具有贝叶斯型模糊集的多阶段分布稳健凸随机优化

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Wentao Ma, Zhiping Chen
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引用次数: 0

摘要

在分布稳健优化中,现有的模糊集构建方法往往存在过度保守和可用数据利用效率低的问题。为了解决这些局限性,并切实解决多阶段分布稳健优化(MDRO)问题,我们提出了一种数据驱动的贝叶斯式方法,从贝叶斯的角度构建可能分布的模糊集。我们证明了贝叶斯型 MDRO 问题可以重新表述为风险规避型多阶段随机编程问题,并随后研究了其理论特性,如一致性、有限样本保证和统计稳健性。此外,重新表述使我们能够在动态环境中采用切割平面算法来解决贝叶斯型 MDRO 问题。为了说明所提模型和算法的实用性和优势,我们将其应用于分布鲁棒库存控制问题和分布鲁棒水热调度问题,并将其与通常的公式和求解方法进行比较,以突出我们方法的优越性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Multi-stage distributionally robust convex stochastic optimization with Bayesian-type ambiguity sets

Multi-stage distributionally robust convex stochastic optimization with Bayesian-type ambiguity sets

The existent methods for constructing ambiguity sets in distributionally robust optimization often suffer from over-conservativeness and inefficient utilization of available data. To address these limitations and to practically solve multi-stage distributionally robust optimization (MDRO), we propose a data-driven Bayesian-type approach that constructs the ambiguity set of possible distributions from a Bayesian perspective. We demonstrate that our Bayesian-type MDRO problem can be reformulated as a risk-averse multi-stage stochastic programming problem and subsequently investigate its theoretical properties such as consistency, finite sample guarantee, and statistical robustness. Moreover, the reformulation enables us to employ cutting planes algorithms in dynamic settings to solve the Bayesian-type MDRO problem. To illustrate the practicality and advantages of the proposed model and algorithm, we apply it to a distributionally robust inventory control problem and a distributionally robust hydrothermal scheduling problem, and compare it with usual formulations and solution methods to highlight the superior performance of our approach.

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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
36
审稿时长
>12 weeks
期刊介绍: This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.
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