An Efficient Simulated Annealing Approach to the Travelling Tournament Problem
- 1 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
- 2 Faculty of department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
- 3 Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Abstract
Scheduling sports leagues has drawn significant attention to itself in recent years, as it involves considerable revenue as well as challenging combinatorial optimization problems. A particular class of these problems is the Traveling Tournament Problem (TTP) which focuses on minimizing the total traveling distance for teams. In this paper, an efficient simulated annealing approach is presented for TTP which applies two simultaneous and disparate models for the problem in order to search the solutions space more effectively. Also, a computationally efficient modified greedy scheme is proposed for constructing a favorable initial solution for the simulated annealing algorithm. Our computational experiments, carried out on standard instances, demonstrate that this approach competes with previous offered methods in quality of found solutions and their computational time.
- A. K. Easton, G. Nemhauser and M. Trick, “The Traveling Tournament Problem: Description and Benchmarks,” Lecture Notes in Computer Science, Vol. 2239, 2001, pp. 580-585. doi:10.1007/3-540-45578-7_43
- J. C. Bean and J. R. Birge, “Reducing Travelling Costs and Player Fatigue in the National Basketball Association,” Interfaces, Vol. 10, No. 3, 1980, pp. 98-102. doi:10.1287/inte.10.3.98
- A. Anagnostopoulos, L. Michel, P. Van Hentenryck and Y. Vergados, “A Simulated Annealing Approach to the Traveling Tournament Problem,” International Workshop on Integration of AI and OR Techniques, Montreal, 2003.
- J. A. M. Schreuder, “Constructing Timetables for Sport Competitions,” Mathematical Programming Study, Vol. 13, 1980, pp. 58-67. doi:10.1007/BFb0120907
- D. de Werra, “Scheduling in Sports,” Studies on Graphs and Discrete Programming, 1981, pp. 381-395.
- D. de Werra, “Some Models of Graphs for Scheduling Sports Competitions,” Discrete Applied Mathematics, Vol. 21, No. 1, 1988, pp. 47-65. doi:10.1016/0166-218X(88)90033-9
- R. T. Campbell and D. S. Chen, “A Minimum Distance Basketball Scheduling Problem,” Management Science in Sports, Studies in the Management Sciences, Vol. 4, 1976, pp. 15-26.
- D. Costa, “An Evolutionary Tabu Search Algorithm and the NHL Scheduling Problem,” Information Systems and Operational Research, Vol. 33, 1995, pp. 161-178.
- M. B. Wright, “Scheduling Fixtures for Basketball New Zealand,” Computers & Operations Research, Vol. 33, No. 7, 2006, pp. 1875-1893. doi:10.1016/j.cor.2004.09.024
- T. Benoist, F. Laburthe and B. Rottembourg, “Lagrange Relaxation and Constraint Programming Collaborative Schemes for Traveling Tournament Problems,” International Workshop on Integration of AI and OR Techniques, Ashford, Kent, 2001.
- K. Easton, G. Nemhauser and M. Trick, “Solving the Traveling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach,” Lecture Notes in Computer Science, Vol. 2740, 2003, pp. 100-109. doi:10.1007/978-3-540-45157-0_6
- J. H. Lee, Y. H. Lee and Y. H. Lee, “Mathematical Modeling and Tabu Search Heuristic for the Traveling Tournament Problem,” Lecture Notes in Computer Science, Vol. 3982, 2006, pp. 875-884. doi:10.1007/11751595_92
- K. K. H. Cheung, “Solving Mirrored Traveling Tournament Problem Benchmark Instances with Eight Teams,” Discrete Optimization, Vol. 5, No. 1, 2008, pp. 138-143. doi:10.1016/j.disopt.2007.11.003