Optimization Under Uncertainty Using the Generalized Inverse Distribution Function

TL;DR

This paper introduces a robust optimization framework leveraging the generalized inverse distribution function, enabling comprehensive probabilistic analysis and multi-objective decision-making with quantifiable estimation errors.

Contribution

It proposes a novel optimization approach using the GIDF, allowing for full probabilistic information utilization and flexible risk-based design selection.

Findings

The GIDF-based method captures complete probabilistic information.

It enables multi-objective optimization with risk considerations.

Estimation errors of objectives are quantifiable.

Abstract

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