Sudholt, D. (2017) How Crossover Speeds Up Building-Block Assembly in Genetic Algorithms. Evolutionary Computation, 25 (2). pp. 237-274. ISSN 1530-9304
Abstract
We re-investigate a fundamental question: how effective is crossover in Genetic Algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter we show that using crossover makes every (\mu+\lambda) Genetic Algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate \mu and \lambda. Crossover is beneficial because it effectively turns fitness-neutral mutations into improvements by combining the right building blocks at a later stage. Compared to mutation-based evolutionary algorithms, this makes multi-bit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from 1/n to (1+\sqrt{5})/2 \cdot 1/n \approx 1.618/n. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building-block functions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Massachusetts Institute of Technology. This is an author-produced version of a paper accepted for publication in Evolutionary Computation. Uploaded in accordance with the publisher's self-archiving policy |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 20 Jan 2016 16:48 |
Last Modified: | 15 Jan 2020 14:09 |
Published Version: | http://dx.doi.org/10.1162/EVCO_a_00171 |
Status: | Published |
Publisher: | Massachusetts Institute of Technology Press |
Refereed: | Yes |
Identification Number: | 10.1162/EVCO_a_00171 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:93026 |