Efficient computer experiment-based optimization through variable selection

Abstract

A computer experiment-based optimization approach employs design of experiments and statistical modeling to represent a complex objective function that can only be evaluated pointwise by running a computer model. In large-scale applications, the number of variables is huge, and direct use of computer experiments would require an exceedingly large experimental design and, consequently, significant computational effort. If a large portion of the variables have little impact on the objective, then there is a need to eliminate these before performing the complete set of computer experiments. This is a variable selection task. The ideal variable selection method for this task should handle unknown nonlinear structure, should be computationally fast, and would be conducted after a small number of computer experiment runs, likely fewer runs (N) than the number of variables (P). Conventional variable selection techniques are based on assumed linear model forms and cannot be applied in this "large P and small N" problem. In this paper, we present a framework that adds a variable selection step prior to computer experiment-based optimization, and we consider data mining methods, using principal components analysis and multiple testing based on false discovery rate, that are appropriate for our variable selection task. An airline fleet assignment case study is used to illustrate our approach.