Abstract
The Traveling Salesman Problem (TSP) is one of the most widely discussed problems in combinatorial optimization. It has many practical applications in fields of distribution and logistics management, scheduling problems etc. Since these problems are hard, in addition to exact algorithms, research has focused on heuristic techniques to solve TSPs. Computational time is a major concern while solving large TSPs. This problem intensifies further if the graph becomes asymmetric (ATSP). Metaheuristics like tabu search are widely used to find a reasonably good tour fast. Given the practical relevance of ATSPs the lack of literature on it is surprising. The primary objective of our work is to implement tabu search for large ATSPs to obtain good tours in reasonable time. To do that, we make the underlying graph sparse by developing an elite tour based preprocessing scheme. Tabu search is implemented on this reduced graph which results in a reduction of computational time. We also create diversified initial tours suitable for multi-start tabu search in this process. We present our computational experiences both on randomly generated instances and benchmark instances.
Similar content being viewed by others
References
Ahr, D., Reinelt, G.: A tabu search algorithm for the min-max k-Chinese postman problem. Comput. Oper. Res. 33(12), 3403–3422 (2006)
Amberg, A., Domschke, W., Vob, S.: Multiple center capacitated arc routing problems: a tabu search algorithm using capacitated trees. Eur. J. Oper. Res. 124(2), 360–376 (2000)
Applegate, D.A., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press (2006)
Augerat, P., Belenguer, J.M., Benavent E., Corberán, A., Naddef, D.: Separating capacity constraints in the cvrp using tabu search. Eur. J. Oper. Res. 106(2–3), 546–557 (1998)
Badeau, P., Gendreau, M., Guertin, F., Potvin, J.-Y., Taillard, E.: A parallel tabu search heuristic for the vehicle routing problem with time windows. Transp. Res. 5, 109–122 (1997)
Barbarosoglu, G., Ozgur, D.: A tabu search algorithm for the vehicle routing problem. Comput. Oper. Res. 26(3), 255–270 (1999)
Basu, S., Ghosh, D.: A review of the tabu search literature on traveling salesman problems. W.P. No. 2008-10-01, IIM Ahmedabad Working Paper Series (2008)
Basu, S., Ghosh, D.: A review of the tabu search literature on traveling salesman problems. Working Paper Series, Indian Institute of Management Ahmedabad, W.P. No. 2008-10-01 (2008)
Bianchessi, N., Righini, G.: Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery. Comput. Oper. Res. 34(2), 578–594 (2007)
Bolduc, M., Laporte, G., Renaud, J., Boctor, F.F.: A tabu search heuristic for the split delivery vehicle routing problem with production and demand calendars. Eur. J. Oper. Res. 202, 122–130 (2010)
Bouthillier, A.L., Crainic, T.G.: A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Comput. Oper. Res. 32(7), 1685–1708 (2005)
Brandão, J.: A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. Eur. J. Oper. Res. 195, 716–728 (2009)
Brandão, J.: A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem. Comput. Oper. Res. 38, 140–151 (2011)
Brandão, J., Mercer, A.: A tabu search algorithm for the multi-trip vehicle routing and scheduling problem. Eur. J. Oper. Res. 100(1), 180–191 (1997)
Brandão, J.C.S., Mercer, A.: The multi-trip vehicle routing problem. J. Oper. Res. Soc. 49(8), 799–805 (1998)
Bräysy, O., Gendreau, M.: Tabu search heuristics for the vehicle routing problem with time windows. Technical report, SINTEF Applied Mathematics, Department of Optimisation, Oslo, Norway (2001)
Breedam, A.V.L Comparing descent heuristics and metaheuristics for the vehicle routing problem. Comput. Oper. Res. 24(4), 289–315 (2001)
Chao, I.M.: A tabu search method for the truck and trailer routing problem. Comput. Oper. Res. 29(1), 33–51 (2002)
Chiang, W.C., Russell, R.A.: A reactive tabu search metaheuristic for the vehicle routing problem with time windows. INFORMS J. Comput. 9, 417–430 (1997)
