Advertisement

Journal of Heuristics

, Volume 17, Issue 6, pp 729–753 | Cite as

Hybridized evolutionary local search algorithm for the team orienteering problem with time windows

  • Nacima Labadie
  • Jan Melechovský
  • Roberto Wolfler Calvo
Article

Abstract

The orienteering problem (OP) consists in finding an elementary path over a subset of vertices. Each vertex is associated with a profit that is collected on the visitor’s first visit. The objective is to maximize the collected profit with respect to a limit on the path’s length. The team orienteering problem (TOP) is an extension of the OP where a fixed number m of paths must be determined. This paper presents an effective hybrid metaheuristic to solve both the OP and the TOP with time windows. The method combines the greedy randomized adaptive search procedure (GRASP) with the evolutionary local search (ELS). ELS generates multiple distinct child solutions using a mutation mechanism. Each child solution is further improved by a local search procedure. GRASP provides multiple starting solutions to the ELS. The method is able to improve several best known results on available benchmark instances.

Keywords

Team orienteering problem Time windows GRASP ELS 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Archetti, C., Hertz, A., Speranza, M.G.: Metaheuristics for the team orienteering problem. J. Heuristics 13(1), 49–76 (2007) CrossRefGoogle Scholar
  2. Balas, E., Martin, G.: Roll-a-round: Software package for scheduling the rounds of a rolling mill. Copyright Balas and Martin Associates (1985) Google Scholar
  3. Belenguer, J.M., Benavent, E., Labadi, N., Prins, C., Reghioui, M.: Split delivery capacitated arc routing problem: lower bound and metaheuristic. Transp. Sci. 44, 206–220 (2010) CrossRefGoogle Scholar
  4. Blum, A., Chawla, S., Karger, D.R., Lane, T., Meyerson, A., Minkoff, M.: Approximation algorithms for orienteering and discounted-reward tsp. SIAM J. Comput. 37(2), 653–670 (2007) MathSciNetMATHCrossRefGoogle Scholar
  5. Bouly, H., Dang, D.C., Moukrim, A.: A memetic algorithm for the team orienteering problem. 4OR. Published online (2009) Google Scholar
  6. Boussier, S., Feillet, D., Gendreau, M.: An exact algorithm for team orienteering problems. 4OR 5(3), 211–230 (2007) MathSciNetMATHCrossRefGoogle Scholar
  7. Chao, I.M., Golden, B.L., Wasil, E.A.: A fast and effective heuristic for the orienteering problem. Eur. J. Oper. Res. 88(3), 475–489 (1996a) MATHCrossRefGoogle Scholar
  8. Chao, I.M., Golden, B.L., Wasil, E.A.: The team orienteering problem. Eur. J. Oper. Res. 88(3), 464–474 (1996b) MATHCrossRefGoogle Scholar
  9. Chekuri, C., Korula, N., Pál, M.: Improved algorithms for orienteering and related problems. In: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, SODA ’08, Philadelphia, PA, USA, pp. 661–670 (2008) Google Scholar
  10. Chen, K., Har-Peled, S.: The orienteering problem in the plane revisited. In: Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, SCG ’06, pp. 247–254. ACM, New York (2006) CrossRefGoogle Scholar
  11. Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2), 105–119 (1997) MATHCrossRefGoogle Scholar
  12. Deitch, R., Ladany, S.P.: The one-period bus touring problem: Solved by an effective heuristic for the orienteering tour problem and improvement algorithm. Eur. J. Oper. Res. 127(1), 69–77 (2000) MATHCrossRefGoogle Scholar
  13. Dell’Amico, M., Maffioli, F., Värbrand, P.: On prize-collecting tours and the asymmetric travelling salesman problem. Int. Trans. Oper. Res. 2(3), 297–308 (1995) MATHCrossRefGoogle Scholar
