Simultaneous model building and validation with uniform designs of experiments

Abstract

This article describes an implementation of a particular design of experiment (DoE) plan based upon optimal Latin hypercubes that have certain space-filling and uniformity properties with the goal of maximizing the information gained. The feature emphasized here is the concept of simultaneous model building and model validation plans whose union contains the same properties as the component sets. Two Latin hypercube DoE are constructed simultaneously for use in a meta-modelling context for model building and model validation. The goal is to optimize the uniformity of both sets with respect to space-filling properties of the designs whilst satisfying the key concept that the merged DoE, comprising the union of build and validation sets, has similar space-filling properties. This represents a development of an optimal sampling approach for the first iteration—the initial model building and validation where most information is gained to take the full advantage of parallel computing. A permutation genetic algorithm using several genetic operator strategies is implemented in which fitness evaluation is based upon the Audze-Eglais potential energy function, and an example is presented based upon the well-known six-hump camel back function. The relative efficiency of the strategies and the associated computational aspects are discussed with respect to the quality of the designs obtained. The requirement for such design approaches arises from the need for multiple calls to traditionally expensive system and discipline analyses within iterative multi-disciplinary optimisation frameworks.