Using Genetic Programming with Prior Formula Knowledge to Solve Symbolic Regression Problem

Abstract EN

A researcher can infer mathematical expressions offunctions quickly by using his professional knowledge (calledPrior Knowledge).

But the results he finds may be biased andrestricted to his research field due to limitation of his knowledge.

In contrast, Genetic Programming method can discover fittedmathematical expressions from the huge search space throughrunning evolutionary algorithms.

And its results can be generalizedto accommodate different fields of knowledge.

However,since GP has to search a huge space, its speed of finding theresults is rather slow.

Therefore, in this paper, a frameworkof connection between Prior Formula Knowledge and GP (PFK-GP)is proposed to reduce the space of GP searching.

The PFKis built based on the Deep Belief Network (DBN) which canidentify candidate formulas that are consistent with the featuresof experimental data.

By using these candidate formulas as theseed of a randomly generated population, PFK-GP finds the rightformulas quickly by exploring the search space of data features.

We have compared PFK-GP with Pareto GP on regression ofeight benchmark problems.

The experimental results confirmthat the PFK-GP can reduce the search space and obtain thesignificant improvement in the quality of SR.