  14. Dongarra, J.J.: Performance of various computers using standard linear equations software in a fortran environment. Tech. rep., Electrical Engineering and Computer Science Department, University of Tennessee, Knoxville, TN 37996-1301, http://www.netlib.org/benchmark/performance.ps (2009)
  15. Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transp. Sci. 39(2), 188–205 (2005) CrossRefGoogle Scholar
  16. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995) MathSciNetMATHCrossRefGoogle Scholar
  17. Fink, A., Schneidereit, G., Voß, S.: Solving general ring network design problems by meta-heuristics. In: Laguna, M., Velarde, J.G. (eds.) Computing Tools for Modeling, Optimization and Simulation (Interfaces in Computer Science and Operations Research), pp. 91–113. Kluwer, Boston (2000) CrossRefGoogle Scholar
  18. Fischetti, M., Toth, P.: An additive approach for the optimal solution of the prize-collecting traveling salesman problem. In: Golden, B.L., Assad, A.A. (eds.) Vehicle Routing: Methods and Studies, pp. 319–343. Elsevier, Amsterdam (1988) Google Scholar
  19. Fischetti, M., Gonzalez, J.J.S., Toth, P.: Solving the orienteering problem through branch-and-cut. INFORMS J. Comput. 10(2), 133–148 (1998) MathSciNetMATHCrossRefGoogle Scholar
  20. Fomin, F.V., Lingas, A.: Approximation algorithms for time-dependent orienteering. Inf. Process. Lett. 83(2), 57–62 (2002) MathSciNetMATHCrossRefGoogle Scholar
  21. Gendreau, M., Laporte, G., Semet, F.: A tabu search heuristic for the undirected selective travelling salesman problem. Eur. J. Oper. Res. 106(2–3), 539–545 (1998) MATHCrossRefGoogle Scholar
  22. Golden, B.L., Levy, L., Vohra, R.: The orienteering problem. Nav. Res. Logist. 34(3), 307–456 (1987) MATHCrossRefGoogle Scholar
  23. Golden, B.L., Wang, Q., Liu, L.: A multifaceted heuristic for the orienteering problem. Nav. Res. Logist. 35(3), 359–366 (1988) MATHCrossRefGoogle Scholar
  24. Kantor, M.G., Rosenwein, M.B.: The orienteering problem with time windows. J. Oper. Res. Soc. 43(6), 629–635 (1992) MATHGoogle Scholar
  25. Kataoka, S., Yamada, T., Morito, S.: Minimum directed 1-subtree relaxation for score orienteering problem. Eur. J. Oper. Res. 104(1), 139–153 (1998) MATHCrossRefGoogle Scholar
  26. Ke, L., Archetti, C., Feng, Z.: Ants can solve the team orienteering problem. Comput. Ind. Eng. 54(3), 648–665 (2008) CrossRefGoogle Scholar
  27. Kindervater, G.A.P., Savelsbergh, M.W.P.: Vehicle routing: handling edge exchanges. In: Aarts, E., Lenstra, J. (eds.) Local Search in Combinatorial Optimization, pp. 311–336. Wiley, New York (1997) Google Scholar
  28. Laporte, G., Martello, S.: The selective travelling salesman problem. Discrete Appl. Math. 26(2–3), 193–207 (1990) MathSciNetMATHCrossRefGoogle Scholar
  29. Mansini, R., Pelizzari, M., Wolfler-Calvo, R.: The tour orienteering problem with time windows. In: Odysseus 2006—Third International Workshop on Freight Transportation and Logistics. Altea Spain, Universitat de València, May 23–26 (2006) Google Scholar
  30. Merz, P., Wolf, S.: Evolutionary local search for the super-peer selection problem and the p-hub median problem. In: Bartz-Beielstein, T., et al. (ed.) Lecture notes in computer science, vol. 4771, pp. 1–15 Springer, Berlin (2007) Google Scholar
  31. Montemanni, R., Gambardella, L.M.: Ant colony system for team orienteering problem with time windows. Foundations of Computing and Decision Sciences (34) (2009) Google Scholar
