Genetic Programming with Model Driven Dimension Repair for Learning Interpretable Appointment Rules

Appointment scheduling is a great challenge in healthcare operations management. Appointment rules (AR) provide medical practitioners with a simple yet effective tool to determine patient appointment times. Genetic programming (GP) can be used to evolve ARs. However, directly applying GP to design ARs may lead to rules that are difficult for end-users to interpret and trust. A key reason is that GP is unaware of the dimensional consistency, which ensures that the evolved rules align with users’ domain knowledge and intuitive understanding. In this paper, we develop a new dimensionally aware GP algorithm that integrates a dimension repair procedure to evolve ARs with high interpretability and performance. The repair procedure is formulated as a mixed-integer linear programming model, which minimizes the structural changes to convert an original tree to a dimensionally consistent tree. This procedure allows our method to explore a wider range of AR structures while maintaining their overall structure, thereby identifying individuals with greater potential advantages. We evaluated the proposed method in a comprehensive set of simulated and real clinics. The experimental results demonstrate that our approach managed to evolve high-quality ARs that significantly outperform not only the manually designed ARs but also existing state-of-the-art dimensionally aware GP methods in terms of both objective values and dimensional consistency. In addition, we analyzed the semantics of the evolved ARs, providing insight into the design of more effective and interpretable ARs.