Robust Pareto Front Genetic Programming Parameter Selection Based on Design of Experiments and Industrial Data

Abstract

Symbolic regression based on Pareto-Front GP is a very effective approach for generating high-performance parsimonious empirical models acceptable for industrial applications. The chapter addresses the issue of finding the optimal parameter settings of Pareto-Front GP which direct the simulated evolution toward simple models with acceptable prediction error. A generic methodology based on statistical design of experiments is proposed. It includes determination of the number of replicates by half width confidence intervals, determination of the significant factors by fractional factorial design of experiments, approaching the optimum by steepest ascent/descent, and local exploration around the optimum by Box Behnken design of experiments. The results from implementing the proposed methodology to different types of industrial data sets show that the statistically significant factors are the number of cascades, the number of generations, and the population size. The optimal values for the three parameters have been defined based on second order regression models with R ² hig herthan 0.97 for small, medium, and large-sized data sets. The robustness of the optimal parameters toward the types of data sets was explored and a robust setting for the three significant parameters was obtained. It reduces the calculation time by 30% to 50% without statistically significant reduction in the mean response.