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Minimum and Maximum Category Constraints in the Orienteering Problem with Time Windows

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Book cover Analysis of Experimental Algorithms (SEA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11544))

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Abstract

We introduce a new variation of the Orienteering Problem (OP), the Minimum-Maximum Category Constraints Orienteering Problem with Time Windows. In the Orienteering Problem we seek to determine a path from node \( S \) to node \( T \) in a weighted graph where each node has a score. The total weight of the path must not exceed a predetermined budget and the goal is to maximize the total score. In this variation, each Activity is associated with a category and the final solution is required to contain at least a minimum and at most a maximum of specific categories. This variation better captures the problem of tourists visiting cities. For example, the tourists can decide to visit exactly one restaurant at a specific time window and at least one park. We present a Replace Local Search and an Iterated Local Search which utilizes Stochastic Gradient Descent to identify the tightness of the constraints. We perform exhaustive experimental evaluation of our results against state of the art implementations for the unconstrained problem and examine how it performs against increasingly more restricting settings.

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References

  1. The orienteering problem: Test instances. https://www.mech.kuleuven.be/en/cib/op

  2. Archetti, C., Hertz, A., Speranza, M.G.: Metaheuristics for the team orienteering problem. J. Heuristics 13(1), 49–76 (2007)

    Article  Google Scholar 

  3. Bolzoni, P., Helmer, S.: Hybrid best-first greedy search for orienteering with category constraints. In: Gertz, M., et al. (eds.) SSTD 2017. LNCS, vol. 10411, pp. 24–42. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-64367-0_2

    Chapter  Google Scholar 

  4. Boussier, S., Feillet, D., Gendreau, M.: An exact algorithm for team orienteering problems. 4OR 5(3), 211–230 (2007)

    Article  MathSciNet  Google Scholar 

  5. Campos, V., Martí, R., Sánchez-Oro, J., Duarte, A.: Grasp with path relinking for the orienteering problem. J. Oper. Res. Soc. 65(12), 1800–1813 (2014)

    Article  Google Scholar 

  6. 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 (1996)

    Article  Google Scholar 

  7. Chao, I.M., Golden, B.L., Wasil, E.A.: The team orienteering problem. Eur. J. Oper. Res. 88(3), 464–474 (1996)

    Article  Google Scholar 

  8. Dang, D.-C., El-Hajj, R., Moukrim, A.: A branch-and-cut algorithm for solving the team orienteering problem. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 332–339. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38171-3_23

    Chapter  MATH  Google Scholar 

  9. Dang, D.-C., Guibadj, R.N., Moukrim, A.: A PSO-based memetic algorithm for the team orienteering problem. In: Di Chio, C., et al. (eds.) EvoApplications 2011. LNCS, vol. 6625, pp. 471–480. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20520-0_48

    Chapter  Google Scholar 

  10. Dang, D.C., Guibadj, R.N., Moukrim, A.: An effective PSO-inspired algorithm for the team orienteering problem. Eur. J. Oper. Res. 229(2), 332–344 (2013)

    Article  Google Scholar 

  11. Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transp. Sci. 39(2), 188–205 (2005)

    Article  Google Scholar 

  12. Ferreira, J., Quintas, A., Oliveira, J.A., Pereira, G.A.B., Dias, L.: Solving the team orienteering problem: developing a solution tool using a genetic algorithm approach. In: Snášel, V., Krömer, P., Köppen, M., Schaefer, G. (eds.) Soft Computing in Industrial Applications. AISC, vol. 223, pp. 365–375. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-00930-8_32

    Chapter  Google Scholar 

  13. Fischetti, M., Gonzalez, J.J.S., Toth, P.: Solving the orienteering problem through branch-and-cut. Inf. J. Comput. 10(2), 133–148 (1998)

    Article  MathSciNet  Google Scholar 

  14. Gambardella, L.M., Montemanni, R., Weyland, D.: An enhanced ant colony system for the sequential ordering problem. In: Klatte, D., Lüthi, H.J., Schmedders, K. (eds.) Operations Research Proceedings 2011. Operations Research Proceedings (GOR (Gesellschaft für Operations Research e.V.)), pp. 355–360. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29210-1_57

    Chapter  Google Scholar 

  15. Gendreau, M., Laporte, G., Semet, F.: A branch-and-cut algorithm for the undirected selective traveling salesman problem. Networks 32(4), 263–273 (1998)

    Article  MathSciNet  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Golden, B., Levy, L., Dahl, R.: Two generalizations of the traveling salesman problem. Omega 9(4), 439–441 (1981)

    Article  Google Scholar 

  18. Golden, B.L., Levy, L., Vohra, R.: The orienteering problem. Nav. Res. Logist. 34(3), 307–318 (1987)

    Article  Google Scholar 

  19. Gunawan, A., Lau, H.C., Lu, K.: An iterated local search algorithm for solving the orienteering problem with time windows. In: Ochoa, G., Chicano, F. (eds.) EvoCOP 2015. LNCS, vol. 9026, pp. 61–73. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16468-7_6

    Chapter  Google Scholar 

  20. Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column Generation, pp. 33–65. Springer, Boston (2005). https://doi.org/10.1007/0-387-25486-2_2

    Chapter  Google Scholar 

  21. Ke, L., Archetti, C., Feng, Z.: Ants can solve the team orienteering problem. Comput. Ind. Eng. 54(3), 648–665 (2008)

