Optimal Parameter Settings for the $(1+(\lambda, \lambda))$ Genetic Algorithm

TL;DR

This paper rigorously analyzes the parameter space of the $(1+( lambda, lambda))$ genetic algorithm, proving that the previously suggested intuitive parameters are asymptotically optimal for its time complexity.

Contribution

It provides a comprehensive theoretical analysis showing the optimality of the original parameter settings for the algorithm's asymptotic runtime.

Findings

Original parameters are asymptotically optimal.

Super-constant speed-up proven for these parameters.

Theoretical bounds match the intuitive choices.

Abstract

The $(1+(\lambda,\lambda))$ genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven. So far, this algorithm has been used with parameters based also on intuitive considerations. In this work, we rigorously regard the whole parameter space and show that the asymptotic time complexity proven by Doerr and Doerr (GECCO 2015) for the intuitive choice is best possible among all settings for population size, mutation probability, and crossover bias.