Lissovoi, A. and Oliveto, P.S. (2018) On the Time and Space Complexity of Genetic Programming for Evolving Boolean Conjunctions. In: McIlraith, S.A. and Weinberger, K.Q., (eds.) Thirty-Second AAAI Conference on Artificial Intelligence. Thirty-Second AAAI Conference on Artificial Intelligence, 02-07 Feb 2017, New Orleans, Louisiana, USA. Association for the Advancement of Artificial Intelligence
Abstract
Genetic Programming (GP) is a general purpose bio-inspired meta-heuristic for the evolution of computer programs. In contrast to the several successful applications, there is little understanding of the working principles behind GP. In this paper we present a performance analysis that sheds light on the behaviour of simple GP systems for evolving conjunctions of n variables (ANDn). The analysis of a random local search GP system with minimal terminal and function sets reveals the relationship between the number of iterations and the expected error of the evolved program on the complete training set. Afterwards we consider a more realistic GP system equipped with a global mutation operator and prove that it can efficiently solve ANDn by producing programs of linear size that fit a training set to optimality and with high probability generalise well. Additionally, we consider more general problems which extend the terminal set with undesired variables or negated variables. In the presence of undesired variables, we prove that, if non-strict selection is used, then the algorithm fits the complete training set efficiently while the strict selection algorithm may fail with high probability unless the substitution operator is switched off. In the presence of negations, we show that while the algorithms fail to fit the complete training set, the constructed solutions generalise well. Finally, from a problem hardness perspective, we reveal the existence of small training sets that allow the evolution of the exact conjunctions even in the presence of negations or of undesired variables.
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: | © 2018 Association for the Advancement of Artificial Intelligence. |
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: | 06 Aug 2018 09:49 |
Last Modified: | 19 Dec 2022 13:50 |
Published Version: | https://www.aaai.org/ocs/index.php/AAAI/AAAI18/sch... |
Status: | Published |
Publisher: | Association for the Advancement of Artificial Intelligence |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133966 |