An Improved Neighbourhood for the Traveling Tournament Problem

Abstract: The Traveling Tournament Problem (TTP) is a challenging combinatorial optimization problem that has attracted the interest of researchers around the world. This paper proposes an improved search neighbourhood for the TTP that has been tested in a simulated annealing context. The neighbourhood encompasses both feasible and infeasible schedules, and can be generated efficiently. For the largest TTP challenge problems with up to 40 teams, solutions found using this neighbourhood are the best currently known, and for smaller problems with 10 teams, three solutions found were subsequently proven optimal.