Multi-objective design under uncertainty using a Kriging-based evolutionary optimizer

Abstract

Μulti-objective design problems with probabilistic objectives estimated through stochastic simulation are examined in this paper. For the efficient solution of such problems a surrogate model based optimization scheme, termed MODU-AIM, was recently developed by the authors. Foundations of MODU-AIM are the formulation of the surrogate model in the augmented input space, composed of both the design variables and the uncertain model parameters, and an iterative implementation that adaptively controls surrogate model accuracy. At each iteration, a new surrogate model is developed, and a new Pareto front is identified using epsilon-constraint numerical optimization scheme. This front is then compared to the previous iterations front to examine convergence. If convergence has not been established, a set of refinement experiments is identified for the surrogate model development and process proceeds to the next iteration. In this paper, integration of multi-objective evolutionary optimizers (MOEA) is considered for MODU-AIM. This integration extends MODU-AIMs applicability and numerical efficiency and requires a number of modifications and enhancements to address the unique traits of MOEA optimizers with respect to the Pareto front identification.