An Improved Neighbourhood for the Traveling Tournament Problem

TL;DR

This paper introduces an enhanced search neighborhood for the Traveling Tournament Problem, improving solution quality and efficiency, and achieving the best known solutions for large instances and proven optimal solutions for smaller ones.

Contribution

It presents a novel search neighborhood that includes feasible and infeasible schedules, enabling more effective exploration in simulated annealing for TTP.

Findings

Achieved best known solutions for TTP with up to 40 teams.

Found three proven optimal solutions for TTP with 10 teams.

Demonstrated efficiency in generating solutions for large and small instances.

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.