A Matrix-Based Multi-Objective Genetic Algorithm for Nurse Scheduling Optimization

Hongshen Kang, Xiao-Fang Liu, Dan-Ting Duan, Jian-Ming Jiang

Abstract: In healthcare management, nurse scheduling optimization usually involves multiple complex constraints and conflicting objectives, such as minimizing costs, maximizing nurse satisfaction, ensuring workload equity, and so on. Although existing methods have achieved promising results, the nurse scheduling problem still faces challenges regarding convergence difficulty and a lack of solution diversity. Therefore, this paper proposes a Matrix-based Multi-objective Genetic Algorithm (MMOGA). Specifically, we define the problem as a multi-objective optimization that comprehensively considers factors such as nurse income, fatigue, and preference matching. The final goal is to simultaneously optimize the satisfaction of both nurses and the hospital with the scheduling results. To address this problem, we first establish two distinct populations to optimize the two objectives separately, followed by sharing superior solutions between the populations to enhance solution quality. Furthermore, we design matrix-based personalized genetic operators, aiming to achieve efficient and diverse genetic operations Experimental results on multiple instances demonstrate that MMOGA outperforms traditional algorithms in terms of running time, solution quality, hypervolume and inverted generational distance indicators.