Solving the traveling tournament problem with iterative-deepening A∗
This work presents an iterative-deepening A∗ (IDA∗) based approach to the traveling tournament problem (TTP). The TTP is a combinatorial optimization problem which abstracts the Major League Baseball schedule. IDA∗ is able to find optimal solutions to this problem, with performance improvements coming from the incorporation of various past concepts including disjoint pattern databases, symmetry breaking, and parallelization along with new ideas of subtree skipping, forced deepening, and elite paths to help to reduce the search space. The results of this work show that an IDA∗ based approach can find known optimal solutions to most TTP instances much faster than past approaches. More importantly, it has been able to optimally solve two larger instances that have been unsolved since the problem’s introduction in 2001. In addition, a new problem set called GALAXY is introduced, using a 3D space to create a challenging problem set.
KeywordsSports scheduling Traveling tournament problem Heuristic search Iterative-deepening A∗
Unable to display preview. Download preview PDF.
- Benoist, T., Laburthe, F., & Rottembourg, B. (2001). Lagrange relaxation and constraint programming collaborative schemes for travelling tournament problems. In CP-AI-OR 2001 (pp. 15–26). Wye College, UK. Google Scholar
- Dechter, R. (2003). Constraint processing. San Francisco: Morgan Kaufmann. Google Scholar
- Easton, K., Nemhauser, G. L., & Trick, M. A. (2001). The traveling tournament problem: Description and benchmarks. In T. Walsh (Ed.), Lecture notes in computer science (Vol. 2239, pp. 580–584). Berlin: Springer. Google Scholar
- Easton, K., Nemhauser, G., & Trick, M. (2003). Solving the travelling tournament problem: A combined integer programming and constraint programming approach. In Lecture notes in computer science: Vol. 2740. Practice and theory of automated timetabling IV (pp. 100–109). Berlin/Heidelberg: Springer. CrossRefGoogle Scholar
- Hafidi, Z., Talbi, E. G., & Goncalves, G. (1995). Load balancing and parallel tree search: the MPIDA∗ algorithm. In E. H. D’Hollander, G. R. Joubert, F. J. Peters, & D. Trystram (Eds.), ParCo’95 (pp. 93–100). Amsterdam: Elsevier. Google Scholar
- Irnich, S., & Schrempp, U. (2008). A new branch-and-price algorithm for the traveling tournament problem. Presented at Column Generation 2008, Aussois, France, June 17–20, 2008. Available from: http://www.gerad.ca/colloques/ColumnGeneration2008/slides/SIrnich.pdf [Accessed 28 Nov, 2010].
- Rao, V. N., Kumar, V., & Ramesh, K. (1987). A parallel implementation of iterative-deepening-A∗. In Proceedings of AAAI (pp. 178–182). Google Scholar
- Trick, M. A. (2010). Challenge traveling tournament problems. http://mat.gsia.cmu.edu/TOURN/.
- Uthus, D. C., Riddle, P. J., & Guesgen, H. W. (2009b). DFS∗ and the traveling tournament problem. In: CPAIOR’09 (pp. 279–293). Berlin/Heidelberg: Springer. Google Scholar
- Vempaty, N., Kumar, V., & Korf, R. (1991). Depth-first vs best-first search. In Proceedings of AAAI-91 (pp. 434–440). Google Scholar