Optimization Online


The Dao of Robustness

Zhuoyu Long (zylong***at***se.cuhk.edu.hk)
Melvyn Sim (melvynsim***at***gmail.com)
Minglong Zhou (minglong_zhou***at***u.nus.edu)

Abstract: We propose a framework for optimization under uncertainty called robustness optimization, which is similar in purpose to, but philosophically different from, robust optimization. Unlike robust optimization approaches, we do not restrict nature to an uncertainty set but allow her to take its cause and even render solutions infeasible. Among these solutions, we favor those with the least adversarial impact on the model under uncertainty. Moreover, the decision maker does not have to size the uncertainty set, but instead specifies an acceptable target, or loss of optimality compared to the baseline model, as a tradeoff for the modelís ability to withstand greater uncertainty. We axiomatize the decision criterion associated with the robustness optimization, termed as the adversarial impact measure, which relates to the maximum level of model infeasibility that may occur relative to the magnitude of deviation from the baseline uncertainty. We also provide a representation theorem of the decision criterion and uncover different types of adversarial impact measures. Similar to robust optimization, we show that robustness optimization via minimizing the adversarial impact can also be done in a tractable way, i.e., it preserves the complexity of the underlying problems including, inter alia, linear, discrete, data-driven and dynamic optimization problems. We also provide computational studies to show that for the same price of robustness, the solutions to our robustness optimization models can withstand greater impact of uncertainty compared to classical robust optimization models, and doing so without incurring additional computational effort.

Keywords: Robust optimization, robustness optimization, data-driven optimization, stochastic optimization, dynamic optimization

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Applications -- OR and Management Sciences (Finance and Economics )


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Entry Submitted: 11/02/2019
Entry Accepted: 11/02/2019
Entry Last Modified: 01/25/2020

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