A Framework for Multi-fidelity Modeling in Global Optimization Approaches

Optimization of complex systems often involves running a detailed simulation model that requires large computational time per function evaluation. Many methods have been researched to use a few detailed, high-fidelity, function evaluations to construct a low-fidelity model, or surrogate, including Kriging, Gaussian processes, response surface approximation, and meta-modeling. We present a framework for global optimization of a high-fidelity model that takes advantage of low-fidelity models by iteratively evaluating the low-fidelity model and providing a mechanism to decide when and where to evaluate the high-fidelity model. This is achieved by sequentially refining the prediction of the computationally expensive high-fidelity model based on observed values in both high- and low-fidelity. The proposed multi-fidelity algorithm combines Probabilistic Branch and Bound, that uses a partitioning scheme to estimate subregions with near-optimal performance, with Gaussian processes, that provide predictive capability for the high-fidelity function. The output of the multi-fidelity algorithm is a set of subregions that approximates a target level set of best solutions in the feasible region. We present the algorithm for the first time and an analysis that characterizes the finite-time performance in terms of incorrect elimination of subregions of the solution space.