Evolutionary Harmony Search Algorithm for Sport Scheduling Problem

Abstract

In this paper, an original enhanced harmony search algorithm (HS-TTP) is proposed for the well-known NP-hard traveling tournament problem (TTP) in sports scheduling. TTP is concerned with finding a tournament schedule that minimizes the total distances traveled by the teams. TTP is well-known, and an important problem within the collective sports communities since a poor optimization in TTP can cause heavy losses in the budget of managing the league’s competition. In order to apply HS to TTP, we use a largest-order-value rule to trans-form harmonies from real vectors to abstract schedules. We introduce a new heuristic for rearranging the scheduled rounds which give us a significant enhancement in the quality of the solutions. Further, we use a local search as a subroutine in HS to improve its intensification mechanism. The overall method (HS-TTP) is evaluated on publicly available standard benchmarks and compared with the state-of-the-art techniques. Our approach succeeds in finding optimal solutions for several instances. For the other instances, the general deviation from optimality is equal to 4.45%. HS-TTP is able to produce high-quality results compared to existing methods.