Combining discrete and continuous information for multi-criteria optimization problems

Pub Date : 2024-02-23 DOI:10.1007/s00186-024-00849-0

引用次数: 0

Abstract

In multi-criteria optimization problems that originate from real-world decision making tasks, we often find the following structure: There is an underlying continuous, possibly even convex model for the multiple outcome measures depending on the design variables, but these outcomes are additionally assigned to discrete categories according to their desirability for the decision maker. Multi-criteria deliberations may then take place at the level of these discrete labels, while the calculation of a specific design remains a continuous problem. In this work, we analyze this type of problem and provide theoretical results about its solution set. We prove that the discrete decision problem can be tackled by solving scalarizations of the underlying continuous model. Based on our analysis we propose multiple algorithmic approaches that are specifically suited to handle these problems. We compare the algorithms based on a set of test problems. Furthermore, we apply our methods to a real-world radiotherapy planning example.

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结合离散和连续信息，解决多标准优化问题

摘要在源于现实世界决策任务的多标准优化问题中，我们经常会发现以下结构：对于取决于设计变量的多种结果测量，存在一个基本的连续模型，甚至可能是凸模型，但这些结果又根据决策者的可取性被分配到离散类别中。然后，可以在这些离散标签的层面上进行多标准审议，而具体设计的计算仍然是一个连续问题。在这项工作中，我们分析了这类问题，并提供了有关其解决方案集的理论结果。我们证明，离散决策问题可以通过求解底层连续模型的标量化来解决。基于我们的分析，我们提出了专门适用于处理这些问题的多种算法方法。我们根据一组测试问题对这些算法进行了比较。此外，我们还将我们的方法应用于现实世界中的放射治疗规划实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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