Alternative variable-fidelity acquisition functions for efficient global optimization of black-box functions

Surrogate-Based Optimization has been gaining significant interest in recent years due to its capability of performing optimization of expensive problems using few individual evaluations, thus reducing the computational cost. In that context, multi-fidelity models are able to show higher accuracy by using lower and higher fidelity sources to build the approximate response surface. This allows for a better exploration of the design space while not requiring an excessive number of expensive evaluations. However, for adaptive sampling Surrogate-Based Optimization, there are few robust techniques able to determine the optimal location and fidelity of new data points simultaneously. Also, handling of constrained problems has not yet been extensively explored for Surrogate-Based Optimization using multi-fidelity models. In this work, two alternative variable-fidelity acquisition functions are proposed, namely the Variable-Fidelity Lower Confidence Bound (VF-LCB) and the Variable-Fidelity Weighted Expected Improvement (VF-WEI). Constraint-handling methods which have been proposed for single-fidelity models are also extended to multi-fidelity model-based optimization. State-of-the-art modeling techniques will be used and compared, namely Co-Kriging and Hierarchical Kriging, as well as the popular single-fidelity Kriging model. We also show that Co-Kriging is not able to provide a smooth approximation for the HF source when sources are related by a constant additive term. Whenever possible, results found in this paper are to those from the literature in terms of accuracy and efficiency.