Abstract
A player b in a round-robin sports tournament receives a carry-over effect from another player a if some third player opposes a in round i and b in round i+1. Let γ(ab) denote the number of times player b receives a carry-over effect from player a during a tournament. Then the carry-over effects value of the entire tournament T on n players is given by Γ(T)=ΣΣγ(ij)^2. Furthermore, let Γ(n) denote the minimum carry-over effects value over all round-robin tournaments on n players. A strict lower bound on Γ(n) is n(n-1) (in which case there exists a round-robin tournament of order n such that each player receives a carry-over effect from each other player exactly once), and it is known that this bound is attained for n=2^r or n=20,22. It is also known that round-robin tournaments can be constructed from so-called starters; round-robin tournaments constructed in this way are called cyclic. It has previously been shown that cyclic round-robin tournaments have the potential of admitting small values for Γ(T), and in this paper a tabu-search is used to find starters which produce cyclic tournaments with small carry-over effects values. The best solutions in the literature are matched for n
Highlights
The scheduling of round-robin sports tournaments has given rise to a number of interesting optimisation problems in the theory of sports tournament scheduling, as recently summarised in the excellent annotation by Kendall et al [12]
In this paper a tabu-search algorithm was implemented in order to find a starter that produces a round-robin tournament with a small COE-value
The best previously published solutions were validated for round-robin tournaments of orders 4 ≤ n ≤ 22, and for n = 24 the best previously published solution found was improved
Summary
The scheduling of round-robin sports tournaments has given rise to a number of interesting optimisation problems in the theory of sports tournament scheduling, as recently summarised in the excellent annotation by Kendall et al [12]. In the majority of the wellstudied problems concerning sports tournament scheduling, the venues of the matches for a certain team throughout the tournament (often classified as home or away) play a significant role. Examples include the minimum breaks problem [3] (where a break in the tournament occurs when a team plays two consecutive home games or two consecutive away games) and the travelling-tournament problem [5], where the distances travelled between venues by the various teams are to be minimised
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
