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Data-Driven Robust Optimization Based on Kernel Learning

Chao Shang (cs849***at***cornell.edu)
Xiaolin Huang (xiaolinhuang***at***sjtu.edu.cn)
Fengqi You (fengqi.you***at***cornell.edu)

Abstract: 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.

Keywords: Robust optimization, Uncertainty set, Data-driven methods, Support vector clustering, Piecewise linear modeling

Category 1: Robust Optimization

Category 2: Applications -- Science and Engineering (Chemical Engineering )

Citation: Smith School of Chemical and Biomolecular Engineering, Cornell University. June 2017.

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Entry Submitted: 06/02/2017
Entry Accepted: 06/02/2017
Entry Last Modified: 07/05/2017

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