Data-driven robust optimization based on kernel learning
Data-driven robust optimization based on kernel learning
复制标题
基于核学习的数据驱动鲁棒优化
DOI：
10.1016/j.compchemeng.2017.07.004
复制
发表时间：
2017-11-02
影响因子：
4.3
通讯作者：
You, Fengqi
中科院分区：
文献类型：
--
作者：
Shang, Chao;Huang, Xiaolin;You, Fengqi
我们提出了一种基于分段线性核的支持向量聚类(SVC)，作为一种适合于数据驱动的稳健优化的新方法。通过求解二次规划，可以将海量不确定数据的分布几何有效地捕获为一个紧致的凸不确定集，从而大大降低了稳健优化问题的保守性。诱导鲁棒对应问题保持了与确定性问题相同的类型，这提供了显著的计算优势。此外，通过利用SVC的统计特性，只需调整一个参数，就可以很容易地选择数据驱动的不确定性集合中数据覆盖的比例，这为控制保守性和排除孤立点提供了一种可解释的实用方法。数值研究和过程网络规划的工业应用表明，提出的数据驱动方法可以有效地利用海量数据中的有用信息，更好地对冲不确定性，并产生不那么保守的解。(C)2017爱思唯尔有限公司。保留所有权利。
We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart problem retains the same type as the deterministic problem, which provides significant computational benefits. In addition, by exploiting statistical properties of SVC, the fraction of data coverage of the data-driven uncertainty set can be easily selected by adjusting only one parameter, which furnishes an interpretable and pragmatic way to control conservatism and exclude outliers. Numerical studies and an industrial application of process network planning demonstrate that, the proposed data-driven approach can effectively utilize useful information with massive data, and better hedge against uncertainties and yield less conservative solutions. (C) 2017 Elsevier Ltd. All rights reserved.