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

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.