Journal of the Operational Research Society

, Volume 65, Issue 12, pp 1800–1813 | Cite as

GRASP with path relinking for the orienteering problem

  • Vicente Campos
  • Rafael Martí
  • Jesús Sánchez-Oro
  • Abraham Duarte
General Paper


In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.


metaheuristics GRASP path relinking orienteering problem 



This research has been partially supported by the Ministerio de Educación y Ciencia of Spain (Grant Refs. TIN2009-07516 and TIN2012-35632-C02) and the Generalitat Valenciana (Prometeo 2013/049). The authors thank Profs Schilde, Doerner, Hartl, and Kiechle for sharing their results with them. The authors also thank Profs. Fischetti, Salazar, and Toth for sharing their branch-and-cut code with them.


  1. Chao IM, Golden BL and Wasil EA (1996). A fast and effective heuristic for the orienteering problem. European Journal of Operational Research 88 (3): 475–489.CrossRefGoogle Scholar
  2. Duarte A, Martí R, Resende MGC and Silva RMA (2011). GRASP with path relinking heuristics for the antibandwidth problem. Networks 58 (3): 171–189.CrossRefGoogle Scholar
  3. Fischetti M, Salazar JJ and Toth P (1998). Solving the orienteering problem through branch-and-cut. INFORMS Journal on Computing 10 (2): 133–148.CrossRefGoogle Scholar
  4. Glover F and Laguna M (1997). Tabu Search. Kluwer Academic Publishers: Boston, MA.CrossRefGoogle Scholar
  5. Jozefowiez N, Glover F and Laguna M (2008). Multi-objective meta-heuristics for the traveling salesman problem with profits. Journal of Mathematical Modelling and Algorithms 7 (2): 177–195.CrossRefGoogle Scholar
  6. Laguna M and Martí R (1999). GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS Journal on Computing 11 (1): 44–52.CrossRefGoogle Scholar
  7. Lawler AEL, Lenstra JK, Rinooy Kan AHG and Shwoys DB (1985). The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley Series in Discrete Mathematics & Optimization: New York.Google Scholar
  8. Martí R, Campos V, Resende MGC and Duarte A (2011). Multi-objective GRASP with Path Relinking. Technical Report, Universidad de Valencia: Valencia.Google Scholar
  9. Miller CE, Tucker AW and Zemlin RA (1960). Integer programming formulation of traveling salesman problems. Journal ACM 7 (4): 326–329.CrossRefGoogle Scholar
  10. Pacheco J, Alvarez A, Casado S and González-Velarde JL (2009). A tabu search approach to an urban transport problem in Northern Spain. Computers and Operations Research 36 (3): 967–979.CrossRefGoogle Scholar
  11. Pantrigo JJ, Duarte A, Martí R and Pardo EG (2012). Scatter search for the cutwidth minimization problem. Annals of Operations Research 199 (1): 285–304.CrossRefGoogle Scholar
  12. Resende MGC, Martí R, Gallego M and Duarte A (2010). GRASP and path relinking for the max-min diversity problem. Computers and Operations Research 37 (3): 498–508.CrossRefGoogle Scholar
  13. Resende MGC and Ribeiro CC (2003). Greedy randomized adaptive search procedures. In: Glover F and Kochenberger G (eds). State-of-the-Art Handbook in Metaheuristics. Kluwer Academic Publishers: Boston, MA, pp. 219–250.CrossRefGoogle Scholar
  14. Resende MGC and Werneck RF (2004). A hybrid heuristic for the p-median problem. Journal of Heuristics 10 (1): 59–88.CrossRefGoogle Scholar
  15. Schilde M, Doerner KF, Hartl RF and Kiechle G (2009). Metaheuristics for the bi-objective orienteering problem. Swarm Intell 3 (3): 179–201.CrossRefGoogle Scholar
  16. Souffriau W, Vansteenwegen P, Vanden Berghe G and Oudheusden DV (2010). A path relinking approach for the team orienteering problem. Computers and Operations Research 37 (11): 1853–1859.CrossRefGoogle Scholar
  17. Tsiligirides T (1984). Heuristic methods applied to orienteering. Journal of the Operational Research Society 35 (9): 797–809.CrossRefGoogle Scholar
  18. Vansteenwegen P, Souffriau W and Oudheusden DV (2011). The orienteering problem: A survey. European Journal of Operational Research 209 (1): 1–10.CrossRefGoogle Scholar
  19. Vansteenwegen P, Souffriau W, Vanden Berghe G and Oudheusden DV (2009). A guided local search metaheuristic for the team orienteering problem. European Journal of the Operational Research 196 (1): 118–127.CrossRefGoogle Scholar

Copyright information

© Operational Research Society Ltd. 2013

Authors and Affiliations

  • Vicente Campos
    • 1
  • Rafael Martí
    • 1
  • Jesús Sánchez-Oro
    • 2
  • Abraham Duarte
    • 2
  1. 1.Universitat de ValènciaValènciaSpain
  2. 2.Universidad Rey Juan CarlosMostolesSpain

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