A simulated annealing approach to the traveling tournament problem

Automating the scheduling of sport leagues has received considerable attention in recent years, as these applications involve significant revenues and generate challenging combinatorial optimization problems. This paper considers the traveling tournament problem (TTP) which abstracts the salient features of major league baseball (MLB) in the United States. It proposes a simulated annealing algorithm (TTSA) for the TTP that explores both feasible and infeasible schedules, uses a large neighborhood with complex moves, and includes advanced techniques such as strategic oscillation and reheats to balance the exploration of the feasible and infeasible regions and to escape local minima at very low temperatures. TTSA matches the best-known solutions on the small instances of the TTP and produces significant improvements over previous approaches on the larger instances. Moreover, TTSA is shown to be robust, because its worst solution quality over 50 runs is always smaller or equal to the best-known solutions.