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

  • Dimitris E. Simos
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 38)


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.


Response surface designs Genetic algorithms Efficiency Optimization 



This work was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. This Programme is supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission. This work was partly funded by COMET K1, FFG—Austrian Research Promotion Agency.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.SBA ResearchViennaAustria

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