Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/99626
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Type: Journal article
Title: A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms
Author: Corus, D.
Lehre, P.
Neumann, F.
Pourhassan, M.
Citation: Evolutionary Computation, 2016; 24(1):183-203
Publisher: MIT Press Journals
Issue Date: 2016
ISSN: 1063-6560
1530-9304
Statement of
Responsibility: 
Dogan Corus, Per Kristian Lehre, Frank Neumann, Mojgan Pourhassan
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.
Keywords: Bi-level optimisation; evolutionary algorithms; combinatorial optimisation
Rights: © 2016 Massachusetts Institute of Technology
RMID: 0030032511
DOI: 10.1162/EVCO_a_00147
Grant ID: http://purl.org/au-research/grants/arc/DP130104395
http://purl.org/au-research/grants/arc/DP140103400
Appears in Collections:Computer Science publications

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