# Semantic variation operators for multidimensional genetic programming

## TL;DR

This paper introduces semantic variation operators for multidimensional genetic programming, using machine learning to improve crossover by promoting useful building blocks, leading to state-of-the-art results in regression tasks.

## Contribution

It proposes two semantic operators that bias component promotion during crossover, enhancing the evolutionary process in multidimensional genetic programming.

## Key findings

- Forward stagewise crossover improves regression performance
- Achieves state-of-the-art results in benchmark studies
- Analyzes data representation complexity and disentanglement

## Abstract

Multidimensional genetic programming represents candidate solutions as sets of programs, and thereby provides an interesting framework for exploiting building block identification. Towards this goal, we investigate the use of machine learning as a way to bias which components of programs are promoted, and propose two semantic operators to choose where useful building blocks are placed during crossover. A forward stagewise crossover operator we propose leads to significant improvements on a set of regression problems, and produces state-of-the-art results in a large benchmark study. We discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. Finally, we look at the collinearity and complexity of the data representations that result from these architectures, with a view towards disentangling factors of variation in application.