On the Analysis of the Simple Genetic Algorithm

Pietro S. Oliveto; Carsten Witt

doi:10.1145/2330163.2330349

On the Analysis of the Simple Genetic Algorithm

Pietro S. Oliveto, Carsten Witt

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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 μ≤ n1/8-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.

Original language	English
Title of host publication	Proceedings of the fourteenth international conference on Genetic and evolutionary computation
Publisher	Association for Computing Machinery
Publication date	2012
Pages	1341-1348
ISBN (Print)	978-1-4503-1177-9
DOIs	https://doi.org/10.1145/2330163.2330349
Publication status	Published - 2012
Event	2012 Genetic and Evolutionary Computation Conference - Philadelphia, United States Duration: 7 Jul 2012 → 11 Jul 2012 http://www.sigevo.org/gecco-2012/

Conference

Conference	2012 Genetic and Evolutionary Computation Conference
Country	United States
City	Philadelphia
Period	07/07/2012 → 11/07/2012
Internet address	http://www.sigevo.org/gecco-2012/

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10.1145/2330163.2330349

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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 μ≤ n1/8-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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AU - Witt, Carsten

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AB - 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≤ n1/8-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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DO - 10.1145/2330163.2330349

M3 - Article in proceedings

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EP - 1348

BT - Proceedings of the fourteenth international conference on Genetic and evolutionary computation

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T2 - 2012 Genetic and Evolutionary Computation Conference

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