Soft Computing

, Volume 20, Issue 10, pp 3787–3802 | Cite as

Bag of local landscape features for fitness landscape analysis

Focus

Abstract

Evolutionary computation is a research field dealing with black-box and complex optimization problems whose fitness landscapes are usually unknown in advance. It is difficult to select an appropriate evolutionary algorithm and parameters for a given problem due to the black-box setting although many evolutionary algorithms have been developed. In this context, several landscape features have been proposed and their usefulness examined for understanding the problem. In this paper, we propose a novel feature vector by focusing on the local landscape in order to characterize the fitness landscape. The proposed landscape features are a vector form and composed of a histogram of quantized local landscape features. We introduce two implementation methods of this concept, called the bag of local landscape patterns (BoLLP) and the bag of evolvability (BoEvo). The BoLLP uses the fitness pattern of the neighbors of a certain candidate solution, and the BoEvo uses the number of better candidate solutions in the neighbors as the local landscape features. Furthermore, the hierarchical versions of the BoLLP and the BoEvo, concatenated feature vectors with different sample sizes, are considered to capture the landscape characteristic with various resolutions. We extract the proposed landscape feature vectors from well-known continuous optimization benchmark functions and the BBOB benchmark function set to investigate their properties; the visualization of the proposed landscape features, clustering and running time prediction experiments are conducted. Then the effectiveness of the proposed landscape features for the fitness landscape analysis is discussed based on the experimental results.

Keywords

Fitness landscape analysis Local features Problem understanding Continuous optimization problem 

