A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.
A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.
复制标题
DOI：
10.1021/ie201651s
复制
发表时间：
2012
影响因子：
4.2
通讯作者：
Floudas, Christodoulos A.
中科院分区：
文献类型：
--
作者：
Li, Zukui;Tang, Qiuhua;Floudas, Christodoulos A.
研究了鲁棒对偶优化问题约束满足的概率保证问题。所研究的鲁棒对应优化公式是从盒、椭球、多面体、“区间+椭球”和“区间+多面体”不确定性集导出的（Li，Z.，丁河，巴西-地和Floudas，C.A.，鲁棒对应优化的理论与计算比较研究：I。鲁棒线性和鲁棒混合线性优化，工业工程化学研究，2011，50，10567）。对于这些鲁棒对应优化公式，针对不同类型的不确定性特征（即，有界或无界的不确定性，具有或不具有详细的概率分布信息）。这项工作的结果扩展了文献中的结果，并提供了更大的灵活性，强大的优化从业者在选择更严格的概率界，以找到更保守的强大的解决方案。进行了广泛的数值研究，比较不同的概率界和保守性不同的鲁棒对应的优化配方的紧密性。讨论了选择鲁棒对应优化模型和确定不确定性集大小的指导原则。在生产计划和过程调度问题的应用。
Probabilistic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedral, “interval+ellipsoidal” and “interval+polyhedral” uncertainty sets (Li, Z., Ding, R., and Floudas, C.A., A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear and Robust Mixed Integer Linear Optimization, Ind. Eng. Chem. Res, 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented.
登录
查看更多内容
影响因子：
1.1
作者：
Bertsimas, D;Pachamanova, D;Sim, M
通讯作者：
Sim, M
影响因子：
3.1
作者：
El Ghaoui, L;Oustry, F;Lebret, H
通讯作者：
Lebret, H
影响因子：
4.3
作者：
Janak, Stacy L.;Lin, Xiaoxia;Floudas, Christodoulos A.
通讯作者：
Floudas, Christodoulos A.
影响因子：
4.3
作者：
Lin, XX;Janak, SL;Floudas, CA
通讯作者：
Floudas, CA
影响因子：
2.7
作者：
Delage, Erick;Ye, Yinyu
通讯作者：
Ye, Yinyu