This paper addresses the general and challenging Sports Timetabling Problem proposed during the International Timetabling Competition of 2021 (ITC2021). The problem is expressed in a flexible format which enables modeling a number of real-world constraints that often occur in Sports Timetabling. An integer programming (IP) formulation and a fix-and-optimize heuristic are proposed to address the problem. The fix-and-optimize approach uses the IP formulation to heuristically decompose the problem into sub-problems and efficiently search on very large neighborhoods. The diverse ITC2021 benchmark instances were used to evaluate the proposed methods. The formulation resulted in proven optimal solutions for two instances. However, it failed to produce feasible solutions for most instances. The proposed fix-and-optimize, which uses an automatic sub-problem size calibration strategy, resulted in feasible solutions for 37 out of the 45 ITC2021 instances. Among these solutions, four are the best known in the literature. The proposed approach participated in the ITC2021 and was one of the finalists.

本文解决了 2021 年国际计时赛 (ITC2021) 期间提出的普遍且具有挑战性的体育计时问题。该问题以一种灵活的格式表示，该格式可以对体育时间表中经常出现的许多现实世界的约束进行建模。提出了整数规划 (IP) 公式和修复优化启发式算法来解决该问题。修复优化方法使用 IP 公式将问题启发式地分解为子问题，并在非常大的邻域上进行有效搜索。不同的 ITC2021 基准实例用于评估所提出的方法。该公式为两个实例提供了经过验证的最佳解决方案。但是，它未能为大多数情况提供可行的解决方案。建议的修复和优化，它使用自动子问题大小校准策略，为 45 个 ITC2021 实例中的 37 个提供了可行的解决方案。在这些解决方案中，有四个是文献中最著名的。提议的方法参加了 ITC2021 并且是决赛入围者之一。