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A note on symmetry reduction for circular traveling tournament problems

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  • Gschwind, Timo
  • Irnich, Stefan

Abstract

The traveling tournament problem (TTP) consists of finding a distance-minimal double round-robin tournament where the number of consecutive breaks is bounded. Easton et al. (2001) introduced the so-called circular TTP instances, where venues of teams are located on a circle. The distance between neighboring venues is one, so that the distance between any pair of teams is the distance on the circle. It is empirically proved that these instances are very hard to solve due to the inherent symmetry. This note presents new ideas to cut off essentially identical parts of the solution space. Enumerative solution approaches, e.g. relying on branch-and-bound, benefit from this reduction. We exemplify this benefit by modifying the DFS* algorithm of Uthus et al. (2009) and show that speedups can approximate factor 4n.

Suggested Citation

  • Gschwind, Timo & Irnich, Stefan, 2011. "A note on symmetry reduction for circular traveling tournament problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 452-456, April.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:452-456
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    References listed on IDEAS

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    1. Irnich, Stefan, 2010. "A new branch-and-price algorithm for the traveling tournament problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 218-228, July.
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    Cited by:

    1. Zheng, Feifeng & Cheng, Yongxi & Xu, Yinfeng & Liu, Ming, 2013. "Competitive strategies for an online generalized assignment problem with a service consecution constraint," European Journal of Operational Research, Elsevier, vol. 229(1), pages 59-66.

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