Variable Neighbourhood Search for Nurse Rostering Problems

Nurse rostering problems consist of assigning varying tasks, represented as shift types, to hospital personnel with different skills and work regulations. We want to satisfy as many constraints and personal preferences as possible while constructing a schedule which meets the personnel requirements of the hospital over a predefined planning period. Real world situations are often so constrained that finding a good quality solution requires advanced heuristics to keep the calculation time down. In previous research, heuristics based on Tabu Search [3] and Memetic Algorithms [1] were successfully applied to the problem. Due to the very diverse nature of the constraints, good quality solutions are often very hard to find. Some constraints refer to particular duties of the nurses while other constraints restrict consecutive duties, days, weekends, etc. The cost function used by the meta-heuristics sums the penalties of the violations of each of the soft constraints. Meta-heuristics are not always powerful enough to escape from local minima, because of the broad variety of constraints. The characteristics of the constraints are so different that the solution space seems to consist of a hilly landscape with very deep and narrow valleys. In this paper, we present a variable neighbourhood search approach for the nurse rostering problem. The method allows for a better exploration of the search space, by combining short sighted neighbourhoods and very greedy ones.