Blackbox Optimization in Engineering Design: Adaptive Statistical Surrogates and Direct Search Algorithms

Simulation-based design optimization relies on computational models to evaluate objective and constraint functions. Typical challenges of solving simulation-based design optimization problems include unavailable gradients or unreliable approximations thereof, excessive computational cost, numerical noise, multi-modality and even the models’ failure to return a value. It has become common to use the term “blackbox” for a computational model that features any of these characteristics and/or is inaccessible by the design engineer (i.e., cannot be modified directly to address these issues). A possible remedy for dealing with blackboxes is to use surrogate-based derivative-free optimization methods. However, this has to be done carefully using appropriate formulations and algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivative-free optimization. We present different formulations for the surrogate problem considered at each search step of the Mesh Adaptive Direct Search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on two simulation-based multidisciplinary design optimization problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.