Problem Formulations for Simulation-Based Design Optimization Using Statistical Surrogates and Direct Search

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Typical challenges of simulation-based 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. The remedy for all these issues is to use surrogate models in lieu of the computational models or simulations and derivative-free optimization 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.