Improving Model-Based Genetic Programming for Symbolic Regression of Small Expressions

Area of Science:

• Computational Intelligence
• Machine Learning
• Evolutionary Computation

Background:

• Traditional Evolutionary Algorithms (EAs) often apply variation operators without considering genotype interdependencies (linkage).
• Model-based EAs, like the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), learn linkage to guide variation effectively.
• GOMEA has demonstrated success in various domains, including Genetic Programming (GP).

Purpose of the Study:

• To investigate the role and impact of Linkage Learning (LL) within GOMEA specifically for Symbolic Regression (SR).
• To address challenges in LL caused by non-uniform genotype distributions and ephemeral random constants in GP-based SR.
• To enhance GOMEA's performance and applicability to SR through improved LL and parameter tuning strategies.

Main Methods:

• Developed a corrected Linkage Learning method to mitigate negative biases from non-uniform genotype distributions in GP populations.
• Proposed techniques to improve LL when ephemeral random constants are employed in SR.
• Adapted an interleaving runs scheme to reduce sensitivity to population size, a critical parameter for LL in SR.

Main Results:

• The novel LL method demonstrated superior performance compared to the standard approach on 10 real-world datasets.
• GOMEA, utilizing the improved LL, outperformed traditional GP and semantic GP methods.
• Evolved solutions by GOMEA were highly interpretable (due to size limitations) and competitive with tuned decision trees.

Conclusions:

• Linkage Learning is crucial for GOMEA's success in Symbolic Regression.
• The proposed LL enhancements significantly improve GOMEA's effectiveness and robustness for SR tasks.
• GOMEA presents a promising, interpretable alternative to existing methods for Symbolic Regression.