective Evolutionary Algorithm for The Vehicle Routing Problem.” Computers and Operations Research 31, 1985–2002.
Punnen, A.P. and F. Glover. (1996). “Ejection Chains With Combinatorial Leverage for The TSP.” Research Report, University of Colorado-Boulder.
Ralphs, T.K., L. Kopman, W.R. Pulleyblank, and L.E. Trotter, Jr. (2000). “On The Capacitated Vehicle Routing Problem.” Research Report. Updates available at http://www.branchandcut.org.
Rego, C. and C. Roucairol. (1996). “A Parallel Tabu Search Algorithm Using Ejection Chains for The Vehicle Routing Problem. In I.H. Osman and J.P. Kelly (eds.), Meta-Heuristics: Theory & Applications. Boston: Kluwer Academic Publisher, MA, pp. 661–675
Rego, C. (1998). “A Subpath Ejection Method for The Vehicle Routing Problem.” Management Science 44, 1447–1459.
Rochat, Y. and E. Taillard. (1995). “Probabilistic Diversification and Intensification in Local Search for Vehicle Routing.” Journal of Heuristics 1, 147–167.
Taillard, E. (1993). “Parallel Iterative Search Methods for Vehicle Routing Problem.” Networks 23, 661–673.
Thompson, P.M. and J.B. Orlin. (1989). “The Theory of Cyclic Transfers.” Operations Research Center Working Paper, MIT.
Thompson, P.M. and H.N. Psaraftis. (1993). “Cyclic Transfer Algorithms for Multivehicle Routing and Scheduling Problems.” Operations Research 41.
Toth, P. and Vigo, D. (2003). “The Granular Tabu Search and Its Application to The Vehicle Routing Problem.” INFORMS Journal on Computing 15, 333–346.
Toth, P. and D. Vigo. (2002). Vehicle Routing Problem. Philadelphia: Society for Industrial and Applied Mathematics, PA.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ergun, Ö., Orlin, J.B. & Steele-Feldman, A. Creating very large scale neighborhoods out of smaller ones by compounding moves. J Heuristics 12, 115–140 (2006). https://doi.org/10.1007/s10732-006-5561-5
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10732-006-5561-5