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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2019 / Cilt: 9 - Sayı: 2

Robust reformulations of ambiguous chance constraints with discrete probability distributions

İhsan YANIKOĞLU
Pages
236–252
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then, we compare optimality and computa-tional performances of the safe approximation algorithm with those of the ex-act and the randomized approaches for larger sized instances via Monte Carlosimulation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper proposes robust reformulations of ambiguous chance constraintswhen the underlying family of distributions is discrete and supported in aso-called “p-box” or “p-ellipsoidal” uncertainty set.
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Key Findings & Data:Using the robust opti-mization paradigm, the deterministic counterparts of the ambiguous chanceconstraints are reformulated as mixed-integer programming problems whichcan be tackled by commercial solvers for moderate sized instances.
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Conclusion & Impact:Then, we compare optimality and computa-tional performances of the safe approximation algorithm with those of the ex-act and the randomized approaches for larger sized instances via Monte Carlosimulation.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper proposes robust reformulations of ambiguous chance constraintswhen the underlying family of distributions is discrete and supported in aso-called “p-box” or “p-ellipsoidal” uncertainty set. Using the robust opti-mization paradigm, the deterministic counterparts of the ambiguous chanceconstraints are reformulated as mixed-integer programming problems whichcan be tackled by commercial solvers for moderate sized instances. For largersized instances, we propose a safe approximation algorithm that is compu-tationally efficient and yields high quality solutions. The associated approachand the algorithm can be easily extended to joint chance constraints, nonlinearinequalities, and dependent data without introducing additional mathemati-cal optimization complexity to that of the original robust reformulation. Innumerical experiments, we first present our approach over a toy-sized chanceconstrained knapsack problem. Then, we compare optimality and computa-tional performances of the safe approximation algorithm with those of the ex-act and the randomized approaches for larger sized instances via Monte Carlosimulation.

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Cite This Article

YANIKOĞLU, İ. (2022). Robust reformulations of ambiguous chance constraints with discrete probability distributions. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 9 - Sayı: 2, 236–252. https://ajindex.com/articles/440623

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