Corus, D., He, J., Jansen, T. et al. (3 more authors) (2017) On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation. Algorithmica, 78 (2). pp. 714-740. ISSN 0178-4617
Abstract
Understanding which function classes are easy and which are hard for a given algorithm is a fundamental question for the analysis and design of bio-inspired search heuristics. A natural starting point is to consider the easiest and hardest functions for an algorithm. For the (1+1) EA using standard bit mutation (SBM) it is well known that OneMax is an easiest function with unique optimum while Trap is a hardest. In this paper we extend the analysis of easiest function classes to the contiguous somatic hypermutation (CHM) operator used in artificial immune systems. We define a function MinBlocks and prove that it is an easiest function for the (1+1) EA using CHM, presenting both a runtime and a fixed budget analysis. Since MinBlocks is, up to a factor of 2, a hardest function for standard bit mutations, we consider the effects of combining both operators into a hybrid algorithm. We rigorously prove that by combining the advantages of k operators, several hybrid algorithmic schemes have optimal asymptotic performance on the easiest functions for each individual operator. In particular, the hybrid algorithms using CHM and SBM have optimal asymptotic performance on both OneMax and MinBlocks. We then investigate easiest functions for hybrid schemes and show that an easiest function for a hybrid algorithm is not just a trivial weighted combination of the respective easiest functions for each operator.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2016. This article is published with open access at Springerlink.com |
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 EUROPEAN COMMISSION - FP6/FP7 SAGE - 138086 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/M004252/1 European Cooperation in Science and Technology CA15140 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 13 Sep 2016 15:22 |
Last Modified: | 29 Oct 2018 14:27 |
Published Version: | http://dx.doi.org/10.1007/s00453-016-0201-4 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-016-0201-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104614 |