  Single-elimination tournaments are the standard paradigm both for the main
tennis professional associations. Schedules are generated by allocating first
seeded and then unseeded players with seeds prevented from encountering each
other early in the competition. Besides, the distribution of pairings in the
first round between unseeded players and seeds for a yearly season may be
strongly unbalanced. This provides often a great disadvantage to some "unlucky"
unseeded players in terms of money prizes. Also, a fair distribution of matches
during a season would benefit from limiting in first rounds the presence of
Head-to-Head (H2H) matches between players that met in the recent past. We
propose a tournament generation approach in order to reduce in the first round
"unlucky" pairings and replay of H2H matches. The approach consists in a
clustering optimization problem inducing a consequent draw within each cluster.
A Non-Linear Mathematical Programming (NLMP) model is proposed for the
clustering problem so as to reach a fair schedule. The solution reached by a
commercial NLMP solver on the model is compared to the one reached by a faster
hybrid algorithm based on multi-start local search. The approach is
successfully tested on historical records from the recent Grand Slams
tournaments.
