Genetic Algorithms for the Construction of \(2^{2}\) and \(2^{3}\)-Level Response Surface Designs

Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 38)

Abstract

Response surface methodology is widely used for developing, improving and optimizing processes in various fields. In this paper, we present a general algorithmic method for constructing \(2^q\)-level design matrices in order to explore and optimize response surfaces where the predictor variables are each at \(2^q\) equally spaced levels, by utilizing a genetic algorithm. We emphasize on various properties that arise from the implementation of the genetic algorithm, such as symmetries in different objective functions used and the representation of the \(2^q\) levels of the design with a \(q\)-bit Gray Code. We executed the genetic algorithm for \(q=2, 3\) and the produced four and eight-level designs achieve both properties of near-rotatability and estimation efficiency thus demonstrating the efficiency of the proposed heuristic.

Keywords

Response surface designs Genetic algorithms Efficiency Optimization 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.SBA ResearchViennaAustria

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