用可修复维度的遗传编程，自动学出好懂又靠谱的预约规则
Genetic Programming with Model Driven Dimension Repair for Learning Interpretable Appointment Scheduling Rules
- 引入维度修复机制，让进化规则始终符合领域常识
- 在模拟诊所中表现优于人工规则和现有顶尖方法
- 适合医疗调度优化与可解释性要求高的场景
预约调度是医疗运营管理中的重大挑战。预约规则（AR）为医护人员提供了一种简单有效的患者排班工具。遗传编程（GP）可用于演化AR。然而，直接应用GP可能导致规则难以理解与信任，关键原因是GP不关注维度一致性，无法保证规则符合用户领域知识和直觉。本文提出一种具备维度修复功能的新型维度感知遗传编程算法，以生成兼具维度一致性和高性能的预约规则。核心创新在于维度修复流程：在保持表达式树整体结构最小变动的前提下，优化其维度一致性，并确保输出维度满足问题需求。该任务被建模为混合整数线性规划，可用通用数学规划方法高效求解。借助维度修复机制，本方法可在临时打破维度一致性的情况下探索更广的规则结构空间，再恢复一致性而不改变整体结构，从而发现更具优势的个体。我们在一组模拟诊所中进行了全面评估。实验结果表明，该方法演化出的高质量规则，在目标值和维度一致性上均显著优于人工设计规则及现有最先进的维度感知GP方法。此外，我们分析了演化规则的语义，为设计更有效、可解释的规则提供了洞见。
原文摘要 · Abstract (English)
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 with dimension repair to evolve ARs with dimensional consistency and high performance. A key innovation of our method is the dimension repair procedure, which optimizes the dimensional consistency of an expression tree while minimizing structural changes and ensuring that its output dimension meets the problem's requirements. We formulate the task as a mixed-integer linear programming model that can be efficiently solved using common mathematical programming methods. With the support of the dimension repair procedure, our method can explore a wider range of AR structures by temporarily breaking the dimensional consistency of individuals, and then restoring it without altering their overall structure, thereby identifying individuals with greater potential advantages. We evaluated the proposed method in a comprehensive set of simulated 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.
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