Abstract
This paper proposes an original and effective heuristic approach for solving the unconstrained traveling tournament problem (denoted by UTTP) in sport scheduling. UTTP is an interesting variant of the well-known NP-hard traveling tournament problem (TTP) where the main objective is to find a tournament schedule that minimizes the total distances traveled by the teams. The proposed graph-based heuristic method starts with a set of n teams \((n< 10)\). The method models the problem by representing the home locations of the teams as vertices and each arc corresponds to the matching between two teams. Each round corresponds to a 1-factor of the generated graph. We use the Bron-Kerbosch clique detection algorithm to enumerate all the possible \(2(n-1)\) cliques from the 1-factors. Then, the vertices of each \(2(n-1)\) cliques are sorted to create double round robin tournament (DRRT) schedules. The schedule with lowest cost travel is selected to be the solution of the problem. The proposed method is evaluated on several instances and compared with the state-of-the-art. The numerical results are promising and show the benefits of our method. The proposed method significantly improves the current best solutions for the US National Baseball League (NL) instances and produces new good solutions for the Rugby League (SUPER) instances.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anagnostopoulos, A., Michel, L., Van Hentenryck, P., Vergados, Y.: A simulated annealing approach to the traveling tournament problem. J. Sched. 9(2), 177–193 (2006)
Bellmore, M., Nemhauser, G.L.: The traveling salesman problem: a survey. Oper. Res. 16(3), 538–558 (1968)
Bhattacharyya, R.: Complexity of the unconstrained traveling tournament problem. Oper. Res. Lett. 44(5), 649–654 (2016)
Biajoli, F.L., Lorena, L.A.N.: Clustering search approach for the traveling tournament problem. In: Gelbukh, A., Kuri Morales, Á.F. (eds.) MICAI 2007. LNCS (LNAI), vol. 4827, pp. 83–93. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76631-5_9
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)
de Carvalho, M.A.M., Lorena, L.A.N.: New models for the mirrored traveling tournament problem. Comput. Ind. Eng. 63(4), 1089–1095 (2012)
De Werra, D.: Scheduling in sports. Stud. Graphs Discrete Program. 11, 381–395 (1981)
Easton, K., Nemhauser, G., Trick, M.: The traveling tournament problem description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–584. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45578-7_43
Imahori, S., Matsui, T., Miyashiro, R.: A 2.75-approximation algorithm for the unconstrained traveling tournament problem. Ann. Oper. Res. 218(1), 237–247 (2014)
Irnich, S.: A new branch-and-price algorithm for the traveling tournament problem. Eur. J. Oper. Res. 204(2), 218–228 (2010)
Kendall, G., Knust, S., Ribeiro, C.C., Urrutia, S.: Scheduling in sports: an annotated bibliography. Comput. Oper. Res. 37(1), 1–19 (2010)
Khelifa, M., Boughaci, D.: A variable neighborhood search method for solving the traveling tournaments problem. Electr. Notes Discrete Math. 47, 157–164 (2015)
Khelifa, M., Boughaci, D.: Hybrid harmony search combined with variable neighborhood search for the traveling tournament problem. In: Nguyen, N.-T., Manolopoulos, Y., Iliadis, L., Trawiński, B. (eds.) ICCCI 2016, Part I. LNCS (LNAI), vol. 9875, pp. 520–530. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45243-2_48
Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59(2), 231–247 (1992)
Lim, A., Rodrigues, B., Zhang, X.: A simulated annealing and hill-climbing algorithm for the traveling tournament problem. Eur. J. Oper. Res. 174(3), 1459–1478 (2006)
Michael, T.: Challenge traveling tournament instances. http://mat.tepper.cmu.edu/TOURN/. Accessed Jan 2018
Rasmussen, R.V., Trick, M.A.: A Benders approach for the constrained minimum break problem. Eur. J. Oper. Res. 177(1), 198–213 (2007)
Rasmussen, R.V., Trick, M.A.: Round robin scheduling-a survey. Eur. J. Oper. Res. 188(3), 617–636 (2008)
Rasmussen, R.V., Trick, M.A.: The timetable constrained distance minimization problem. Ann. Oper. Res. 171(1), 45 (2009)
Ribeiro, C.C., Urrutia, S.: Heuristics for the mirrored traveling tournament problem. Eur. J. Oper. Res. 179(3), 775–787 (2007)
Rosenkrantz, D.J., Stearns, R.E., Lewis, P.M.: An analysis of several heuristics for the traveling salesman problem. In: Ravi, S.S., Shukla, S.K. (eds.) Fundamental Problems in Computing, pp. 45–69. Springer, Dordrecht (2009). https://doi.org/10.1007/978-1-4020-9688-4_3
Thielen, C., Westphal, S.: Complexity of the traveling tournament problem. Theor. Comput. Sci. 412(4–5), 345–351 (2011)
Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363(1), 28–42 (2006)
Westphal, S., Noparlik, K.: A 5.875-approximation for the traveling tournament problem. Ann. Oper. Res. 218(1), 347–360 (2014)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Khelifa, M., Boughaci, D., Aïmeur, E. (2018). A Novel Graph-Based Heuristic Approach for Solving Sport Scheduling Problem. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-98334-9_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98333-2
Online ISBN: 978-3-319-98334-9
eBook Packages: Computer ScienceComputer Science (R0)