Corus, D., Oliveto, P.S. and Yazdani, D. (2019) Artificial immune systems can find arbitrarily good approximations for the NP-hard number partitioning problem. Artificial Intelligence, 274. pp. 180-196. ISSN 0004-3702
Abstract
Typical artificial immune system (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which evolutionary algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that these two operators have similar behaviour also in more realistic problems. In this paper we perform an analysis for the standard NP-hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and random local search (RLS) may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio (1+) within n(−(2/)−1)(1 − )−2e322/ + 2n322/ + 2n3 function evaluations in expectation. This expectation is polynomial in the problem size and exponential only in 1/.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier. This is an author produced version of a paper subsequently published in Artificial Intelligence. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Randomized search heuristics; Evolutionary algorithms; Artificial immune systems; Approximation algorithms; Makespan scheduling |
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: | 11 Apr 2019 08:56 |
Last Modified: | 27 Mar 2020 01:39 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.artint.2019.03.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144833 |