Cordeau, J., Maischberger, M.: A parallel iterated tabu search heuristic for vehicle routing problems. Comput. Oper. Res. 39, 2033–2050 (2012)
Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2), 105–119 (1998)
Cordeau, J.F., Laporte, G.: A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp. Res., Part B: Methodol. 37(6), 579–594 (2003)
Cordeau, J.F., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Oper. Res. Soc. 52(8), 928–936 (2001)
Côté, J., Potvin, J.-Y.: A tabu search heuristic for the vehicle routing problem with private fleet and common carrier. Eur. J. Oper. Res. 198, 464–469 (2009)
Crainic, T.G., Gendreau, M., Soriano, P., Toulouse, M.: A tabu search procedure for multicommodity location/allocation with balancing requirements. Ann. Oper. Res. 41, 359–383 (1993)
Crevier, B., Cordeau, J.F., Laporte, G.: The multi-depot vehicle routing problem with inter-depot routes. Eur. J. Oper. Res. 176(2), 756–773 (2007)
Daniels, R.L., Rummel, J.L., Schantz, R.: A model for warehouse order picking. Eur. J. Oper. Res. 105(1), 1–17 (1998)
Franca, P.M., Sosa, N.M., Pureza, V.: An adaptive tabu search algorithm for the capacitated clustering problem. Int. Trans. Oper. Res. 6, 665–678 (1999)
Garcia, B.L., Potvin, J.Y., Rousseau, J.M.: A parallel implementation of the tabu search heuristic for vehicle routing problems with time window constraints. Comput. Oper. Res. 21(9), 1025–1033 (1994)
Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Manage. Sci. 40(10), 1276–1290 (1994)
Gendreau, M., Iori, M., Laporte, G., Martello, S.: A tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51(1), 4–18 (2008)
Gendreau, M., Laporte, G., Séguin, R.: A tabu search heuristic for the vehicle routing problem with stochastic demands and customers. Oper. Res. 44(3), 469–477 (1996)
Gendreau, M., Laporte, G., Semet, F.: A tabu search heuristic for the undirected selective travelling salesman problem. Eur. J. Oper. Res. 106, 539–545 (1998)
Gendreau, M., Laporte, G., Vigo, D.: Heuristics for the traveling salesman problem with pickup and delivery. Comput. Oper. Res. 26(7), 699–714 (1999)
Glover, F., Laguna, M.: Tabu Search. Kluwer, Boston, MA (1998)
Goossens, J., Baruah, S.: Multiprocessor preprocessing algorithms for uniprocessor on-line scheduling. In: In the 21th International Conference on Distributed Computing Systems (2001)
Gutin, G., Punnen, A.P.: The Treveling Salesman Problem and its Variations. Kluwer, Boston, MA (2002)
Held, M., Karp, R.M.: The traveling salesman problem and minimum spanning trees. Oper. Res. 18, 1138–1162 (1970)
Held, M., Karp, R.M.: The traveling salesman problem and minimum spanning trees: part II. Math. Program. 1, 6–25 (1971)
Hertz, A., Laporte, G., Mittaz, M.: A tabu search heuristic for the capacitated arc routing problem. Oper. Res. 48(1), 129–135 (2000)
Homberger, J., Gehring, H.: A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. Eur. J. Oper. Res. 162(1), 220–238 (2005)
Ho, S.C., Haugland, D.: A tabu search heuristic for the vehicle routing problem with time windows and split deliveries. Comput. Oper. Res. 31(12), 1947–1964 (2004)
Ichoua, S., Gendreau, M., Potvin, J.Y.: Vehicle dispatching with time-dependent travel times. Eur. J. Oper. Res. 144(2), 379–396 (2003)
Johnson, D.S., Gutin, G., McGeoch, L.A., Yeo, A., Zhang, W., Zverovich, A.: The traveling salesman problem and its variations. In: Experimental Analysis of Heuristics for the ATSP. Kluwer, Boston, MA (2002)
Khumawala, B.M.: An efficient branch and bound algorithm for the warehouse location problem. Manage. Sci. 18, B718–B731 (1975)
Lau, H.C., Sim, M., Teo, K.M.: Vehicle routing problem with time windows and a limited number of vehicles. Eur. J. Oper. Res. 148(3), 559–569 (2003)
Lin, C.K.Y., Kwok, R.C.W.: Multi-objective metaheuristics for a location-routing problem with multiple use of vehicles on real data and simulated data. Eur. J. Oper. Res. 175(3), 1833–1849 (2006)
