基于广义逆分布函数的不确定性Optimization
Optimization Under Uncertainty Using the Generalized Inverse Distribution Function
摘要：
提出了一种基于广义逆分布函数（GIDF）的不确定性鲁棒优化框架。与依赖于使用统计矩作为定义优化过程的目标的确定性属性的更经典的方法相比，逆累积分布函数允许使用概率域中可用的所有可能的信息。此外，使用基于分位数的方法自然会导致多目标方法，该方法允许基于设计者定义的风险/机会标准对候选设计进行后验选择。最后，由于GIDF的分辨率而导致的目标估计误差将被证明是可量化的
英文摘要：
A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows for the use of all the possible information available in the probabilistic domain. Furthermore, the use of a quantile based approach leads naturally to a multi-objective methodology which allows an a-posteriori selection of the candidate design based on risk/opportunity criteria defined by the designer. Finally, the error on the estimation of the objectives due to the resolution of the GIDF will be proven to be quantifiable
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