2022 年 16 巻 4 号 p. JAMDSM0042
Roundrobin tournaments are widely used in sports leagues such as football and baseball leagues. The roundrobin tournament scheduling problem is one of the most wellknown problems in sports scheduling. When creating a schedule for a roundrobin tournament, various factors are considered such as travel distance of teams and the number of breaks. Among such factors, the carryover effect is often considered to evaluate a schedule from the viewpoint of fairness. In this paper, we propose a metaheuristic algorithm for the problem of minimizing the carry-over effect value. For a complete graph whose edges describe all possible matches in a roundrobin tournament, we consider a rainbow perfect matching, which we call a base matching, to describe a round of a schedule. By using the circle method, a roundrobin tournament schedule can be generated from any base matching. Then we design a metaheuristic algorithm based on iterated local search to search for a “good” base matching, that is, one that generates a roundrobin tournament schedule with a low carryover effect value. We confirmed through computational experiments that our proposed algorithm obtained solutions with carryover effect values equal to or lower than the bestknown values for 15 out of the 17 tested instances with up to 40 teams. In addition, we updated the bestknown records for 2 instances.
