[Paper Review] Positional Cartesian Genetic Programming

Dennis G. Wilson, Julian F. Miller+2 more|arXiv (Cornell University)|Oct 9, 2018

Evolutionary Algorithms and Applications17 references6 citations

TL;DR

This paper introduces Positional Cartesian Genetic Programming (PCGP), a novel CGP variant that evolves node positions using a floating-point genome representation, enabling advanced genetic operators like graph-based crossover and mutation. PCGP outperforms standard CGP on benchmark problems, particularly in reinforcement learning, and reveals optimal parameter configurations through extensive hyper-parameter search across evolutionary strategies.

ABSTRACT

Cartesian Genetic Programming (CGP) has many modifications across a variety of implementations, such as recursive connections and node weights. Alternative genetic operators have also been proposed for CGP, but have not been fully studied. In this work, we present a new form of genetic programming based on a floating point representation. In this new form of CGP, called Positional CGP, node positions are evolved. This allows for the evaluation of many different genetic operators while allowing for previous CGP improvements like recurrency. Using nine benchmark problems from three different classes, we evaluate the optimal parameters for CGP and PCGP, including novel genetic operators.

Motivation & Objective

• To develop a new form of Cartesian Genetic Programming (CGP) that evolves node positions using a floating-point genome representation.
• To evaluate novel genetic operators—such as subgraph and output graph crossover, and mixed node mutation—made possible by positional evolution.
• To identify optimal hyper-parameters for both standard CGP and PCGP across diverse problem classes using $1+\lambda$ EA and GA.
• To compare the effectiveness of enhancements like node weights, recurrence, and elitism across classification, regression, and reinforcement learning tasks.
• To provide a comprehensive guide to CGP configuration, especially for GA-based evolution, which has been underexplored in prior work.

Proposed method

• Represents CGP genomes using continuous floating-point values in [0.0, 1.0] for node positions, connection genes, function indices, and parameters.
• Uses 'snapping' to map floating-point connection coordinates to the nearest actual node, enabling flexible and dynamic connectivity.
• Introduces Positional CGP (PCGP) by evolving node positions as part of the genome, allowing new mutation and crossover strategies.
• Applies a $1+\lambda$ evolutionary algorithm and a generational GA to evolve PCGP and standard CGP across nine benchmark problems.
• Incorporates enhancements such as recurrent connections (via parameter $r$), node weights, and active mutation, treating them as tunable hyper-parameters.
• Uses a parameter search across 20 top-performing configurations to identify optimal settings for each problem class and evolutionary strategy.

Experimental results

Research questions

• RQ1 Can evolving node positions in CGP using a floating-point representation enable more effective genetic operators and improve performance on benchmark problems?
• RQ2 Which genetic operators—gene mutation, subgraph crossover, or output graph crossover—are most effective in PCGP across classification, regression, and reinforcement learning tasks?
• RQ3 How do enhancements like node weights, recurrence ($r$), and elitism affect performance in PCGP compared to standard CGP?
• RQ4 What are the optimal hyper-parameter configurations for $1+\lambda$ EA and GA when applied to PCGP and standard CGP?
• RQ5 Can graph-based operations such as subgraph and output graph crossover be viable and effective in PCGP evolution, especially in modular domains like reinforcement learning?

Key findings

• PCGP significantly improves performance on reinforcement learning problems, particularly when using output graph crossover and mixed node mutation.
• Gene mutation with higher mutation rates on output genes outperforms other mutation strategies in both $1+\lambda$ EA and GA configurations.
• Node weights are highly beneficial in reinforcement learning but detrimental in classification and regression tasks, indicating problem-dependent utility.
• In GA configurations, subgraph crossover and mixed subtree mutation are preferred in classification, while random node crossover and gene mutation dominate in regression.
• Elitism levels of 0.1 to 0.5 are most effective across RL and classification tasks, with high elitism improving convergence in PCGP.
• The use of floating-point positional evolution enables viable and effective graph-based genetic operators, suggesting a path toward adaptive and self-optimizing CGP systems.