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Genetic programming of polynomial harmonic models using the discrete Fourier transform

The paper presents a genetic programming (GP) system that evolves polynomial harmonic networks. The hybrid tree-structured network representation suggests that terminal harmonics with non-multiple frequencies may enter polynomial function nodes as variables. The harmonics with non-multiple, irregular frequencies are derived analytically using the discrete Fourier transform. The development of polynomial harmonic GP includes also design of a regularized statistical fitness function for improved search control and overfitting avoidance. Empirical results show that this hybrid version outperforms the previous GP system manipulating polynomials STROGANOFF, the traditional Koza-style GP, and the harmonic GMDH network algorithm on processing time series.