Identification of Pareto‐fronts in the presence of epistemic uncertainty

Abstract

AbstractNumerical design methods based on deterministic multi‐objective optimization provide — for conflicting objective functions — a Pareto‐optimal set including diverse trade‐off solutions. Based on the visualization of the set in the objective space — the Pareto‐front — the decision maker is able to choose a satisfying design. Though, the presence of uncertain input variables in the optimization task requires a new concept for the identification of the Pareto‐front and the projection of uncertainty within the front. In this contribution, an approach for considering the epistemic uncertainty within the evolutionary multi‐objective optimization method based on Nondominated Sorting Genetic Algorithm (NSGA‐II) is presented. The description of uncertainty occurs within the framework of the Fuzzy set theory. The proposed approach is coupled to the Finite Element Analysis and response surface approximations based on artificial neural networks. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)