Journal of the Operational Research Society

, Volume 63, Issue 2, pp 207–217 | Cite as

The travelling salesperson problem with hotel selection

General Paper


In this paper, we present the travelling salesperson problem with hotel selection (TSPHS), an extension of the TSP with a number of interesting applications. We present a mathematical formulation, explain the difference with related optimization problems and indicate what makes this problem inherently more difficult. We develop a simple but efficient heuristic that uses two constructive initialization procedures and an improvement procedure consisting of several neighbourhood search operators designed specifically for this problem, as well as some typical neighbourhoods from the literature. We generate several benchmark instances of varying sizes and compare the performance of our heuristic with CPLEX (10.0). We also generate some problems with known optimal solutions and use these to further demonstrate that our heuristic achieves good results in very limited computation times.


travelling salesperson problem hotel selection heuristic 


  1. Applegate DL, Bixby RE, Chvatal V and Cook WJ (2007). The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press: Princeton, NJ, USA.Google Scholar
  2. Bektas T (2006). The multiple traveling salesman problem: An overview of formulations and solution procedures. Omega 34 (3): 209–219.CrossRefGoogle Scholar
  3. Cordeau JF, Gendreau M and Laporte G (1997). A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30 (2): 105–119.CrossRefGoogle Scholar
  4. Cordeau JF, Laporte G and Mercier A (2001). A unified tabu search heuristic for vehicle routing problems with time windows. J Opl Res Soc 52: 928–936.CrossRefGoogle Scholar
  5. Lin CKY, Chow CK and Chen A (2002). A location-routing-loading problem for bill delivery services. Comput Indust Eng: 43 (1–2): 5–25.CrossRefGoogle Scholar
  6. Lin S (1965). Computer solutions of the traveling salesman problem. Bell System Tech J 44: 2245–2269.CrossRefGoogle Scholar
  7. Miller CE, Tucker AW and Zemlin RA (1960). Integer programming formulation of traveling salesman problems. J ACM 7 (4): 326–329.CrossRefGoogle Scholar
  8. Nagy G and Salhi S (2007). Location-routing: Issues, models and methods. Eur J Opl Res 177 (2): 649–672.CrossRefGoogle Scholar
  9. Or I. (1976). Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. PhD thesis, Northwestern University, Evanston, IL.Google Scholar
  10. Polacek M, Hartl RF, Doerner K and Reimann M (2004). A variable neighborhood search for the multi depot vehicle routing problem with time windows. J Heuristics 10 (6): 613–627.CrossRefGoogle Scholar
  11. Prins C (2004). A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Opns Res 31 (12): 1985–20021.CrossRefGoogle Scholar
  12. Savelsbergh M (1992). The vehicle routing problem with time windows: Minimizing route duration. J Comput 4: 146–154.Google Scholar
  13. Solomon MM (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Opns Res 35 (2): 254–265.CrossRefGoogle Scholar
  14. Souffriau W, Vansteenwegen P, Vertommen J, Vanden Berghe G and Van Oudheusden D (2008). A personalized tourist trip design algorithm for mobile tourist guides. Appl Artif Intell 22 (10): 964–985.CrossRefGoogle Scholar
  15. Toth P and Vigo D (2002). The vehicle routing problem. SIAM monographs on discrete mathematics and applications, SIAM.Google Scholar
  16. Tsiligirides T (1984). Heuristic methods applied to orienteering. J Opl Res Soc 35: 797–809.CrossRefGoogle Scholar
  17. Vansteenwegen P, Souffriau W and Sörensen K (2010). Solving the mobile mapping van problem: A hybrid metaheuristic for capacitated arc routing with soft time windows. Comput Opns Res (in press).Google Scholar
  18. Vansteenwegen P, Souffriau W and Oudheusden D (2011). The orienteering problem: A survey. Eur J Opl Res 209 (1): 1–10.CrossRefGoogle Scholar
  19. Wu TH, Low C and Bai JW (2002). Heuristic solutions to multi-depot location-routing problems. Comput Opns Res 29 (10): 1393–1415.CrossRefGoogle Scholar

Copyright information

© Operational Research Society 2011

Authors and Affiliations

  1. 1.Ghent UniversityGhentBelgium
  2. 2.Centre for Industrial Management, Katholieke Universiteit LeuvenKatholiekeBelgium
  3. 3.University of AntwerpAntwerpenBelgium

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