A Variable-Size Local Domain Approach for Concurrent Design Optimization and Model Validation Using Parametric Bootstrap

Abstract

A common approach to the validation of simulation models focuses on validation throughout the entire design space. In a more recent methodology, we proposed to validate designs as they are generated during a simulation-based optimization process, relying on validating the simulation model through calibration in a sequence of local domains. In that work, the size of the local domains was held fixed and not linked to uncertainty, and the confidence in designs was quantified using Bayesian hypothesis testing. In this article, we present an improved methodology where the size and shape of the local domain at each stage of a sequential design optimization process, are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters. Validation through calibration is carried out in the local domain at each stage. The sequential process continues until the local domain does not change from stage to stage during the design optimization process, ensuring convergence to an optimal design. The proposed methodology is illustrated with the design of a thermal insulator using one-dimensional, linear heat conduction in a solid slab with heat flux boundary conditions.