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.
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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 | ||||
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) | ||||
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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: | https://doi.org/10.1145/3321707.3321851 | ||||
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