Mixed-Level Response Surface Designs via a Hybrid Genetic Algorithm

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 q1 4 q2 mixed-level designs in order to explore and optimize response surfaces with respect to D-efficiency, where the predictor variables are at two and four equally s paced levels, by utilizing a hybrid genetic algorithm. Emphasis is given on various properties that arise fro m the implementation of the genetic algorithm, such as using genetic operators as local optimizers and the representation of the four le vels of the design with a 2-bit Gray Code. We applied the genetic algorithm in several cases and the optimized mixed-level designs achieve good properties, thus demonstrating the efficiency of the proposed hybrid heuristic.