Application of an Artificial Fish Swarm Algorithm in Symbolic Regression

Abstract

An artificial fish swarm algorithm for solving symbolic regression problems is introduced in this paper. In the proposed AFSA, AF individuals represent candidate solutions, which are represented by the gene expression scheme in GEP. For evaluating AF individuals, a penalty-based fitness function, in which the node number of the parse tree is considered to be a constraint, was designed in order to obtain a solution expression that not only fits the given data well but is also compact. A number of important conceptions are defined, including distance, partners, congestion degree, and feature code. Based on the above concepts, we designed four behaviors, namely, randomly moving behavior, preying behavior, following behavior, and avoiding behavior, and present their respective formalized descriptions. The exhaustive simulation results demonstrate that the proposed algorithm can not only obtain a high-quality solution expression but also provides remarkable robustness and quick convergence.