Using Genetic Programming with Prior Formula Knowledge to Solve Symbolic Regression Problem.

Area of Science:

• Computational intelligence
• Machine learning
• Symbolic regression

Background:

• Prior knowledge in function inference can be domain-specific and biased.
• Genetic Programming (GP) offers broad applicability but suffers from slow search speeds.
• A need exists for methods combining prior knowledge with GP to enhance efficiency.

Purpose of the Study:

• To propose a novel framework, Prior Formula Knowledge and Genetic Programming (PFK-GP), integrating prior knowledge with GP.
• To leverage Deep Belief Networks (DBN) for identifying relevant candidate formulas.
• To accelerate the discovery of mathematical expressions and improve symbolic regression quality.

Main Methods:

• Developed a PFK-GP framework connecting prior formula knowledge with GP.
• Utilized Deep Belief Networks (DBN) to identify candidate formulas from experimental data features.
• Employed candidate formulas as seeds for GP's evolutionary algorithms to narrow the search space.

Main Results:

• PFK-GP demonstrated a significant reduction in the search space compared to standard GP.
• The framework achieved substantial improvements in the quality of Symbolic Regression (SR).
• Experimental results on eight benchmark problems validated the PFK-GP's effectiveness.

Conclusions:

• The PFK-GP framework successfully integrates prior knowledge to enhance GP efficiency.
• DBN-driven candidate formula identification effectively guides the GP search process.
• PFK-GP offers a promising approach for faster and more accurate symbolic regression.