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Robust optimization approximation for joint chance constrained optimization problem

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Abstract

Chance constraint is widely used for modeling solution reliability in optimization problems with uncertainty. Due to the difficulties in checking the feasibility of the probabilistic constraint and the non-convexity of the feasible region, chance constrained problems are generally solved through approximations. Joint chance constrained problem enforces that several constraints are satisfied simultaneously and it is more complicated than individual chance constrained problem. This work investigates the tractable robust optimization approximation framework for solving the joint chance constrained problem. Various robust counterpart optimization formulations are derived based on different types of uncertainty set. To improve the quality of robust optimization approximation, a two-layer algorithm is proposed. The inner layer optimizes over the size of the uncertainty set, and the outer layer optimizes over the parameter t which is used for the indicator function upper bounding. Numerical studies demonstrate that the proposed method can lead to solutions close to the true solution of a joint chance constrained problem.

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Acknowledgments

The authors would like to acknowledge the financial support from the Natural Sciences and Engineering Resource Council (NSERC) of Canada Discovery Grant Program.

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Authors and Affiliations

  1. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G2V4, Canada

    Yuan Yuan, Zukui Li & Biao Huang

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  1. Yuan Yuan
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  2. Zukui Li
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  3. Biao Huang
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Correspondence to Zukui Li.

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Yuan, Y., Li, Z. & Huang, B. Robust optimization approximation for joint chance constrained optimization problem. J Glob Optim 67, 805–827 (2017). https://doi.org/10.1007/s10898-016-0438-0

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  • DOI: https://doi.org/10.1007/s10898-016-0438-0

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