title: A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms.
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.
authors.affiliation: School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK psxdc1@nottingham.ac.uk.
authors.forename: Dogan
authors.initials: D
authors.lastname: Corus
authors.affiliation: School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK perkristian.lehre@nottingham.ac.uk.
authors.forename: Per Kristian
authors.initials: PK
authors.lastname: Lehre
authors.affiliation: Optimisation and Logistics, University of Adelaide, Adelaide, SA 5005, Australia frank.neumann@adelaide.edu.au.
authors.forename: Frank
authors.initials: F
authors.lastname: Neumann
authors.affiliation: Optimisation and Logistics, University of Adelaide, Adelaide, SA 5005, Australia mojgan.pourhassan@adelaide.edu.au.
authors.forename: Mojgan
authors.initials: M
authors.lastname: Pourhassan
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D013598:Systems Theory
keywords: Bi-level optimisation; combinatorial optimisation.; evolutionary algorithms