Design of Computer Experiments for Optimization, Estimation of Function Contours, and Related Objectives

TL;DR

This paper discusses methods for designing computer experiments to optimize functions, estimate contours, and achieve related objectives, emphasizing sequential strategies based on expected improvement for efficient exploration of input spaces.

Contribution

It introduces a framework for designing computer experiments that efficiently optimize and estimate function features using sequential expected improvement methods.

Findings

Effective sequential design strategies for optimization.

Improved estimation of function contours.

Application to tidal power simulation demonstrates practical utility.

Abstract

A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs. For instance, one application we use for illustration simulates the average tidal power, y, generated as a function of the turbine location, x = (x1, x2), in the Bay of Fundy, Nova Scotia, Canada (Ranjan et al. 2011). Performing scientific or engineering experiments via such a computer code is often more time and cost effective than running a physical experiment. Choosing new runs sequentially for optimization, moving y to a target, etc. has been formalized using the concept of expected improvement (Jones et al. 1998). The next experimental run is made where the expected improvement in the function of interest is largest. This expectation is with respect to the predictive distribution of y from a statistical model relating y to x. By considering a set of possible inputs x for the new run, we can choose that which gives the largest expectation.