Mixed-Integer Programming Approaches for Risk-Averse Multicriteria Optimization

用于规避风险的多标准优化的混合整数规划方法

• 批准号: 1537317
• 负责人: Simge Kucukyavuz
• 金额: $ 25.86万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2017-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1537317&HistoricalAwards=false
• 关键词: Mixed; Integer; Programming; Approaches; Risk

Risk-averse optimization aims to address decision-making problems in the presence of uncertainty that involves events of low probability but severe consequences. In addition, decision makers are often required to consider multiple and conflicting performance criteria when faced with such problems. Despite their ubiquity and wide-ranging impact, risk-averse optimization problems that involve multiple criteria, discrete decisions and recourse actions are not well studied. The goal of this project is to bridge this gap by developing novel models and effective methods that will enhance our knowledge base, and enable the solution of more realistic and general risk-averse multicriteria optimization problems. In particular, the problems that will be studied are prevalent in homeland security and humanitarian relief applications. By developing models and effective methods for such problems, this project will improve our ability to prepare for and respond to national emergencies.This project involves three major thrusts that will advance the development of models and methods for risk-averse multicriteria optimization. First, in the realm of single-stage optimization, a novel model for risk-averse multiobjective optimization is proposed, where the relative importance of the multiple criteria is ambiguous. To this end, a new robust multivariate risk measure with desirable theoretical properties must be defined. In this project, the problem of optimizing such a risk measure will be formulated as a concave minimization problem for which effective solution methods will be developed. Second, a rigorous study of the fundamental non-convex polyhedral substructures arising in the cut generation problems for optimization under multivariate risk will be conducted. Third, two-stage optimization problems under multivariate risk will be formulated to allow recourse decisions. For these problems, decomposition algorithms that involve successive linear approximations of the second-stage problems will be devised.

风险规避优化旨在解决存在不确定性的决策问题，这些不确定性涉及低概率但严重后果的事件。此外，决策者在面对这些问题时往往需要考虑多种相互冲突的业绩标准。 尽管其无处不在和广泛的影响，风险规避优化问题，涉及多个标准，离散决策和追索行动没有得到很好的研究。该项目的目标是通过开发新的模型和有效的方法来弥补这一差距，这些模型和方法将增强我们的知识库，并能够解决更现实和更一般的风险规避多目标优化问题。特别是，将研究的问题是普遍存在的国土安全和人道主义救济的应用。本项目通过开发解决这些问题的模型和有效方法，将提高我们防备和应对国家紧急情况的能力。本项目包括三个主要方面，将推动开发规避风险的多标准优化模型和方法。首先，在单阶段优化领域，提出了一种新的风险规避多目标优化模型，其中多个标准的相对重要性是模糊的。为此，必须定义一个新的稳健的多变量风险度量与理想的理论属性。在这个项目中，优化这样的风险措施的问题将被制定为一个凹最小化问题，有效的解决方法将被开发。其次，将对多变量风险下优化的切割生成问题中产生的基本非凸多面体子结构进行严格的研究。第三，两个阶段的优化问题下的多变量风险将制定允许追索权的决定。对于这些问题，分解算法，涉及连续的线性近似的第二阶段的问题将被设计。