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Locally Optimized Crossover for the Traveling Umpire Problem

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  • Trick, Michael A.
  • Yildiz, Hakan

Abstract

This paper presents a genetic algorithm (GA) to solve the Traveling Umpire Problem, which is a recently introduced sports scheduling problem that is based on the most important features of the real Major League Baseball umpire scheduling problem. In our GA, contrary to the traditional way of randomly obtaining new solutions from parent solutions, we obtain partially optimized solutions with a Locally Optimized Crossover operator. This operator also presents a link between the evolutionary mechanism on a population of solutions and the local search on a single solution. We present improved results over other methods on benchmark instances.

Suggested Citation

  • Trick, Michael A. & Yildiz, Hakan, 2012. "Locally Optimized Crossover for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 216(2), pages 286-292.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:286-292
    DOI: 10.1016/j.ejor.2011.07.049
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    References listed on IDEAS

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    1. Charu C. Aggarwal & James B. Orlin & Ray P. Tai, 1997. "Optimized Crossover for the Independent Set Problem," Operations Research, INFORMS, vol. 45(2), pages 226-234, April.
    2. Dirk Briskorn, 2008. "Sports Leagues Scheduling," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-75518-0, December.
    3. James R. Evans, 1988. "A Microcomputer-Based Decision Support System for Scheduling Umpires in the American Baseball League," Interfaces, INFORMS, vol. 18(6), pages 42-51, December.
    4. Adam Farmer & Jeffrey S. Smith & Luke T. Miller, 2007. "Scheduling Umpire Crews for Professional Tennis Tournaments," Interfaces, INFORMS, vol. 37(2), pages 187-196, April.
    5. Rasmussen, Rasmus V. & Trick, Michael A., 2008. "Round robin scheduling - a survey," European Journal of Operational Research, Elsevier, vol. 188(3), pages 617-636, August.
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    Cited by:

    1. Xue, Li & Luo, Zhixing & Lim, Andrew, 2015. "Two exact algorithms for the traveling umpire problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 932-943.
    2. Mills, Brian M. & Salaga, Steven, 2018. "A natural experiment for efficient markets: Information quality and influential agents," Journal of Financial Markets, Elsevier, vol. 40(C), pages 23-39.
    3. Guillermo Durán, 2021. "Sports scheduling and other topics in sports analytics: a survey with special reference to Latin America," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 125-155, April.
    4. Toffolo, Túlio A.M. & Wauters, Tony & Van Malderen, Sam & Vanden Berghe, Greet, 2016. "Branch-and-bound with decomposition-based lower bounds for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 250(3), pages 737-744.
    5. Mancini Simona & Isabello Andrea, 2014. "Fair referee assignment for the Italian soccer serieA," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 1-8, June.
    6. de Oliveira, Lucas & de Souza, Cid C. & Yunes, Tallys, 2014. "Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic," European Journal of Operational Research, Elsevier, vol. 236(2), pages 592-600.
    7. Yun-Chia Liang & Yen-Yu Lin & Angela Hsiang-Ling Chen & Wei-Sheng Chen, 2021. "Variable Neighborhood Search for Major League Baseball Scheduling Problem," Sustainability, MDPI, vol. 13(7), pages 1-18, April.
    8. Wauters, Tony & Van Malderen, Sam & Vanden Berghe, Greet, 2014. "Decomposition and local search based methods for the traveling umpire problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 886-898.
    9. Bender Marco & Westphal Stephan, 2016. "A combined approximation for the traveling tournament problem and the traveling umpire problem," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(3), pages 139-149, September.

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