Skip to main content

Neutrality in the Graph Coloring Problem

  • Conference paper
  • First Online:
Learning and Intelligent Optimization (LION 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7997))

Included in the following conference series:

Abstract

In this paper, the neutrality of some hard instances of the graph coloring problem (GCP) is quantified. This neutrality property has to be detected as it impacts the search process. Indeed, local optima may belong to plateaus that represent a barrier for local search methods. Then, we also aim at pointing out the interest of exploiting neutrality during the search. Therefore, a generic local search dedicated to neutral problems, NILS, is performed on several hard instances.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://dimacs.rutgers.edu/Challenges/

References

  1. Caramia, M., Dell’Olmo, P., Italiano, G.F.: Checkcol: improved local search for graph coloring. J. Discrete Algorithms 4, 277–298 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Galinier, P., Hertz, A.: A survey of local search methods for graph coloring. Comput. Oper. Res. 33(9), 2547–2562 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., San Francisco (1990)

    Google Scholar 

  4. Marmion, M.-E., Blot, A., Jourdan, L., Dhaenens, C.: Neutrality in the graph coloring problem. Technical Report RR-8215, INRIA (2013)

    Google Scholar 

  5. Marmion, M.-E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: NILS: a neutrality-based iterated local search and its application to flowshop scheduling. In: Merz, P., Hao, J.-K. (eds.) EvoCOP 2011. LNCS, vol. 6622, pp. 191–202. Springer, Heidelberg (2011)

    Google Scholar 

  6. Marmion, M.-E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: On the neutrality of flowshop scheduling fitness landscapes. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 238–252. Springer, Heidelberg (2011)

    Google Scholar 

  7. Paquete, L., Stützle, T.: An experimental investigation of iterated local search for coloring graphs. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G. (eds.) EvoWorkshops 2002. LNCS, vol. 2279, pp. 122–131. Springer, Heidelberg (2002)

    Google Scholar 

  8. Porumbel, D.C., Hao, J.K., Kuntz, P.: An evolutionary approach with diversity guarantee and well-informed grouping recombination for graph coloring. Comput. Oper. Res. 37(10), 1822–1832 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Porumbel, D.C., Hao, J.K., Kuntz, P.: A search space “cartography" for guiding graph coloring heuristics. Comput. Oper. Res. 37(4), 769–778 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Reidys, C.M., Stadler, P.F.: Neutrality in fitness landscapes. Appl. Math. Comput. 117, 321–350 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Stadler, P.F.: Landscapes and their correlation functions. J. Math. Chem. 20, 1–45 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Verel, S., Collard, P., Tomassini, M., Vanneschi, L.: Fitness landscape of the cellular automata majority problem: view from the “Olympus”. Theor. Comput. Sci. 378, 54–77 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wilke, C.O.: Adaptative evolution on neutral networks. Bull. Math. Biol. 63, 715–730 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marie-Eléonore Marmion .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marmion, ME., Blot, A., Jourdan, L., Dhaenens, C. (2013). Neutrality in the Graph Coloring Problem. In: Nicosia, G., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2013. Lecture Notes in Computer Science(), vol 7997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-44973-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-44973-4_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-44972-7

  • Online ISBN: 978-3-642-44973-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics