A Multi-Objective Genetic Programming with Size Diversity for Symbolic Regression Problem

Genetic programming has been positioned as a fit-for-purpose approach for symbolic regression. Researchers tend to select algorithms that produce a model with low complexity and high accuracy. Multi-objective genetic programming (MOGP) is a promising approach for finding appropriate models by considering tradeoffs between accuracy and complexity. The MOGP has gained significant attention for non-dominated sorting genetic algorithm II (NSGA-II). However, NSGA-II tends to excessively select individuals of lower complexity, making NSGA-II inefficient in real world applications. SD can be a strategy to promote the evolutionary process by adapting selection pressures for individuals of various size. It deals with the excessive tendency to select low complexity individuals in NSGA-II.We also introduce a practical industrial case of defect detection for dispensing machines. By modeling the dispensing volume of the fluid dispensing systems, defects in the dispensing machine can be detected under different external environmental factors.For the validation of SD, other MOGP algorithms are compared with the improved NSGA-II algorithm, NSGA-II with SD. By comparing multi-objective optimization methods tested on seven general datasets and an industrial case about defect prediction, the experimental results show that performance of the proposed approach is superior or same to other models in terms of accuracy. In terms of complexity, performance of the proposed approach is satisfactory.