Efficient initialization for multi-fidelity surrogate-based optimization

The performance of surrogate-based optimization is dependent on the surrogate training set, certainly for realistic optimizations where the high cost of computing the training set data imposes small training set sizes. This is especially true for multi-fidelity surrogate models, where different training sets exist for each fidelity. Adaptive sampling methods have been developed to improve the fitting capabilities of surrogate models, adding training points only where necessary or most useful to the optimization process (i.e., providing the highest knowledge gain) and avoiding the need for an a priori design of experiments. Nevertheless, the efficiency of the adaptive sampling is highly affected by its initialization. The paper presents and discusses a novel initialization strategy with a limited training set for adaptive sampling. The proposed strategy aims to reduce the computational cost of evaluating the initial training set. Furthermore, it allows the surrogate model to adapt more freely to the data. In this work, the proposed approach is applied to single- and multi-fidelity stochastic radial basis functions for an analytical test problem and the shape optimization of a NACA hydrofoil. Numerical results show that the results of the surrogate-based optimization are improved, thanks to a more effective and efficient domain space exploration and a significant reduction of high-fidelity evaluations.