Statistical Surrogate Formulations for Simulation Based Design Optimization

Abstract

Typical challenges of simulationbased design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima, and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and derivativefree optimization algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivativefree optimization. We present different formulations for the surrogate problem (SP) considered at each search step of the mesh adaptive direct search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on 20 analytical benchmark problems and two simulationbased multidisciplinary design optimization (MDO) problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.