A method to efficiently localize non-dominated regions using surrogate modeling with multi-fidelity data from a sequential decision process

Abstract

In recent studies, it has been shown that models of increasing fidelity can be used in a sequence to efficiently filter out dominated designs from a set of discrete designs under consideration by formally viewing design as a sequential decision process (SDP). In the SDP, efficiency is achieved by first using low-fidelity models to construct bounds on decision criteria that are used to filter out dominated design(s) having only performed inexpensive model evaluations, and then higher-fidelity evaluations are performed to precisely evaluate the decision criteria but only for the candidate design(s) that appear to be promising after the lower-fidelity evaluations. In this paper, a method is presented to leverage the information gained in the SDP for the efficient construction of a surrogate model with high accuracy in non-dominated regions. More specifically, a surrogate modeling method using Gaussian process regression is constructed using a composite data set—exact values of decision criteria obtained by the highest-fidelity evaluation, and bounded values of the decision criteria obtained by low-fidelity evaluations—generated by sequentially evaluating a set of discrete design alternatives using a set of multi-fidelity models to generalize across a continuous design domain. The result is a surrogate model that is highly accurate in the non-dominated region(s) of the design domain, and yet captures the trend of the underlying objective function over the complete design domain without performing expensive model evaluations in regions that are not promising. The utility of the surrogate modeling method is illustrated through two applications.