Robust Multi-Objective Optimization: Analysis and Approaches

鲁棒多目标优化：分析和方法

• 批准号: 426002582
• 负责人: Professorin Dr. Anita Schöbel
• 金额: --
• 依托单位: Arbeitsgruppe Optimierung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/426002582?language=en
• 关键词: Robust; Multi; Objective; Optimization; Analysis

This project deals with multi-objective optimization problems under uncertainty, i.e., it combines robust optimization with multi-objective optimization. Although uncertain data is common in most multi-objective real-world problems, research on robust multi-objective optimization started only recently. In the last six years, many concepts have been published which define what a "robust efficient" solution is, but not much theory on robust multi-objective optimization has been developed yet. More importantly, algorithms are scarce and if at all available then only for the simpler case of uncertain multi-objective problems whose robust counterparts are (deterministic) multi-objective problems. However, the robust counterpart of a multi-objective uncertain problem is usually a set-valued optimization problem. We propose to bring the theory on robust multi-objective optimization forward by working on aspects known from multi-objective optimization (such as scalarization or an efficient front) and from robust optimization (such as robust counterparts and the robustness gap). As we have to deal with set-valued optimization problems, a transfer of such aspects and results is not straightforward but needs suitable set order relations.The results obtained should be utilized in solution approaches for robust multi-objective problems which are to be tested with a focus on combinatorial robust multi-objective optimization problems.We furthermore will investigate which of our approaches are also suitable for more general set-valued optimization problems.

该项目处理不确定性下的多目标优化问题，即，它结合了鲁棒优化和多目标优化。虽然不确定数据在大多数多目标现实问题中很常见，但鲁棒多目标优化的研究才刚刚开始。在过去的六年里，许多概念已经发表，定义了什么是“鲁棒有效”的解决方案，但没有太多的理论，鲁棒多目标优化已经发展。更重要的是，算法是稀缺的，如果在所有可用的，然后只为简单的情况下，不确定的多目标问题，其强大的同行（确定性）多目标问题。然而，多目标不确定性问题的鲁棒对应问题通常是集值优化问题。我们建议通过从多目标优化（如标量化或有效前沿）和鲁棒优化（如鲁棒对应物和鲁棒性缺口）中已知的方面进行工作，将鲁棒多目标优化理论向前推进。由于我们必须处理集值优化问题，这些方面和结果的转移不是直接的，而是需要合适的集合顺序关系。所获得的结果应该被用于鲁棒多目标问题的求解方法，这些问题将被测试，重点是组合鲁棒多目标优化问题。我们还将研究哪些方法也适用于更一般的集合顺序关系。值优化问题