Malek, M., Guruswamy M., Pandya M., Owens H.: Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem. Ann. Oper. Res. 21, 59–84 (1989)
Montane, F.A.T., Galvao, R.D.: A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Comput. Oper. Res. 33(3), 595–619 (2006)
Nanry, W.P., Barnes, J.W.: Solving the pickup and delivery problem with time windows using reactive tabu search. Transp. Res., Part B: Methodol. 34(2), 107–121 (2000)
Osman, I.H.: Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann. Oper. Res. 41, 421–451 (1993)
Potvin, J.Y., Kervahut, T., Garcia, B.L., Rousseau, J.M.: The vehicle routing problem with time windows—part i: tabu search. INFORMS J. Comput. 8, 158–164 (1996)
Reinelt, G.: Tsplib—a traveling salesman problem library. INFORMS J. Comput. 3, 376–384 (1991)
Renaud, J., Laporte, G., Boctor, F.F.: A tabu search heuristic for the multi-depot vehicle routing problem. Comput. Oper. Res. 23, 229–235 (1996)
Rochat, Y., Semet, F.: A tabu search approach for delivering pet food and flour in Switzerland. J. Oper. Res. Soc. 45(11), 1233–1246 (1994)
Rochat, Y., Taillard, E.D.: Probabilistic diversification and intensification in local search for vehicle routing. J. Heuristics 1, 147–167 (1995)
Scheuerer, S.: A tabu search heuristic for the truck and trailer routing problem. Comput. Oper. Res. 33(4), 894–909 (2006)
Semet, F., Taillard, E.: Solving real-life vehicle routing problems efficiently using taboo search. Ann. Oper. Res. 41, 469–488 (1993)
Sharaiha, Y.M., Gendreau, M., Laporte, G., Osman, I.H.: A tabu search algorithm for the capacitated shortest spanning tree problem. Networks 29, 209–223 (1997)
Taillard, V.E., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.-Y.: A tabu search heuristic for the vehicle routing problem with soft time windows. Transp. Sci. 31(2), 170–186 (1997)
Tamashiro, H., Nakamura, M., Okazaki, T., Kang, D.: A tabu search approach combined with an extended saving method for multi-depot vehicle routing problems with time windows. Biomed. Soft Comput. Human Sci. 15(1), 31–39 (2010)
Tang, H., Hooks, E.M.: A tabu search heuristic for the team orienteering problem. Comput. Oper. Res. 32(6), 1379–1407 (2005)
Tarantilis, C.D.: Solving the vehicle routing problem with adaptive memory programming methodology. Comput. Oper. Res. 32(9), 2309–2327 (2005)
Tarantilis, C.D., Kiranoudis, C.T.: A flexible adaptive memory-based algorithm for real-life transportation operations: two case studies from dairy and construction sector. Eur. J. Oper. Res. 179(3), 806–822 (2007)
Thangiah, S., Osman, I., Sun, T.: Hybrid genetic algorithm, simulated annealing and tabu search methods for vehicle routing problem with time windows. Technical report, Computer Science Department, Slippery Rock University (1994)
Toth, P., Vigo, D.: The granular tabu search and its application to the vrp. Technical report, University of Bologna (1998)
Tsubakitani, S., Evans, J.R.: Optimizing tabu list size for the traveling salesman problem. Comput. Oper. Res. 25(2), 91–97 (1998)
Tuzun, D., Burke, L.I.: A two-phase tabu search approach to the location routing problem. Eur. J. Oper. Res. 116, 87–99 (1999)
Wassan, N.A., Wassan, A.H., Nagy, G.: A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries. J. Comb. Optim. 15, 368–386 (2008)
Zachariadis, E.E., Tarantilis, C.D., Kiranoudis, C.T.: A guided tabu search for the vehicle routing problem with two-dimensional loading constraints. Eur. J. Oper. Res. 195, 729–743 (2009)
Acknowledgements
I want to thank Prof. Diptesh Ghosh for his valuable inputs and suggestions in different phases of this work. I am also thankful to the anonymous referees for their helpful suggestions and comments which have led to an improvement in both quality and clarity of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Basu, S. Neighborhood reduction strategy for tabu search implementation in asymmetric traveling salesman problem. OPSEARCH 49, 400–412 (2012). https://doi.org/10.1007/s12597-012-0086-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-012-0086-1