Skip to main content

Fitness Landscape Analysis of Circles in a Square Packing Problems

  • Conference paper
Simulated Evolution and Learning (SEAL 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8886))

Included in the following conference series:

  • 2946 Accesses

Abstract

Fitness landscape analysis provides insight into the structural features of optimization problems. Landscape analysis techniques have been individually shown to capture specific continuous landscape features. However, results are typically for benchmark and artificial problems, and so the ability of techniques to capture real-world problem structures remains largely unknown. In this paper we experimentally examine and compare the ability of length scale analysis, dispersion, fitness distance correlation, information content, partial information content and information stability to characterise and distinguish instances of circle packing problems. Circle packing problems are an important abstraction of many real-world problems such as container loading, facility dispersion and sensor network layout problems. Experiments on incrementally scaled packings show that while all of the techniques provide some problem insight, only length scale analysis and information stability were able to clearly differentiate problem instances.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /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

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. Castillo, I., Kampas, F.J., Pintér, J.D.: Solving circle packing problems by global optimization: numerical results and industrial applications. European Journal of Operational Research 191(3), 786–802 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Gallagher, M.: Multi-layer perceptron error surfaces: visualization, structure and modelling. Ph.D. thesis, Dept. Computer Science and Electrical Engineering, University of Queensland (2000)

    Google Scholar 

  3. Gallagher, M.: Beware the parameters: Estimation of distribution algorithms applied to circles in a square packing. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part II. LNCS, vol. 7492, pp. 478–487. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Grosso, A., Jamali, A.R.M.J.U., Locatelli, M., Schoen, F.: Solving the problem of packing equal and unequal circles in a circular container. Journal of Global Optimization 47(1), 63–81 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hansen, N., Auger, A., Finck, S., Ros, R.: Real-Parameter Black-Box Optimization Benchmarking: Experimental Setup. Technical report, INRIA (2013), http://coco.lri.fr/downloads/download13.09/bbobdocexperiment.pdf

  6. Lunacek, M., Whitley, D.: The dispersion metric and the CMA evolution strategy. In: Genetic and Evolutionary Computation (GECCO), pp. 477–484. ACM (2006)

    Google Scholar 

  7. Malan, K.M., Engelbrecht, A.P.: Quantifying ruggedness of continuous landscapes using entropy. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1440–1447 (2009)

    Google Scholar 

  8. Morgan, R., Gallagher, M.: Length scale for characterising continuous optimization problems. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 407–416. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  9. Morgan, R., Gallagher, M.: Analysing and characterising optimization problems using length scale. IEEE Transactions on Evolutionary Computation (2014) (under review)

    Google Scholar 

  10. Morgan, R., Gallagher, M.: Sampling techniques and distance metrics in high dimensional continuous landscape analysis: Limitations and improvements. IEEE Transactions on Evolutionary Computation 18(3), 456–461 (2014)

    Article  Google Scholar 

  11. Muñoz, M.A., Kirley, M., Halgamuge, S.K.: Landscape characterization of numerical optimization problems using biased scattered data. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1180–1187 (2012)

    Google Scholar 

  12. Muñoz, M.A., Kirley, M., Halgamuge, S.K.: A meta-learning prediction model of algorithm performance for continuous optimization problems. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 226–235. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Müller, C.L., Sbalzarini, I.F.: Global characterization of the CEC 2005 fitness landscapes using fitness-distance analysis. In: Di Chio, C., et al. (eds.) EvoApplications 2011, Part I. LNCS, vol. 6624, pp. 294–303. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Müller, C., Baumgartner, B., Sbalzarini, I.: Particle swarm CMA evolution strategy for the optimization of multi-funnel landscapes. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2685–2692 (2009)

    Google Scholar 

  15. Pitzer, E., Affenzeller, M.: A comprehensive survey on fitness landscape analysis. In: Fodor, J., Klempous, R., Suárez Araujo, C.P. (eds.) Recent Advances in Intelligent Engineering Systems. SCI, vol. 378, pp. 161–191. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Sheather, S.J., Jones, M.C.: A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological) 53(3), 683–690 (1991)

    MATH  MathSciNet  Google Scholar 

  17. Specht, E.: Packomania (2012), http://www.packomania.com

  18. Szabó, P.G., Markót, M.C., Csendes, T.: Global optimization in geometry – circle packing into the square. In: Essays and Surveys in Global Optimization, pp. 233–265. Springer (2005)

    Google Scholar 

  19. Vassilev, V.K., Fogarty, T.C., Miller, J.F.: Information characteristics and the structure of landscapes. Evolutionary Computation 8, 31–60 (2000)

    Article  Google Scholar 

  20. Whitley, D., Lunacek, M., Sokolov, A.: Comparing the niches of CMA-ES, CHC and pattern search using diverse benchmarks. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 988–997. Springer, Heidelberg (2006)

    Chapter  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

Morgan, R., Gallagher, M. (2014). Fitness Landscape Analysis of Circles in a Square Packing Problems. In: Dick, G., et al. Simulated Evolution and Learning. SEAL 2014. Lecture Notes in Computer Science, vol 8886. Springer, Cham. https://doi.org/10.1007/978-3-319-13563-2_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13563-2_39

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13562-5

  • Online ISBN: 978-3-319-13563-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics