A study of multi-objective home healthcare routing problem considering interpersonal relationships and complex uncertainty scenarios

Caregiver pathway planning is one of the most important tasks in a home healthcare organization, and the development of practical visit pathways needs to take into account the impact of many factors. Based on this, this paper proposes a multi-objective home healthcare routing and scheduling problem considering a complex uncertain scenario, which takes into account three uncertain parameters: caregiver departure time, patient demand, and travel time, and constructs a robust optimization model. The model accounts for patients with varying numbers of multiple time windows and optimizes three objectives under constraints such as skill matching, patient-caregiver interpersonal relationships, and maximum working hours. These objectives include minimizing total service costs, enhancing patient satisfaction, and balancing caregiver workloads. Then we use the improved multi-task constrained multi-objective optimization algorithm by adding a multi-modal crossover operator, local search operator, and elite guidance strategy to solve the model. Experimental results show that the algorithm can provide a large number of feasible non-dominated solutions for decision-makers to choose from. By comparing with improved multi-task constrained multi-objective optimization algorithm and the second-generation non-dominated sorting genetic algorithms, it is shown that the algorithm can obtain a larger number of feasible non-dominated solutions with good diversity, convergence, and distribution. This study provides decision-makers with a practical framework for optimizing home healthcare routing and scheduling in complex and uncertain environments. It helps decision-makers balance trade-offs between total costs, patient satisfaction, and caregiver workload, and supports adjustments to robustness levels based on risk preferences.