# Hyper-Parameter Tuning for the (1+(\lambda,\lambda)) GA

## TL;DR

This paper conducts an empirical study on the hyper-parameters of the self-adjusting $(1+(nd(mbda,mbda))$ GA, revealing that slight modifications can significantly improve performance and that theoretical parameter settings may extend to dynamic variants.

## Contribution

It provides the first detailed empirical analysis of hyper-parameter effects in the self-adjusting $(1+(nd(mbda,mbda))$ GA, including a new setup that reduces runtime and insights on parameter transferability.

## Key findings

- 15% reduction in average runtime with modified parameters
- Non-identical offspring population sizes improve efficiency
- Theoretical parameter settings extend to non-static variants

## Abstract

It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with self-adjusting parameter choices achieves a linear expected optimization time on OneMax if its hyper-parameters are suitably chosen. However, it is not very well understood how the hyper-parameter settings influences the overall performance of the $(1+(\lambda,\lambda))$~GA. Analyzing such multi-dimensional dependencies precisely is at the edge of what running time analysis can offer. To make a step forward on this question, we present an in-depth empirical study of the self-adjusting $(1+(\lambda,\lambda))$~GA and its hyper-parameters. We show, among many other results, that a 15\% reduction of the average running time is possible by a slightly different setup, which allows non-identical offspring population sizes of mutation and crossover phase, and more flexibility in the choice of mutation rate and crossover bias --a generalization which may be of independent interest. We also show indication that the parametrization of mutation rate and crossover bias derived by theoretical means for the static variant of the $(1+(\lambda,\lambda))$~GA extends to the non-static case.