A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization.
A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization.
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DOI：
10.1021/ie200150p
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发表时间：
2011-09-21
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;Ding, Ran;Floudas, Christodoulos A.
研究了线性优化和混合整数线性优化问题的鲁棒对等优化技术。本文研究了不同的不确定性集，包括文献中研究过的不确定性集（即区间集、组合区间与椭球体集、组合区间与多面体集）和新的不确定性集（即可调框、纯椭球体、纯多面体、组合区间、椭球体、多面体集），并讨论了它们之间的几何关系。针对优化问题的左侧不确定性、右侧不确定性和目标函数的不确定性，导出了由这些不确定性集合引起的鲁棒对应优化公式。通过数值研究比较了鲁棒对等优化模型的求解结果，并给出了鲁棒对等优化模型在炼油厂生产计划和批处理调度问题中的应用。
Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented.
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影响因子：
1.1
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