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Data-driven tuning for chance constrained optimization: analysis and extensions

Author

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  • Ashley M. Hou

    (University of Wisconsin-Madison Engineering Dr)

  • Line A. Roald

    (University of Wisconsin-Madison Engineering Dr)

Abstract

Many optimization problems involve uncertain parameters which, if not appropriately accounted for, can cause solution infeasiblity. In this work, we consider joint chance-constrained optimization problems, which require all constraints to hold with a given probability, and a two-step solution method based on iterative tuning. Previous work established an a priori feasibility guarantee for this tuning approach, which relies on an assumption that must be verified on a case-by-case basis. In this paper, we propose an empirical methodology using statistical hypothesis testing to assess the validity of this assumption, thus providing further insight into the validity of the a priori guarantee. In addition, we provide sample complexity results to assess the requisite amount of data for the tuning method. We find that for large scale optimization problems, the tuning approach may require significantly less samples than the scenario approach. We numerically assess these results via application to the optimal power flow problem as well as further assess the scalability of the method and the optimality and feasibility of solutions obtained from tuning.

Suggested Citation

  • Ashley M. Hou & Line A. Roald, 2022. "Data-driven tuning for chance constrained optimization: analysis and extensions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 649-682, October.
    • Handle: RePEc:spr:topjnl:v:30:y:2022:i:3:d:10.1007_s11750-022-00639-z
    DOI: 10.1007/s11750-022-00639-z
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    References listed on IDEAS

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    1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    2. M. C. Campi & S. Garatti, 2011. "A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 257-280, February.
    3. G. C. Calafiore & L. El Ghaoui, 2006. "On Distributionally Robust Chance-Constrained Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 1-22, July.
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