A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms

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...

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Published in:Evolutionary computation Vol. 24; no. 1; p. 183
Main Authors: Corus, Dogan, Lehre, Per Kristian, Neumann, Frank, Pourhassan, Mojgan
Format: Journal Article
Language:English
Published: United States 01.03.2016
Subjects:
Algorithms
Biological Evolution
Systems Theory
combinatorial optimisation
evolutionary algorithms
Bi-level optimisation
ISSN:1530-9304, 1530-9304
Online Access:Get more information
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Summary: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.
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ISSN:1530-9304
1530-9304
DOI:10.1162/EVCO_a_00147