A variable-size local domain approach for increased design confidence in simulation-based optimization

Simulation-based design optimization utilizes computational models that rely on assumptions and approximations. There is a need therefore, to ensure that the obtained designs will exhibit the desired behavior as anticipated given the model predictions. The common approach to accomplish that is to validate the utilized computational models prior to the design optimization process. However, this is practically an impossible task especially for design problems with high-dimensional design and parameter spaces. We have recently proposed a different approach for maximizing confidence in the designs generated during a sequential simulation-based optimization process based on calibrating the computational models when necessary and within local subdomains of the design space. 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. Specifically, we use a statistical methodology to account for uncertainty and to determine the size of the local domains at each stage of the sequential design optimization process using parametric bootstrapping that involves maximum likelihood estimators of model parameters. 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.