    Article  Google Scholar 

  22. Laporte, G., Martello, S.: The selective travelling salesman problem. Discret. Appl. Math. 26(2–3), 193–207 (1990)

    Article  MathSciNet  Google Scholar 

  23. Leifer, A.C., Rosenwein, M.B.: Strong linear programming relaxations for the orienteering problem. Eur. J. Oper. Res. 73(3), 517–523 (1994)

    Article  Google Scholar 

  24. Liang, Y.C., Kulturel-Konak, S., Lo, M.H.: A multiple-level variable neighborhood search approach to the orienteering problem. J. Ind. Prod. Eng. 30(4), 238–247 (2013)

    Google Scholar 

  25. Lin, S.W., Vincent, F.Y.: Solving the team orienteering problem with time windows and mandatory visits by multi-start simulated annealing. Comput. Ind. Eng. 114, 195–205 (2017)

    Article  Google Scholar 

  26. Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 320–353. Springer, Boston (2003). https://doi.org/10.1007/0-306-48056-5_11

    Chapter  Google Scholar 

  27. Lu, Y., Benlic, U., Wu, Q.: A memetic algorithm for the orienteering problem with mandatory visits and exclusionary constraints. Eur. J. Oper. Res. 268(1), 54–69 (2018)

    Article  MathSciNet  Google Scholar 

  28. Marinakis, Y., Politis, M., Marinaki, M., Matsatsinis, N.: A memetic-GRASP algorithm for the solution of the orienteering problem. In: Le Thi, H.A., Pham Dinh, T., Nguyen, N.T. (eds.) Modelling, Computation and Optimization in Information Systems and Management Sciences. AISC, vol. 360, pp. 105–116. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18167-7_10

    Chapter  Google Scholar 

  29. Montemanni, R., Gambardella, L.M.: An ant colony system for team orienteering problems with time windows. Found. Comput. Decis. Sci. 34(4), 287 (2009)

    MATH  Google Scholar 

  30. Muthuswamy, S., Lam, S.S.: Discrete particle swarm optimization for the team orienteering problem. Memetic Comput. 3(4), 287–303 (2011)

    Article  Google Scholar 

  31. Ramesh, R., Yoon, Y.S., Karwan, M.H.: An optimal algorithm for the orienteering tour problem. ORSA J. Comput. 4(2), 155–165 (1992)

    Article  Google Scholar 

  32. Ramesh, R., Brown, K.M.: An efficient four-phase heuristic for the generalized orienteering problem. Comput. Oper. Res. 18(2), 151–165 (1991)

    Article  MathSciNet  Google 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)

    Article  Google Scholar 

  34. Şevkli, A.Z., Sevilgen, F.E.: StPSO: strengthened particle swarm optimization. Turk. J. Electr. Eng. Comput. Sci. 18(6), 1095–1114 (2010)

    Google Scholar 

  35. Şevkli, Z., Sevilgen, F.E.: Discrete particle swarm optimization for the orienteering problem. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)

    Google Scholar 

  36. Souffriau, W., Vansteenwegen, P., Vanden Berghe, G., Van Oudheusden, D.: The multiconstraint team orienteering problem with multiple time windows. Transp. Sci. 47(1), 53–63 (2013)

    Article  Google Scholar 

  37. Sylejmani, K., Dorn, J., Musliu, N.: A tabu search approach for multi constrained team orienteering problem and its application in touristic trip planning. In: 2012 12th International Conference on Hybrid Intelligent Systems (HIS), pp. 300–305. IEEE (2012)

    Google Scholar 

  38. Thomadsen, T., Stidsen, T.K.: The quadratic selective travelling salesman problem. Technical report (2003)

    Google Scholar 

  39. Tsiligirides, T.: Heuristic methods applied to orienteering. J. Oper. Res. Soc. 35, 797–809 (1984)

    Article  Google Scholar 

  40. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Van Oudheusden, D.: Iterated local search for the team orienteering problem with time windows. Comput. Oper. Res. 36(12), 3281–3290 (2009)

    Article  Google Scholar 

  41. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Van Oudheusden, D.: Metaheuristics for tourist trip planning. In: Sörensen, K., Sevaux, M., Habenicht, W., Geiger, M. (eds.) Metaheuristics in the Service Industry, pp. 15–31. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00939-6_2

    Chapter  MATH  Google Scholar 

  42. Vincent, F.Y., Lin, S.W.: Multi-start simulated annealing heuristic for the location routing problem with simultaneous pickup and delivery. Appl. Soft Comput. 24, 284–290 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Boston University, Boston, MA, 02215, USA

    Konstantinos Ameranis

  2. National Technical University of Athens, 9 Iroon Polytechniou Street, 15780, Zografou, Greece

    Nikolaos Vathis & Dimitris Fotakis

Authors
  1. Konstantinos Ameranis
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  2. Nikolaos Vathis
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  3. Dimitris Fotakis
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Corresponding author

Correspondence to Nikolaos Vathis .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. University of Ioannina, Ioannina, Greece

    Konstantinos E. Parsopoulos

  4. Delft University of Technology, Delft, The Netherlands

    Dimitris Souravlias

  5. University of Florida, Gainesville, FL, USA

    Arsenis Tsokas

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Ameranis, K., Vathis, N., Fotakis, D. (2019). Minimum and Maximum Category Constraints in the Orienteering Problem with Time Windows. In: Kotsireas, I., Pardalos, P., Parsopoulos, K., Souravlias, D., Tsokas, A. (eds) Analysis of Experimental Algorithms. SEA 2019. Lecture Notes in Computer Science(), vol 11544. Springer, Cham. https://doi.org/10.1007/978-3-030-34029-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-34029-2_23

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