关键词: 护理人员调度, 老年人心理煎熬函数, 等级匹配与等级偏差, 改进NSGA-II算法

Abstract: Currently, the elderly care services in China exhibit a “9073” structural characteristic, meaning 90% of elderly individuals choose home-based care, 7% opt for community-based care,and the remaining 3% select institutional care. In the home-based care service system, the primary reliance is on caregivers who provide in-home services. Existing research often explores caregiver scheduling from the perspective of optimizing service center operational costs. The mental health of the elderly is a crucial factor affecting their quality of life, and the timeliness of services has a significant impact on their mental health status. To address the optimization of elderly care worker scheduling, this study introduces psychological stress fuzzy time window constraints, comprehensively considering the differentiated needs of the elderly and the skill level match of caregivers, and constructs a bi-objective programming model to minimize both the psychological burden costs for elders and the operational costs for service centers.
   In response to the NP-hard characteristics of the new model, this paper designs a two-part encoding method based on the NSGA-II algorithm. The first and second parts represent service sequence and service level, respectively. Based on the sorting results of non-dominant relationships and crowding distance, and combined with binary tournament selection of individuals, a selection operation is designed. Aiming at the characteristics of the two-part encoding, crossover and mutation operators are designed to achieve the update operation of algorithm individuals. Meanwhile, an adaptive local search strategy is developed for the elite individuals, incorporating dynamic adjustment of local search probability to fully tap into their potential and seek higher quality solutions, further enhancing the algorithm’s local optimization capability. Finally, to retain higher quality solutions, a new solution acceptance criterion is designed to determine whether to accept a new solution based on three conditions.
   Taking Wujin district in Changzhou, Jiangsu province as an example, and utilizing the standard VRPTW dataset proposed by Solomon, case instances of three different scales are generated. Initially, the characteristics of the problem are analyzed using a small-scale case to verify the feasibility of the new model. The study examines the impact of the maximum psychological distress threshold on the psychological distress of the elderly using a small-scale case as an example. The results indicate that as the maximum psychological distress threshold decreases, the total psychological distress cost for the elderly declines, while total operational costs increase. When this threshold decreases, the time window for elderly individuals to receive services will shrink, and caregivers must arrive within this window to avoid substantial psychological distress costs. Finally, in small, medium, and large-scale cases, the performance comparison analysis shows that the algorithm presented in this paper exhibits better optimization performance than MOPSO and NSGA-II. The new algorithm demonstrates strong overall optimization capabilities across different scales, effectively balancing the psychological burden on the elderly and operational costs, achieving dual optimization of these two objectives. The home care personnel scheduling model and algorithm developed in this study, which consider the psychological burden on the elderly, provide a new and competitive solution for home-based elderly care research. Considering the scheduling of home care workers under emergency situations will be a direction for future research.

Key words: nursing staff scheduling, elderly psychological ordeal function, rank matching and rank deviation, improved NSGA-Ⅱ