Pareto surface construction for multi-objective optimization under uncertainty

This paper presents a novel approach for multi-objective optimization under both aleatory and epistemic sources of uncertainty. Given paired samples of the inputs and outputs from the system analysis model, a Bayesian network (BN) is built to represent the joint probability distribution of the inputs and outputs. In each design iteration, the optimizer provides the values of the design variables to the BN, and copula-based sampling is used to rapidly generate samples of the output variables conditioned on the input values. Samples from the conditional distributions are used to evaluate the objectives and constraints, which are fed back to the optimizer for further iteration. The proposed approach is formulated in the context of reliability-based design optimization (RBDO). The joint probability of multiple objectives and constraints is included in the formulation. The Bayesian network along with conditional sampling is exploited to select training points that enable effective construction of the Pareto front. A vehicle side impact problem is employed to demonstrate the proposed methodology.