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Type: Journal article
Title: Parameterized analysis of multiobjective evolutionary algorithms and the weighted vertex cover problem
Author: Pourhassan, M.
Shi, F.
Neumann, F.
Citation: Evolutionary Computation, 2019; 27(4):559-575
Publisher: Massachusetts Institute of Technology Press (MIT Press)
Issue Date: 2019
ISSN: 1063-6560
Statement of
Mojgan Pourhassan, Feng Shi and Frank Neumann
Abstract: Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann (2013) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann (2013), we provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a (1+ɛ)-approximation in expected time O(n·2min{n,2(1-ɛ)OPT}+n3).
Keywords: Parameterized analysis
global SEMO
weighted vertex cover problem.
Rights: © 2019 Massachusetts Institute of Technology
DOI: 10.1162/evco_a_00255
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