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Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm

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  • Iztok Fister
  • Marjan Mernik
  • Bogdan Filipič

Abstract

This paper proposes a hybrid self-adaptive evolutionary algorithm for graph coloring that is hybridized with the following novel elements: heuristic genotype-phenotype mapping, a swap local search heuristic, and a neutral survivor selection operator. This algorithm was compared with the evolutionary algorithm with the SAW method of Eiben et al., the Tabucol algorithm of Hertz and de Werra, and the hybrid evolutionary algorithm of Galinier and Hao. The performance of these algorithms were tested on a test suite consisting of randomly generated 3-colorable graphs of various structural features, such as graph size, type, edge density, and variability in sizes of color classes. Furthermore, the test graphs were generated including the phase transition where the graphs are hard to color. The purpose of the extensive experimental work was threefold: to investigate the behavior of the tested algorithms in the phase transition, to identify what impact hybridization with the DSatur traditional heuristic has on the evolutionary algorithm, and to show how graph structural features influence the performance of the graph-coloring algorithms. The results indicate that the performance of the hybrid self-adaptive evolutionary algorithm is comparable with, or better than, the performance of the hybrid evolutionary algorithm which is one of the best graph-coloring algorithms today. Moreover, the fact that all the considered algorithms performed poorly on flat graphs confirms that graphs of this type are really the hardest to color. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Iztok Fister & Marjan Mernik & Bogdan Filipič, 2013. "Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm," Computational Optimization and Applications, Springer, vol. 54(3), pages 741-770, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:741-770
    DOI: 10.1007/s10589-012-9496-5
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    Cited by:

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    2. Lucas Cuadra & Miguel Del Pino & José Carlos Nieto-Borge & Sancho Salcedo-Sanz, 2017. "Optimizing the Structure of Distribution Smart Grids with Renewable Generation against Abnormal Conditions: A Complex Networks Approach with Evolutionary Algorithms," Energies, MDPI, vol. 10(8), pages 1-31, July.

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