Cartesian Genetic Programming with Module Mutation for Symbolic Regression

Abstract

Symbolic regression aims to find mathematical expressions of functions that can fit a finite set of given data. This problem is a typical problem for evaluating performance in the field of Genetic Programming (GP). Cartesian GP (CGP) is one of the extensions of GP, which generating the graph structure programs. By using the graph structure, the solutions can be represented by more compact programs. Therefore, CGP is widely applied to the various problems. In standard symbolic regression problem, the sample data is expressed by a simple function, which is continuous and smooth. On the other hand, In a complex system appearing in the real world, they can be produced by a discontinuous or non-smooth function. When conventional GP or CGP is applied to this complex system's modelling, it is difficult to obtain good performance. In this paper, we propose a new CGP framework for complex symbolic regression problem. The proposed CGP modularizes the output nodes, and module mutation is introduced to increase or decrease the number of modules during the search. Each module consists of a node corresponding to the output of the network and a node for selecting the output to be used. By switching the output node for each input, it is possible to output appropriate values for each section of the objective function. We have examined its effectiveness by applying it to symbolic regression problem where the objective function is divided into several different sub-function fields. Experimental results have shown that it outperforms conventional CGP.