Robust reformulations of ambiguous chance constraints with discrete probability distributions

This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of...
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Autor*in:	İhsan Yanıkoğlu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	robust optimization chance constraint ambiguous chance constraint

Übergeordnetes Werk:	In: An International Journal of Optimization and Control: Theories & Applications - Balikesir University, 2012, 9(2019), 2
Übergeordnetes Werk:	volume:9 ; year:2019 ; number:2

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.11121/ijocta.01.2019.00611

Katalog-ID:	DOAJ003035913

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spelling	10.11121/ijocta.01.2019.00611 doi (DE-627)DOAJ003035913 (DE-599)DOAJ6c270d339f9c469e87e175f8477f454e DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 İhsan Yanıkoğlu verfasserin aut Robust reformulations of ambiguous chance constraints with discrete probability distributions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation. robust optimization chance constraint ambiguous chance constraint Applied mathematics. Quantitative methods Mathematics In An International Journal of Optimization and Control: Theories & Applications Balikesir University, 2012 9(2019), 2 (DE-627)684962780 (DE-600)2648853-X 21465703 nnns volume:9 year:2019 number:2 https://doi.org/10.11121/ijocta.01.2019.00611 kostenfrei https://doaj.org/article/6c270d339f9c469e87e175f8477f454e kostenfrei http://www.ijocta.org/index.php/files/article/view/611 kostenfrei https://doaj.org/toc/2146-0957 Journal toc kostenfrei https://doaj.org/toc/2146-5703 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2019 2
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allfieldsGer	10.11121/ijocta.01.2019.00611 doi (DE-627)DOAJ003035913 (DE-599)DOAJ6c270d339f9c469e87e175f8477f454e DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 İhsan Yanıkoğlu verfasserin aut Robust reformulations of ambiguous chance constraints with discrete probability distributions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation. robust optimization chance constraint ambiguous chance constraint Applied mathematics. Quantitative methods Mathematics In An International Journal of Optimization and Control: Theories & Applications Balikesir University, 2012 9(2019), 2 (DE-627)684962780 (DE-600)2648853-X 21465703 nnns volume:9 year:2019 number:2 https://doi.org/10.11121/ijocta.01.2019.00611 kostenfrei https://doaj.org/article/6c270d339f9c469e87e175f8477f454e kostenfrei http://www.ijocta.org/index.php/files/article/view/611 kostenfrei https://doaj.org/toc/2146-0957 Journal toc kostenfrei https://doaj.org/toc/2146-5703 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2019 2
allfieldsSound	10.11121/ijocta.01.2019.00611 doi (DE-627)DOAJ003035913 (DE-599)DOAJ6c270d339f9c469e87e175f8477f454e DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 İhsan Yanıkoğlu verfasserin aut Robust reformulations of ambiguous chance constraints with discrete probability distributions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation. robust optimization chance constraint ambiguous chance constraint Applied mathematics. Quantitative methods Mathematics In An International Journal of Optimization and Control: Theories & Applications Balikesir University, 2012 9(2019), 2 (DE-627)684962780 (DE-600)2648853-X 21465703 nnns volume:9 year:2019 number:2 https://doi.org/10.11121/ijocta.01.2019.00611 kostenfrei https://doaj.org/article/6c270d339f9c469e87e175f8477f454e kostenfrei http://www.ijocta.org/index.php/files/article/view/611 kostenfrei https://doaj.org/toc/2146-0957 Journal toc kostenfrei https://doaj.org/toc/2146-5703 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2019 2
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author	İhsan Yanıkoğlu
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topic_title	T57-57.97 QA1-939 Robust reformulations of ambiguous chance constraints with discrete probability distributions robust optimization chance constraint ambiguous chance constraint
topic	misc T57-57.97 misc QA1-939 misc robust optimization misc chance constraint misc ambiguous chance constraint misc Applied mathematics. Quantitative methods misc Mathematics
topic_unstemmed	misc T57-57.97 misc QA1-939 misc robust optimization misc chance constraint misc ambiguous chance constraint misc Applied mathematics. Quantitative methods misc Mathematics
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title	Robust reformulations of ambiguous chance constraints with discrete probability distributions
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title_full	Robust reformulations of ambiguous chance constraints with discrete probability distributions
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title_sort	robust reformulations of ambiguous chance constraints with discrete probability distributions
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title_auth	Robust reformulations of ambiguous chance constraints with discrete probability distributions
abstract	This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation.
abstractGer	This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation.
abstract_unstemmed	This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation.
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title_short	Robust reformulations of ambiguous chance constraints with discrete probability distributions
url	https://doi.org/10.11121/ijocta.01.2019.00611 https://doaj.org/article/6c270d339f9c469e87e175f8477f454e http://www.ijocta.org/index.php/files/article/view/611 https://doaj.org/toc/2146-0957 https://doaj.org/toc/2146-5703
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Robust reformulations of ambiguous chance constraints with discrete probability distributions

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