Evolutionary Polynomial Regression (EPR) is a recently developed hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming/symbolic regression technique. The original version of EPR works with formulae based on true or pseudo-polynomial expressions using a single-objective genetic algorithm. Therefore, to obtain a set of formulae with a variable number of pseudo-polynomial coefficients, the sequential search is performed in the formulae space. This article presents an improved EPR strategy that uses a multi-objective genetic algorithm instead. We demonstrate that multi-objective approach is a more feasible instrument for data analysis and model selection. Moreover, we show that EPR can also allow for simple uncertainty analysis (since it returns polynomial structures that are linear with respect to the estimated coefficients). The methodology is tested and the results are reported in a case study relating groundwater level predictions to total monthly rainfall.

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