We propose a self-adaptive Ant Colony Optimization (AD-ACO) approach that exploits a parameter adaptation mechanism to reduce the requirement of a preliminary parameter tuning. The proposed AD-ACO is based on an ACO algorithm adopting a pheromone model with a new global pheromone update mechanism. We applied this algorithm to the single machine total weighted tardiness scheduling problem with sequence-dependent setup times and we executed an experimental campaign on a benchmark available in literature. Results, compared with the ones produced by the ACO algorithm without adaptation mechanism and with those obtained by recently proposed metaheuristic algorithms for the same problem, highlight the quality of the proposed approach.