Robust reformulations of ambiguous chance constraints with discrete probability distributions

Name: Robust reformulations of ambiguous chance constraints with discrete probability distributions
Author: Yanıkoğlu, İhsan

İsim	Robust reformulations of ambiguous chance constraints with discrete probability distributions
Yazar	Yanıkoğlu, İhsan
Basım Tarihi:	2019
Basım Yeri	- Balikesir University
Konu	Robust optimization, Chance constraint, Ambiguous chance constraint
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	2146-0957
Kayıt Numarası	75f9ff11-8423-4da8-8321-e07f4c73692a
Lokasyon	Industrial Engineering
Tarih	2019
Örnek Metin	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.
DOI	10.11121/ijocta.01.2019.00611
Cilt	9

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Robust reformulations of ambiguous chance constraints with discrete probability distributions

Yazar Yanıkoğlu, İhsan

Basım Tarihi 2019

Basım Yeri - Balikesir University

Konu Robust optimization, Chance constraint, Ambiguous chance constraint

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 2146-0957

Kayıt Numarası 75f9ff11-8423-4da8-8321-e07f4c73692a

Lokasyon Industrial Engineering

Tarih 2019

Örnek Metin 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.

DOI 10.11121/ijocta.01.2019.00611

Cilt 9