Local Landscape Patterns for Fitness Landscape Analysis

  • Shinichi Shirakawa
  • Tomoharu Nagao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8886)


Almost all problems targeted by evolutionary computation are black-box or heavily complex, and their fitness landscapes usually are unknown. Selection of the appropriate search algorithm and parameters is a crucial topic when the landscape of a given target problem could be unknown in advance. Although several landscape features have been proposed in this context, examining a variety of landscape features is useful for problem understanding. In this paper, we propose a novel feature vector for characterizing the fitness landscape using the local landscape patterns (LLP). The proposed feature vector is composed by the histogram of the fitness patterns of the local candidate solutions. We extract the proposed LLP feature vector from well-known continuous optimization benchmark functions and BBOB 2013 benchmark set to investigate the properties of the proposed landscape feature and discuss about its effectiveness.


Fitness Landscape Analysis Local Feature Problem Understanding Continuous Optimization Problem 


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  1. 1.
    Altenberg, L.: The evolution of evolvability in genetic programming. In: Kinnear Jr., K.E. (ed.) Advances in Genetic Programming, pp. 47–74. MIT Press, Cambridge (1994)Google Scholar
  2. 2.
    Csurka, G., Dance, C.R., Fan, L., Willamowski, J., Bray, C.: Visual categorization with bags of keypoints. In: Workshop on Statistical Learning in Computer Vision, ECCV, pp. 1–22 (2004)Google Scholar
  3. 3.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann (1995)Google Scholar
  4. 4.
    Liu, J., Abbass, H.A., Green, D.G., Zhong, W.: Motif difficulty (MD): a predictive measure of problem difficulty for evolutionary algorithms using network motifs. Evolutionary Computation 20(3), 321–347 (2012)CrossRefGoogle Scholar
  5. 5.
    Loshchilov, I., Schoenauer, M., Sèbag, M.: Bi-population CMA-ES agorithms with surrogate models and line searches. In: Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation (GECCO 2013) Companion, pp. 1177–1184. ACM, New York (2013)CrossRefGoogle Scholar
  6. 6.
    Lunacek, M., Whitley, D.: The dispersion metric and the CMA evolution strategy. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (GECCO 2006), pp. 477–484. ACM, New York (2006)CrossRefGoogle Scholar
  7. 7.
    McClymont, K.: Recent advances in problem understanding: Changes in the landscape a year on. In: Proceeding of the 15th Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion (GECCO 2013) Companion, pp. 1071–1078. ACM, New York (2013)Google Scholar
  8. 8.
    Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., Rudolph, G.: Exploratory landscape analysis. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation (GECCO 2011), pp. 829–836. ACM, New York (2011)CrossRefGoogle Scholar
  9. 9.
    Mersmann, O., Preuss, M., Trautmann, H.: Benchmarking evolutionary algorithms: Towards exploratory landscape analysis. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 73–82. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Merz, P.: Advanced fitness landscape analysis and the performance of memetic algorithms. Evolutionary Computation 12(3), 303–325 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Morgan, R., Gallagher, M.: Sampling techniques and distance metrics in high dimensional continuous landscape analysis: limitations and improvements. IEEE Trans. Evol. Comput. 18(3), 456–461 (2014)CrossRefGoogle Scholar
  13. 13.
    Muñoz, M., Kirley, M., Halgamuge, S.: 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)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Müller, C., Baumgartner, B., Sbalzarini, I.: Particle swarm cma evolution strategy for the optimization of multi-funnel landscapes. In: 2009 IEEE Congress on Evolutionary Computation (CEC 2009), pp. 2685–2692 (2009)Google Scholar
  16. 16.
    Murphy, K.P.: Machine Learning: A Probabilistic Perspective. The MIT Press (2012)Google Scholar
  17. 17.
    Philippe, C., Vérel, S., Manuel, C.: Local search heuristics: Fitness Cloud versus Fitness Landscape. In: Proceedings of the 16th Eureopean Conference on Artificial Intelligence (ECAI 2004), pp. 973–974. IOS Press (2004)Google Scholar
  18. 18.
    Pietikäinen, M., Zhao, G., Hadid, A., Ahonen, T.: Computer Vision Using Local Binary Patterns. Computational Imaging and Vision, vol. 40. Springer (2011)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Reidys, C.M., Stadler, P.F.: Neutrality in fitness landscapes. Applied Mathematics and Computation 117(2-3), 321–350 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Smith, T., Husbands, P., Layzell, P., O’Shea, M.: Fitness landscapes and evolvability. Evolutionary Computation 10(1), 1–34 (2002)CrossRefGoogle Scholar
  22. 22.
    Smith-Miles, K., Tan, T.: Measuring algorithm footprints in instance space. In: 2012 IEEE Congress on Evolutionary Computation (CEC 2012), pp. 1–8 (2012)Google Scholar
  23. 23.
    Vanneschi, L., Tomassini, M., Collard, P., Vérel, S.: Negative Slope Coefficient: A Measure to Characterize Genetic Programming Fitness Landscapes. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds.) EuroGP 2006. LNCS, vol. 3905, pp. 178–189. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  24. 24.
    Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics 63(5), 325–336 (1990)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Shinichi Shirakawa
    • 1
  • Tomoharu Nagao
    • 2
  1. 1.College of Science and EngineeringAoyama Gakuin UniversitySagamiharaJapan
  2. 2.Graduate School of Environment and Information SciencesYokohama National UniversityYokohamaJapan

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