Robust reformulations of ambiguous chance constraints with discrete probability distributions

IF 2.2 Q1 MATHEMATICS, APPLIED
Ihsan Yanikoglu
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引用次数: 2

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.
具有离散概率分布的模糊机会约束的鲁棒重新表述
本文提出了在所谓的“p-盒”或“p-椭球”不确定性集中,当潜在的分布族是离散的并被支持时,模糊机会约束的鲁棒重新表述。利用鲁棒优化范式,将模糊机会约束的确定性对应物重新表述为混合整数规划问题,可由中等规模实例的商业求解器解决。对于较大的实例,我们提出了一种安全的近似算法,该算法计算效率高,并产生高质量的解。相关的方法和算法可以很容易地扩展到联合机会约束,非线性不等式和相关数据,而不会在原始鲁棒重构中引入额外的数学优化复杂性。在数值实验中,我们首先在一个玩具大小的机会约束背包问题上提出了我们的方法。然后,我们通过蒙特卡洛模拟比较了安全近似算法与精确方法和随机方法的最优性和计算性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.30
自引率
6.20%
发文量
13
审稿时长
16 weeks
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