Multiform Genetic Programming Framework for Symbolic Regression Problems

genetic programming (GP) is a widely recognized and powerful approach for symbolic regression (SR) problems. However, existing GP methods rely on a single form to solve the problem, which limits their search diversity and increases the likelihood of getting stuck in local optima, especially in complex scenarios. In this article, we propose a general multiform GP (MFGP) framework to improve the performance of GP on complicated SR problems. As far as we know, this articel is the first attempt to integrate the multiform optimization paradigm with GP to accelerate the search performance. The key idea of the proposed framework is to construct multiple forms to solve the same problem cooperatively at the same time. During the evolution process, knowledge gained from different forms is shared among the solvers to improve the search diversity and efficiency. A knowledge transfer mechanism is specifically designed to facilitate knowledge transfer among GP solvers with different modeling forms. In addition, an adaptive resource control mechanism is designed to reallocate computing resources according to the problem solving efficiency of different solvers to further improve search efficiency. To demonstrate the effectiveness of the proposed framework, a multiform gene expression programming algorithm is designed and tested on 20 problems, including physical datasets, synthetic datasets, and real-world datasets. The experimental results have demonstrated the effectiveness of the proposed framework.