Satisficing Models Under Uncertainty

P. Jaillet, S. D. Jena, T. S. Ng, Melvyn Sim
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引用次数: 2

Abstract

Satisficing, as an approach to decision making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision making include the P-model. In this paper, we propose a general framework of satisficing decision criteria and show a representation termed the S-model, of which the P-model and robust optimization models are special cases. We then focus on the linear optimization case and obtain a tractable probabilistic S-model, termed the T-model, whose objective is a lower bound of the P-model. We show that when probability densities of the uncertainties are log-concave, the T-model can admit a tractable concave objective function. In the case of discrete probability distributions, the T-model is a linear mixed integer optimization problem of moderate dimensions. Our computational experiments on a stochastic maximum coverage problem suggest that the T-model solutions can be highly competitive compared with standard sample average approximation models.
不确定性下的满意模型
满足作为一种不确定条件下的决策方法,其目的是获得尽可能满足问题约束的解决方案。与这种决策形式相关的数学优化问题包括p模型。本文提出了满足决策准则的一般框架,并给出了s模型的表示,其中p模型和鲁棒优化模型是特例。然后,我们将重点放在线性优化情况下,并获得一个易于处理的概率s模型,称为t模型,其目标是p模型的下界。我们证明了当不确定性的概率密度为对数凹时,t模型可以允许一个可处理的凹目标函数。在离散概率分布情况下,t模型是一个中等维数的线性混合整数优化问题。我们对随机最大覆盖问题的计算实验表明,与标准样本平均近似模型相比,t模型解具有很强的竞争力。
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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