Dynamical Sphere Regrouping Particle Swarm Optimization Programming: An Automatic Programming Algorithm Avoiding Premature Convergence

Abstract

Symbolic regression plays a crucial role in machine learning and data science by allowing the extraction of meaningful mathematical models directly from data without imposing a specific structure. This level of adaptability is especially beneficial in scientific and engineering fields, where comprehending and articulating the underlying data relationships is just as important as making accurate predictions. Genetic Programming (GP) has been extensively utilized for symbolic regression and has demonstrated remarkable success in diverse domains. However, GP’s heavy reliance on evolutionary mechanisms makes it computationally intensive and challenging to handle. On the other hand, Particle Swarm Optimization (PSO) has demonstrated remarkable performance in numerical optimization with parallelism, simplicity, and rapid convergence. These attributes position PSO as a compelling option for Automatic Programming (AP), which focuses on the automatic generation of programs or mathematical models. Particle Swarm Programming (PSP) has emerged as an alternative to Genetic Programming (GP), with a specific emphasis on harnessing the efficiency of PSO for symbolic regression. However, PSP remains unsolved due to the high-dimensional search spaces and local optimal regions in AP, where traditional PSO can encounter issues such as premature convergence and stagnation. To tackle these challenges, we introduce Dynamical Sphere Regrouping PSO Programming (DSRegPSOP), an innovative PSP implementation that integrates DSRegPSO’s dynamical sphere regrouping and momentum conservation mechanisms. DSRegPSOP is specifically developed to deal with large-scale, high-dimensional search spaces featuring numerous local optima, thus proving effective behavior for symbolic regression tasks. We assess DSRegPSOP by generating 10 mathematical expressions for mapping points from functions with varying complexity, including noise in position and cost evaluation. Moreover, we also evaluate its performance using real-world datasets. Our results show that DSRegPSOP effectively addresses the shortcomings of PSO in PSP by producing mathematical models entirely generated by AP that achieve accuracy similar to other machine learning algorithms optimized for regression tasks involving numerical structures. Additionally, DSRegPSOP combines the benefits of symbolic regression with the efficiency of PSO.

The authors' abstract, as published at the source. Mathematics, 2024 · DOI ↗