Elsevier

Theoretical Computer Science

Volume 545, 14 August 2014, Pages 2-19
Theoretical Computer Science

On the runtime analysis of the Simple Genetic Algorithm

https://doi.org/10.1016/j.tcs.2013.06.015Get rights and content
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Abstract

For many years it has been a challenge to analyze the time complexity of Genetic Algorithms (GAs) using stochastic selection together with crossover and mutation. This paper presents a rigorous runtime analysis of the well-known Simple Genetic Algorithm (SGA) for OneMax. It is proved that the SGA has exponential runtime with overwhelming probability for population sizes up to μn1/8ε for some arbitrarily small constant ε and problem size n. To the best of our knowledge, this is the first time non-trivial lower bounds are obtained on the runtime of a standard crossover-based GA for a standard benchmark function. The presented techniques might serve as a first basis towards systematic runtime analyses of GAs.

Keywords

Simple Genetic Algorithm
Crossover
Runtime analysis

Cited by (0)

Parts of the results appeared in the Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation (GECCO '12) (Oliveto and Witt, 2012) [25].

1

Supported by EPSRC grant EP/H028900/1.

2

Supported by DFG grant WI 3552/1.