J Sched (2006) 9: 177–193 DOI 10.1007/s10951-006-7187-8 A simulated annealing approach to the traveling tournament problem ∗ A. Anagnostopoulos · L. Michel † · P. Van Hentenryck · Y. Vergados C  Springer Science + Business Media, LLC 2006 Abstract Automating the scheduling of sport leagues has received considerable attention in recent years, as these applications involve significant revenues and generate challenging com- binatorial 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. Keywords Sport scheduling . Travelling tournament problems . Local search . Simulated annealing Introduction The scheduling of sport leagues has become an important class of combinatorial optimization applications in recent years for two main reasons. On the one hand, sport leagues represent sig- nificant sources of revenue for radio and television networks around the world. On the other hand, sport leagues generate extremely challenging optimization problems. See Easton, Nemhauser and Trick (2001) for an excellent review of these problems, recent research activities, and several solution techniques. ∗ A Preliminary version of this paper was presented at the CP’AI’OR’03 Workshop. A. Anagnostopoulos · L. Michel · P. Van Hentenryck ()· Y. Vergados Brown University, Box 1910, Providence, RI 02912 L. Michel Present address: University of Connecticut, Stoors, CT 06269