Corus, D., Lehre, P.K., Neumann, F. et al. (1 more author) (2016) A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms. Evolutionary Computation, 24 (1). pp. 183-203. ISSN 1063-6560
Abstract
Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. In this paper, we analyse the runtime of some evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem and the generalised travelling salesperson problem in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) evolutionary algorithm working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the problem can be solved in fixed-parameter time with the global structure representation. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other’s hard instances very efficiently. For the generalised travelling salesperson problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) evolutionary algorithm working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 MIT Press. This is an author produced version of a paper subsequently published in Evolutionary Computation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Bi-level optimisation; evolutionary algorithms; combinatorial optimisation |
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: | 16 Aug 2017 09:10 |
Last Modified: | 21 Mar 2018 20:10 |
Published Version: | https://doi.org/10.1162/EVCO_a_00147 |
Status: | Published |
Publisher: | Massachusetts Institute of Technology Press |
Refereed: | Yes |
Identification Number: | 10.1162/EVCO_a_00147 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120163 |