Oliveto, P. and Mambrini, A. (2016) On the Analysis of Simple Genetic Programming for Evolving Boolean Functions. In: Heywood, M.I., McDermott, J., Castelli, M., Costa, E. and Sim, K., (eds.) Genetic Programming. 19th European Conference on Genetic Programming, March 30 - April 1, 2016, Porto, Portugal. Lecture Notes in Computer Science, 9594 . Springer , pp. 99-114.
Abstract
This work presents a first step towards a systematic time and space complexity analysis of genetic programming (GP) for evolving functions with desired input/output behaviour. Two simple GP algorithms, called (1+1) GP and (1+1) GP*, equipped with minimal function (F) and terminal (L) sets are considered for evolving two standard classes of Boolean functions. It is rigorously proved that both algorithms are efficient for the easy problem of evolving conjunctions of Boolean variables with the minimal sets. However, if an extra function (i.e. NOT) is added to F, then the algorithms require at least exponential time to evolve the conjunction of n variables. On the other hand, it is proved that both algorithms fail at evolving the difficult parity function in polynomial time with probability at least exponentially close to 1. Concerning generalisation, it is shown how the quality of the evolved conjunctions depends on the size of the training set s while the evolved exclusive disjunctions generalize equally badly independent of s.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2016 Springer International Publishing Switzerland. This is an author produced version of a paper subsequently published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Genetic programming; Theory; Runtime analysis |
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) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/M004252/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Apr 2016 14:55 |
Last Modified: | 21 Mar 2018 21:35 |
Published Version: | http://dx.doi.org/10.1007/978-3-319-30668-1_7 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/978-3-319-30668-1_7 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:97981 |