Sports League Scheduling Problem

Problem description

Parameters :

• $T$ : Set of teams of size $T_{s}ize\in n\in {\text{N}}^{+}|n\mathrm{mod}2=0$
• $W$ : 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 $(t,t^{\prime })$ that represents a match between two teams $t,t^{\prime }\in T$

Model :

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

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