Non-parametric-validated computer-simulation surrogates: a Pareto formulation

摘要

In the surrogate approach to simulation-based optimization, the large-scale simulation is evoked only to construct and validate a simplified input-output model; this simplified input-output model then serves as a simulation surrogate in subsequent engineering optimization studies. We present here 'basic' and Pareto surrogate formulations through an illustrative application from fluid dynamics. The critical ingredient of both formulations is a non-parametric statistical validation and error estimation procedure which, based on verifiable hypotheses, precisely quantifies the effect of surrogate-for-simulation substitution on system predictability, stability, and optimality. The Pareto formulation improves upon the basic approach by operating only in the vicinity of the efficient frontier of the output achievable set A; for problems with many inputs and few outputs, this considerably reduces the dimensionality of the problem, and correspondingly improves the surrogate error estimates.