# Evolving neural networks to follow trajectories of arbitrary complexity

## TL;DR

This paper introduces four enhancements to neuroevolution techniques that enable the evolution of neural networks to produce increasingly complex behaviors, significantly surpassing the complexity achieved by standard methods.

## Contribution

The authors propose four specific modifications to standard neuroevolution methods that allow for approximately linear growth in behavioral complexity over thousands of generations.

## Key findings

- Complexity of evolved behaviors increased up to 100 times compared to standard methods.
- Four proposed features collectively enable sustained growth in behavior complexity.
- Major limiting factor is available runtime, not the method itself.

## Abstract

Many experiments have been performed that use evolutionary algorithms for learning the topology and connection weights of a neural network that controls a robot or virtual agent. These experiments are not only performed to better understand basic biological principles, but also with the hope that with further progress of the methods, they will become competitive for automatically creating robot behaviors of interest. However, current methods are limited with respect to the (Kolmogorov) complexity of evolved behavior. Using the evolution of robot trajectories as an example, we show that by adding four features, namely (1) freezing of previously evolved structure, (2) temporal scaffolding, (3) a homogeneous transfer function for output nodes, and (4) mutations that create new pathways to outputs, to standard methods for the evolution of neural networks, we can achieve an approximately linear growth of the complexity of behavior over thousands of generations. Overall, evolved complexity is up to two orders of magnitude over that achieved by standard methods in the experiments reported here, with the major limiting factor for further growth being the available run time. Thus, the set of methods proposed here promises to be a useful addition to various current neuroevolution methods.