In this article we present an approach designed to solve a real world problem: the Anesthesiology Nurse Scheduling Problem (ANSP) at a public French hospital. The anesthesiology nurses are one of the most shared resources in the hospital and we attempt to find a fair/balanced schedule for them, taking into account a set of constraints and the nurses' stated preferences, concerning the different shifts. We propose a particle swarm optimization algorithm to solve the ANSP. Finally, we compare our technique with previous results obtained using integer programming.