Abstract Despite the multi-objective nature of the nurse rostering problem (NRP), most NRP formulations employ a single evaluation function that minimizes the weighted sum of constraint violations. When solving the NRP in practice, the focus should be on obtaining compromise solutions: those with appropriate trade-offs between different constraints. Due to the real-world characteristics of the problem, appropriate trade-offs may vary substantially across instances, and quantifying these trade-offs does not necessarily translate well into a single evaluation function. This paper introduces a new multi-objective approach for the NRP that promotes controlled trade-offs and guides the solver towards acceptable compromise solutions. The method consists of two phases. The first phase quantifies the characteristics of acceptable compromise solutions by estimating acceptance thresholds that implicitly incorporate trade-offs. This quantification is performed automatically by drawing upon the instance at hand and identifying appropriate trade-offs. The second phase solves the NRP by employing these acceptance thresholds in a lexicographic goal programming framework. By automatically estimating instance-specific acceptance thresholds, we not only require minimal information from the user but also obtain a realistic prediction for solution quality. A case study shows that the methodology produces rosters with little or no deviations from acceptance thresholds, within only a few minutes. Furthermore, this methodology provides the user with clear reasoning behind the trade-offs made, as opposed to methods employing a single evaluation function.

中文翻译：

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通过使用自动估计的接受阈值在护士排班中实现折衷解决方案

摘要 尽管护士排班问题 (NRP) 具有多目标性质，但大多数 NRP 公式采用单一评估函数，以最小化约束违规的加权总和。在实践中解决 NRP 时，重点应该是获得折衷解决方案：在不同约束之间进行适当权衡的解决方案。由于问题的现实特征，适当的权衡可能因实例而异，量化这些权衡并不一定能很好地转化为单一的评估函数。本文介绍了一种新的 NRP 多目标方法，该方法促进了控制权衡并引导求解器走向可接受的折衷解决方案。该方法由两个阶段组成。第一阶段通过估计隐含权衡的接受阈值来量化可接受的折衷解决方案的特征。这种量化是通过利用手头的实例并确定适当的权衡来自动执行的。第二阶段通过在词典目标编程框架中使用这些接受阈值来解决 NRP。通过自动估计特定于实例的接受阈值，我们不仅需要来自用户的最少信息，而且还可以获得对解决方案质量的现实预测。一项案例研究表明，该方法仅在几分钟内即可生成与接受阈值几乎没有偏差或没有偏差的名册。此外，这种方法为用户提供了做出权衡背后的清晰推理，