Sports League Scheduling Problem

Problem description

Parameters :

• $T$ : Set of teams of size $T_size \in {n \in \N^+\ |\ n \mod 2 = 0}$
• $W$ : The number of weeks where $W = T-1$
• $P$ : The number of periods where $P = \frac{T}{2}$

Variables :

• $S$ : Array of size $W \times P$ where each cell is a couple $(t, t')$ that represents a match between two teams $t, t' \in T$

Model :

• $\forall (T_n, T_k) \in S, n < k, \forall n, k \in Tsize$
• $\forall t \in T, (\sum_j^P t \in S_{i, j} == 1) = 1, \forall i \in [0..W]$
• $\forall t \in T, (\sum_i^W t \in S_{i, j} == 1) <= 2, \forall j \in [0..P]$

Strategy

• We first initialize a graph where an edge is a team, an edge is a match and its label the week number
• Swap two matches if at least one of them is conflicting with the model (only matches on the same week)
• Tabou list to prevent from swapping two matches that have been swapped recently