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 veryeffective approach for generating high-performanceparsimonious empirical models acceptable for industrialapplications. The chapter addresses the issue offinding the optimal parameter settings of Pareto frontGP which direct the simulated evolution toward simplemodels with acceptable prediction error. A genericmethodology based on statistical design of experimentsis proposed. It includes determination of the number ofreplicates by half-width confidence intervals,determination of the significant factors by fractionalfactorial design of experiments, approaching theoptimum by steepest ascent/descent, and localexploration around the optimum by Box Behnken design ofexperiments. The results from implementing the proposedmethodology to different types of industrial data setsshow that the statistically significant factors are thenumber of cascades, the number of generations, and thepopulation size. The optimal values for the threeparameters have been defined based on second orderregression models with R2 higher than 0.97 for small,medium, and large-sized data sets. The robustness ofthe optimal parameters toward the types of data setswas explored and a robust setting for the threesignificant parameters was obtained. It reduces thecalculation time by 30per cent to 50per cent withoutstatistically significant reduction in the meanresponse.