A Discrete Cosine Transform Based Evolutionary Algorithm and Its Application for Symbolic Regression

Abstract

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies, the energy-compaction property of which makes itself very suitable for symbolic regression problems with noisy data samples. In this paper, we propose a DCT based genetic programming (DCT-GP) for symbolic regression or other optimization problems with noisy experimental observations. Firstly, a sequence of experimental samples was changed from time domain into frequency domain with DCT. Secondly, the boundary between the low frequency components and high frequency components was decided, by which most of the noise inserted into the sample data can be discarded. The experimental sample sequence was rebuilt with the low frequency components. Finally, the new obtained samples were looked on as another fitness function and were used to direct the evolutionary procedure of GP. In this way, DCT was integrated into the GP algorithm. The major advantage of the DCT-GP algorithm is that, on the one hand, it can deal with the regression problem with noisy data samples and obtain accurate solutions. On the other hand, if the sample scale is very small, it can deal with the over-fitting problem in the regression progress and can avoid losing of structure information when the available samples were departed into training set and validating set. The performance of the proposed DCT-GP algorithm with several regression problems indicates that the proposed algorithm can find the solution more efficiently and effectively than traditional sample-partitioning based GP algorithms.