Classification of Various Neighborhood Operations for the Nurse Scheduling Problem

Since the nurse scheduling problem (NSP) is a problem of finding a feasible solution, the solution space must include infeasible solutions to solve it using a local search algorithm. However, the solution space consisting of all the solutions is so large that the search requires much CPU time. In the NSP, some constraints have higher priority. Thus, we can define the solution space to be the set of solutions satisfying some of the important constraints, which are called the elementary constraints. The connectivity of the solution space is also important for the performance. However, the connectivity is not obvious when the solution space consists only of solutions satisfying the elementary constraints and is composed of small neighborhoods. This paper gives theoretical support for using 4-opt-type neighborhood operations by discussing the connectivity of its solution space and the size of the neighborhood. Another interesting point in our model is a special case of the NSP corresponds to the bipartite transportation problem, and our result also applies to it.