Satisficing Models Under Uncertainty
Satisficing Models Under Uncertainty
复制标题
不确定性下的令人满意的模型
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Melvyn Sim
中科院分区：
文献类型：
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作者：
P. Jaillet;S. D. Jena;T. S. Ng;Melvyn Sim
满意化作为一种不确定性决策方法，其目的是寻求尽可能满足问题约束的解。与这种形式的决策相关的数学优化问题包括P模型。在本文中，我们提出了一个一般的框架，满足决策准则，并显示了一个表示称为S-模型，其中的P-模型和鲁棒优化模型的特殊情况。然后，我们专注于线性优化的情况下，得到一个听话的概率S-模型，称为T-模型，其目标是一个下界的P-模型。我们证明了当不确定性的概率密度是对数凹的时，T-模型可以接受一个易于处理的凹目标函数。在离散概率分布的情况下，T模型是一个中等维度的线性混合整数优化问题。我们的随机最大覆盖问题的计算实验表明，T-模型的解决方案可以是非常有竞争力的标准样本平均近似模型相比。
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.