  32. Prins, C.: A grasp x evolutionary local search hybrid for the vehicle routing problem. In: Pereira, F., Tavares, J. (eds.) Bio-inspired algorithms for the vehicle routing problem, vol. 16, pp. 35–53. Springer, Berlin (2009) CrossRefGoogle Scholar
  33. Righini, G., Salani, M.: Decremental state space relaxation strategies and initialization heuristics for solving the orienteering problem with time windows with dynamic programming. Comput. Oper. Res. 36(4), 1191–1203 (2009) MATHCrossRefGoogle Scholar
  34. Schilde, M., Doerner, K.F., Hartl, R.F., Kiechle, G.: Metaheuristics for the bi-objective orienteering problem. Swarm Intell. 3(3), 179–201 (2009) CrossRefGoogle Scholar
  35. Sevkli, Z., Sevilgen, E.: Computer and information sciences—ISCIS 2006. In: Lecture Notes in Computer Science. Variable neighborhood search for the orienteering problem, vol. 4263, pp. 134–143. Springer, Berlin (2006) Google Scholar
  36. Silberholz, J., Golden, B.L.: The effective application of a new approach to the generalized orienteering problem. Journal of Heuristics published online (2009) Google Scholar
  37. Solomon, M.: Algorithms for the vehicle routing and scheduling problem with time window constraints. 4OR 35, 254–265 (1987) MATHGoogle Scholar
  38. Souffriau, W., Vansteenwegen, P., Berghe, G.V., Oudheusden, D.V.: A path relinking approach for the team orienteering problem. Comput. Oper. Res. In Press (2009) Google Scholar
  39. Tang, H., Miller-Hooks, E.: A tabu search heuristic for the team orienteering problem. Comput. Oper. Res. 32(6), 1379–1407 (2005) CrossRefGoogle Scholar
  40. Tasgetiren, M.F.: A genetic algorithm with an adaptive penalty function for the orienteering problem. J. Econ. Soc. Res. 4(2), 1–26 (2001) Google Scholar
  41. Tricoire, F., Romauch, M., Doerner, K.F., Hartl, R.F.: Heuristics for the multi-period orienteering problem with multiple time windows. Comput. Oper. Res. 37(2), 351–367 (2010) MathSciNetMATHCrossRefGoogle Scholar
  42. Tsiligirides, T.: Heuristic methods applied to orienteering. J. Oper. Res. Soc. Am. 35(9), 797–809 (1984) Google Scholar
  43. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Oudheusden, D.V.: A guided local search metaheuristic for the team orienteering problem. Eur. J. Oper. Res. 196(1), 118–127 (2009a) MATHCrossRefGoogle Scholar
  44. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Oudheusden, D.V.: Iterated local search for the team orienteering problem with time windows. Comput. Oper. Res. 36(12), 3281–3290 (2009b) MATHCrossRefGoogle Scholar
  45. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Oudheusden, D.V.: Metaheuristics for tourist trip planning. In: Sörensen, K., Sevaux, M., Habenicht, W., Geiger, M.J. (eds.) Metaheuristics in the Service Industry. Lecture Notes in Economics and Mathematical Systems, vol. 624, pp. 15–31. Springer, Berlin (2009c) CrossRefGoogle Scholar
  46. Vansteenwegen, P., Souffriau, W., Oudheusden, D.V.: The orienteering problem: A survey. Euro. J. Oper. Res. In Press (2010) Google Scholar
  47. Wang, X., Golden, B.L., Wasil, E.A.: Using a genetic algorithm to solve the generalized orienteering problem. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, Springer US. Operations Research/Computer Science Interfaces Series, vol. 43, pp. 263–274 (2008) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Nacima Labadie
    • 1
  • Jan Melechovský
    • 1
  • Roberto Wolfler Calvo
    • 2
  1. 1.Institute Charles DelaunayUniversity of Technology of TroyesTroyes CedexFrance
  2. 2.Laboratoire d’Informatique de Paris-NordUniversity Paris 13VilletaneuseFrance

Personalised recommendations