Doerr, B., Lissovoi, A. and Oliveto, P.S. (2019) Evolving boolean functions with conjunctions and disjunctions via genetic programming. In: GECCO '19 : Proceedings of the Genetic and Evolutionary Computation Conference. The Genetic and Evolutionary Computation Conference - GECCO 2019, 13-17 Jul 2019, Prague, Czech Republic. ACM Digital Library ISBN 9781450361118
Abstract
Recently it has been proved that simple GP systems can efficiently evolve the conjunction of n variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the behaviour and performance of a GP system for evolving a Boolean function with unknown components, i.e. the target function may consist of both conjunctions and disjunctions. We rigorously prove that if the target function is the conjunction of n variables, then a GP system using the complete truth table to evaluate program quality evolves the exact target function in O(ℓ n log2 n) iterations in expectation, where ℓ ≥ n is a limit on the size of any accepted tree. Additionally, we show that when a polynomial sample of possible inputs is used to evaluate solution quality, conjunctions with any polynomially small generalisation error can be evolved with probability 1 - O(log2(n)/n). To produce our results we introduce a super-multiplicative drift theorem that gives significantly stronger runtime bounds when the expected progress is only slightly super-linear in the distance from the optimum.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. This is an author-produced version of a paper subsequently published in GECCO 2019 Proceedings. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Theory; Genetic programming; Running time 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: | 04 Oct 2019 10:57 |
Last Modified: | 04 Oct 2019 16:00 |
Status: | Published |
Publisher: | ACM Digital Library |
Refereed: | Yes |
Identification Number: | 10.1145/3321707.3321851 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144390 |