Using a Genetic Algorithm to Generate D‐optimal Designs for Mixture Experiments

Abstract

We propose and develop a genetic algorithm (GA) for generating D‐optimal designs where the experimental region is an irregularly shaped polyhedral region. Our approach does not require selection of points from a user‐defined candidate set of mixtures and allows movement through a continuous region that includes highly constrained mixture regions. This approach is useful in situations where extreme vertices (EV) designs or conventional exchange algorithms fail to find a near‐optimal design. For illustration, examples with three and four components are presented with comparisons of our GA designs with those obtained using EV designs and exchange‐point algorithms over an irregularly shaped polyhedral region. The results show that the designs produced by the GA perform better than, if not as well as, the designs produced by the exchange‐point algorithms; however, the designs produced by the GA perform better than the designs produced by the EV. This suggests that GA is an alternative approach for constructing the D‐optimal designs in problems of mixture experiments when EV designs or exchange‐point algorithms are insufficient. Copyright © 2012 John Wiley & Sons, Ltd.

The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm

“…We now describe a GA used to generate optimal designs for a mixture experiment with single component constraints (SCCs) that is based on weighted IV-optimality, which extends and modifies the GA approach of Limmun et al [16] who generated optimal designs for a specified mixture model. Throughout this research paper, we have encoded GA chromosomes using real-value encoding instead of another encoding (e.g., binary) because real-value encoding is easy to interpret, can be modified for many applications, and is flexible enough to allow for a unique representation for every variable.…”

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A hybrid elitist pareto-based coordinate exchange algorithm for constructing multi-criteria optimal experimental designs

“…Since this tuning is problem-specific, it is difficult to imagine routine use of a genetic algorithm in practice. It should be noted that the tuning issue is not unique to the construction of a Pareto front, but is a general issue with genetic algorithms (Limmun et al 2013). Previous work in the experimental design community (Borkowski 2003;Sexton et al 2006) suggests augmenting the genetic algorithm with a local grid search on the generated solutions.…”

Using a genetic algorithm to generate D‐optimal designs for mixture‐process variable experiments

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