Skip to main content

Local Optima and Weight Distribution in the Number Partitioning Problem

  • Conference paper
Parallel Problem Solving from Nature – PPSN XIII (PPSN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8672))

Included in the following conference series:

Abstract

This paper investigates the relation between the distribution of the weights and the number of local optima in the Number Partitioning Problem (NPP). The number of local optima in the 1-bit flip landscape was found to be strongly and negatively correlated with the coefficient of variation (CV) of the weights. The average local search cost using the 1-bit flip operator was also found to be strongly and negatively correlated with the CV of the weights. A formula based on the CV of the weights for estimating the average number of local optima in the 1-bit flip landscape is proposed in the paper. The paper also shows that the CV of the weights has a potentially useful application in guiding the choice of heuristic search algorithm.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alyahya, K., Rowe, J.E.: Phase transition and landscape properties of the number partitioning problem. In: Blum, C., Ochoa, G. (eds.) EvoCOP 2014. LNCS, vol. 8600, pp. 206–217. Springer, Heidelberg (2014)

    Google Scholar 

  2. Borgs, C., Chayes, J., Pittel, B.: Phase transition and finite-size scaling for the integer partitioning problem. Random Structures & Algorithms 19(3-4), 247–288 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ferreira, F.F., Fontanari, J.F.: Probabilistic analysis of the number partitioning problem. Journal of Physics A: Mathematical and General 31(15), 3417 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of books in the mathematical sciences. W. H. Freeman (1979)

    Google Scholar 

  5. Garnier, J., Kallel, L.: How to detect all maxima of a function. In: Theoretical Aspects of Evolutionary Computing. Natural Computing Series, pp. 343–370. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Mertens, S.: A physicist’s approach to number partitioning. Theoretical Computer Science 265(1-2), 79–108 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Prügel-Bennett, A., Tayarani-Najaran, M.: Maximum satisfiability: Anatomy of the fitness landscape for a hard combinatorial optimization problem. IEEE Transactions on Evolutionary Computation 16(3), 319 (2012)

    Article  Google Scholar 

  8. Slaney, J., Walsh, T.: Backbones in optimization and approximation. In: IJCAI, pp. 254–259 (2001)

    Google Scholar 

  9. Stadler, P.F., Hordijk, W., Fontanari, J.F.: Phase transition and landscape statistics of the number partitioning problem. Physical Review E 67(5), 056701 (2003)

    Google Scholar 

  10. Stadler, P.F., Stephens, C.R.: Landscapes and effective fitness. Comments on Theoretical Biology 8(4-5), 389–431 (2002)

    Article  Google Scholar 

  11. Watson, J.P., Whitley, L.D., Howe, A.E.: Linking search space structure, run-time dynamics, and problem difficulty: A step toward demystifying tabu search. J. Artif. Int. Res. 24(1), 221–261 (2005)

    MATH  Google Scholar 

  12. Witt, C.: Worst-case and average-case approximations by simple randomized search heuristics. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 44–56. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Zhang, W.: Configuration landscape analysis and backbone guided local search.: Part i: Satisfiability and maximum satisfiability. Artificial Intelligence 158(1), 1–26 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Alyahya, K., Rowe, J.E. (2014). Local Optima and Weight Distribution in the Number Partitioning Problem. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_85

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10762-2_85

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10761-5

  • Online ISBN: 978-3-319-10762-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics