Enhancing gene expression programming based on space partition and jump for symbolic regression

Abstract

When solving a symbolic regression problem, the gene expression programming (GEP) algorithm could fall into a premature convergence which terminates the optimization process too early, and may only reach a poor local optimum. To address the premature convergence problem of GEP, we propose a novel algorithm named SPJ-GEP, which can maintain the GEP population diversity and improve the accuracy of the GEP search by allowing the population to jump efficiently between segmented subspaces. SPJ-GEP first divides the space of mathematical expressions into k subspaces that are mutually exclusive. It then creates a subspace selection method that combines the multi-armed bandit and the ∊-greedy strategy to choose a jump subspace. In this way, the analysis is made on the population diversity and the range of the number of subspaces. The analysis results show that SPJ-GEP does not significantly increase the computational complexity of time and space than classical GEP methods. Besides, an evaluation is conducted on a set of standard SR benchmarks. The evaluation results show that the proposed SPJ-GEP keeps a higher population diversity and has an enhanced accuracy compared with three baseline GEP methods.