On the analysis of the simple genetic algorithm

PS Oliveto, C Witt - Proceedings of the 14th annual conference on …, 2012 - dl.acm.org
Proceedings of the 14th annual conference on Genetic and evolutionary …, 2012dl.acm.org
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 μ≤ n 1/8-ε 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 …
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 μn1/8-ε 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.
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