Abstract. This paper considers all the variants of the traveling tournament prob) proposed in [17, 7] to abstract the salient features of major league baseball (MLB) in the United States. The variants include different distance metrics and both mirrored and non-mirrored schedules. The paper shows that, with appropriate enhancements, simulated annealing is robust across the distance metrics and mirroring. In particular, the algorithm matches or improves most bestknown solutions and produces numerous new best solutions spread over all classes of problems. The main technical contribution underlying these results is a number of compositive neighborhood moves that aggregate sequences of existing moves; these novel moves preserve the mirroring or distance structure of the candidate schedule, while performing interesting transformations.