A combined mixed integer programming and deep neural network-assisted heuristics algorithm for the nurse rostering problem

The objective of the nurse rostering problem (NRP) is to obtain a scheduling plan that optimizes the allocation of human resources, effectively reducing work pressure on nurses and improving work efficiency and quality. Because various constraints must be considered during scheduling, the NRP is complicated and known to be NP-hard. Existing research has not combined learning mechanisms with NRP. This study constructively explores the possibility of combining an optimization method and a learning mechanism to automatically produce feasible solutions and proposes a feature vector and a reconstruction mechanism to assist in this exploration. We aim to learn a policy that is generalizable for NRPs of various sizes and design a hybrid algorithm with learning and optimization methods to solve the general NRP. The algorithm has two main parts: a deep neural network (DNN) improvement part and a reconstruction part. In the DNN improvement part, a feature vector is used to describe heterogeneous NRP solutions and normalizes these solutions to the same dimension. Then, the DNN model determines the best heuristic for approximating the local optimal solution. The method reconstructs the structure of the current solution with embedded mixed integer programming (MIP), quickly escaping the local optimum and enhancing the diversity of the search process, increasing the likelihood of determining an optimal solution. Different experiments and statistical tests were conducted by comparing various configurations and approaches. The detailed computational and statistical results demonstrate the competitive performance of the proposed method.