An integer programming based ant colony optimisation method for nurse rostering

Nurse rostering problems are typically too large and hard to be solved exactly. In order to achieve quality solutions to these difficult problems, meta-heuristics are often employed. One such meta-heuristic is Ant Colony Optimisation (ACO), inspired by the pheromone trails left by ants. ACO works by guiding a heuristic solution construction by using these pheromones to direct weighted random choices. When the problem to be solved is highly constrained, finding feasible solutions is difficult, which can result in poor performance for ACO. To address this, we propose an ACO algorithm using an integer programming based solution construction method to ensure feasibility and select from a collection of schedules. The approach also uses a novel solution merging step that combines the information from multiple ants to generate a better final roster. We discuss several challenges inherent in this approach, and how they may be overcome. Computational results on highly constrained nurse rostering problem instances from the literature demonstrate the effectiveness of our proposed new hybrid metaheuristic.