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Parallel Metaheuristics for Robust Graph Coloring Problem

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Book cover Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 655))

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Abstract

In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph \({ G(V, E)}\) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties \(0<\mathrm{P(e)}<1\). In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable sum of penalties for color conflicts in graph complementary edges (rigidity level), a new bound called the relative robustness threshold (RRT) is proposed. Then three metaheuristics—SA, TS, EA and their parallel analogues PSA, PTS, PEA—for that version of RGCP are presented and experimentally tested. For comparison we use DIMACS graph coloring instances in which a selected percentage of graph edges E is randomly moved to Ē. Since graph densities and chromatic numbers of DIMACS GCP instances are known in advance, the RGCP instances generated on their basis are more suitable for testing algorithms than totally random instances used so far. The results of the conducted experiments are presented and discussed.

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Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland

    Z. Kokosiński, Ł. Ochał & G. Chrząszcz

Authors
  1. Z. Kokosiński
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  2. Ł. Ochał
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  3. G. Chrząszcz
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Correspondence to Z. Kokosiński .

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Editors and Affiliations

  1. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Kokosiński, Z., Ochał, Ł., Chrząszcz, G. (2016). Parallel Metaheuristics for Robust Graph Coloring Problem. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 655. Springer, Cham. https://doi.org/10.1007/978-3-319-40132-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-40132-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40131-7

  • Online ISBN: 978-3-319-40132-4

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