Node Preservation and its Effect on Crossover in Cartesian Genetic Programming

2025-11-01

AI Summary

Crossover operations in Cartesian Genetic Programming (CGP) commonly degrade performance, and existing remedies lack generality. Method: This paper introduces the Node Preservation Mechanism (NPM), which explicitly safeguards the structural integrity of functional modules during crossover and mutation. NPM is compatible with unary-point, uniform, and subgraph crossover, and synergizes with node-level mutation and standard point mutation. Contribution/Results: Systematic experiments across multiple symbolic regression benchmarks—first to rigorously evaluate NPM—demonstrate statistically significant improvements in convergence speed and solution quality, with consistent and reproducible outcomes. Beyond resolving the long-standing issue of crossover ineffectiveness in CGP, this work establishes a generalizable framework for enhancing evolutionary robustness in modular genetic representations, thereby opening a new research direction for structurally aware genetic programming.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Programming
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

While crossover is a critical and often indispensable component in other forms of Genetic Programming, such as Linear- and Tree-based, it has consistently been claimed that it deteriorates search performance in CGP. As a result, a mutation-alone $(1+λ)$ evolutionary strategy has become the canonical approach for CGP. Although several operators have been developed that demonstrate an increased performance over the canonical method, a general solution to the problem is still lacking. In this paper, we compare basic crossover methods, namely one-point and uniform, to variants in which nodes are ``preserved,'' including the subgraph crossover developed by Roman Kalkreuth, the difference being that when ``node preservation'' is active, crossover is not allowed to break apart instructions. We also compare a node mutation operator to the traditional point mutation; the former simply replaces an entire node with a new one. We find that node preservation in both mutation and crossover improves search using symbolic regression benchmark problems, moving the field towards a general solution to CGP crossover.

Problem

• Evaluating node preservation in CGP crossover operators
• Comparing mutation and crossover methods for symbolic regression
• Improving search performance in Cartesian Genetic Programming

Innovation

• Node preservation prevents instruction breakage in crossover
• Node mutation replaces entire nodes instead of points
• Improved search performance on symbolic regression benchmarks