Using a Genetic Algorithm to Generate Small Exact Response Surface Designs

A genetic algorithm (GA) is an evolutionary search strategy based on simplified rules of biological population genetics and theories of evolution. A GA maintains a population of candidate solutions for a problem, and then selects those candidates most fit to solve the problem. After the selection process, the most fit candidate solutions are combined and/or altered by reproduction operators to produce new solutions for the next generation. The process continues, with each generation evolving more fit solutions until an acceptable solution is evolved. In this research, a GA is developed to generate near-optimal D, A, G, and IV exact N-point response surface designs in the hypercube. The optimal exact designs can be found by applying a local search algorithm to these near-optimal designs. A catalog of designs is given for 1, 2, and 3 design factors. Efficiencies are calculated for classical response surface designs relative to exact optimal designs of the same design size.

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