References

  1. Altenberg L (1994) The evolution of evolvability in genetic programming. In: Kinnear KE Jr (ed) Advances in genetic programming. MIT Press, Cambridge, pp 47–74Google Scholar
  2. Csurka G, Dance CR, Fan L, Willamowski J, Bray C (2004) Visual categorization with bags of keypoints. In: Workshop on statistical learning in computer vision, ECCV, pp 1–22Google Scholar
  3. Hansen N, Finck S, Ros R, Auger A (2009) Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions. Technical report RR-6829, INRIA. http://coco.gforge.inria.fr/lib/exe/fetch.php?media=download3.6:bbobdocfunctionsdef.pdf
  4. Huang D, Shan C, Ardabilian M, Wang Y, Chen L (2011) Local binary patterns and its application to facial image analysis: a survey. IEEE Trans Syst Man Cybern Part C (Appl Rev) 41(6):765–781CrossRefGoogle Scholar
  5. Iqbal M, Browne WN, Zhang M (2014) Improving genetic search in XCS-based classifier systems through understanding the evolvability of classifier rules. Soft Comput 19(7):1863–1880CrossRefGoogle Scholar
  6. Jones T, Forrest S (1995) Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the sixth international conference on genetic algorithms. Morgan Kaufmann, pp 184–192Google Scholar
  7. Liu J, Abbass HA, Green DG, Zhong W (2012) Motif difficulty (MD): a predictive measure of problem difficulty for evolutionary algorithms using network motifs. Evolut Comput 20(3):321–347CrossRefGoogle Scholar
  8. Loshchilov I, Schoenauer M, Sèbag M (2013) Bi-population CMA-ES algorithms with surrogate models and line searches. In: Proceedings of the 15th annual conference companion on genetic and evolutionary computation (GECCO ’13 companion). ACM Press, pp 1177–1184Google Scholar
  9. Lunacek M, Whitley D (2006) The dispersion metric and the CMA evolution strategy. In: Proceedings of the 8th annual conference on genetic and evolutionary computation (GECCO ’06). ACM Press, pp 477–484Google Scholar
  10. Malan K, Engelbrecht A (2009) Quantifying ruggedness of continuous landscapes using entropy. In: Proceedings of the IEEE congress on evolutionary computation 2009 (CEC ’09), pp 1440–1447Google Scholar
  11. Malan KM, Engelbrecht AP (2013) A survey of techniques for characterising fitness landscapes and some possible ways forward. Inf Sci 241:148–163CrossRefGoogle Scholar
  12. McClymont K (2013) Recent advances in problem understanding : changes in the landscape a year on. In: Proceedings of the 15th annual conference companion on genetic and evolutionary computation (GECCO ’13 companion). ACM Press, pp 1071–1077Google Scholar
  13. Mersmann O, Bischl B, Trautmann H, Preuss M, Weihs C, Rudolph G (2011) Exploratory landscape analysis. In: Proceedings of the 13th annual conference on genetic and evolutionary computation (GECCO ’11). ACM Press, pp 829–836Google Scholar
  14. Merz P (2004) Advanced fitness landscape analysis and the performance of memetic algorithms. Evolut Comput 12(3):303–325MathSciNetCrossRefGoogle Scholar
  15. Moraglio A, Poli R (2004) Topological interpretation of crossover. In: Deb K (ed) Genetic and evolutionary computation—GECCO 2004. Lecture notes in computer science, vol 3102. Springer, Berlin, Heidelberg, pp 1377–1388Google Scholar
  16. Morgan R, Gallagher M (2012) Length scale for characterising continuous optimization problems. In: Coello Coello CA, Cutello V, Deb K, Forrest S, Nicosia G, Pavone M (eds) Parallel problem solving from nature—PPSN XII, lecture notes in computer science, vol 7491. Springer, Berlin, Heidelberg, pp 407–416Google Scholar
  17. Morgan R, Gallagher M (2014) Sampling techniques and distance metrics in high dimensional continuous landscape analysis: limitations and improvements. IEEE Trans Evolut Comput 18(3):456–461Google Scholar
  18. Müller CL, Baumgartner B, Sbalzarini IF (2009) Particle Swarm CMA Evolution Strategy for the optimization of multi-funnel landscapes. In: Proceedings of the 2009 IEEE congress on evolutionary computation (CEC ’09). IEEE, pp 2685–2692Google Scholar
  19. Müller CL, Sbalzarini IF (2011) Global characterization of the CEC 2005 fitness landscapes using fitness-distance analysis. In: Di Chio C, Cagnoni S, Cotta C, Ebner M, Ekárt A, Esparcia-Alcázar Al, Merelo JJ, Neri F, Preuss M, Richter H, Togelius J, Yannakakis GN (eds) Applications of evolutionary computation, lecture notes in computer science, vol 6624. Springer, Berlin, Heidelberg, pp 294–303Google Scholar
  20. Muñoz MA, Kirley M, Halgamuge SK (2012) A meta-learning prediction model of algorithm performance for continuous optimization problems. In: Coello Coello CA, Cutello V, Deb K, Forrest S, Nicosia G, Pavone M (eds) Parallel problem solving from nature—PPSN XII, lecture notes in computer science, vol 7491. Springer, Berlin, Heidelberg, pp 226–235Google Scholar
  21. Muñoz MA, Sun Y, Kirley M, Halgamuge SK (2015) Algorithm selection for black-box continuous optimization problems: a survey on methods and challenges. Inf Sci 317:224–245CrossRefGoogle Scholar
  22. Murphy KP (2012) Machine learning: a probabilistic perspective. The MIT Press, CambridgeMATHGoogle Scholar
  23. Ojala T, Pietikäinen M, Harwood D (1994) Performance evaluation of texture measures with classification based on Kullback discrimination of distributions. In: Proceedings of the 12th IAPR international conference on pattern recognition (ICPR), vol 1. IEEE Computer Society Press, pp 582–585Google Scholar
  24. Paulhac L, Makris P, Ramel JY (2008) Comparison between 2D and 3D local binary pattern methods for characterisation of three-dimensional textures. In: Campilho A, Kamel N (eds) Image Analysis and Recognition, lecture notes in computer science, vol 5112. Springer, Heidelberg, pp 973–974Google Scholar
  25. Philippe C, Vérel S, Manuel C (2004) Local search heuristics : fitness cloud versus fitness landscape. In: Proceedings of the 16th European conference on artificial intelligence (ECAI 2004). IOS Press, pp 973–974Google Scholar
  26. Pietikäinen M, Hadid A, Zhao G, Ahonen T (2011) Computer vision using local binary patterns, computational imaging and vision, vol 40. Springer, BerlinCrossRefGoogle Scholar
  27. Pitzer E, Affenzeller M (2012) A comprehensive survey on fitness landscape analysis. In: Fodor J, Klempous R, Suárez Araujo CP (eds) Recent advances in intelligent engineering systems, studies in computational intelligence, vol 378. Springer, Berlin, Heidelberg, pp 161–191Google Scholar
  28. Shirakawa S, Nagao T (2014) Local landscape patterns for fitness landscape analysis. In: Proceedings of the 10th international conference on simulated evolution and learning (SEAL 2014), lecture notes in computer science, vol 8886. Springer, pp 467–478Google Scholar
  29. Smith T, Husbands P, Layzell P, O’Shea M (2002) Fitness landscapes and evolvability. Evolut Comput 10(1):1–34CrossRefGoogle Scholar
  30. Smith-Miles K, Tan TT (2012) Measuring algorithm footprints in instance space. In: Proceedings of the 2012 IEEE congress on evolutionary computation (CEC ’12). IEEE, pp 1–8Google Scholar
  31. Steer K, Wirth A, Halgamuge S (2008) Information theoretic classification of problems for metaheuristics. In: Li X, Kirley M, Zhang M, Green D, Ciesielski V, Abbass H, Michalewicz Z, Hendtlass T, Deb K, Tan K, Branke J, Shi Y (eds) Proceedings of the 7th international conference on simulated evolution and learning (SEAL 2008), lecture notes in computer science, vol 5361. Springer, Berlin, Heidelberg, pp 319–328Google Scholar
  32. Tang H, Yin B, Sun Y, Hu Y (2013) 3D face recognition using local binary patterns. Signal Process 93(8):2190–2198Google Scholar
  33. Vanneschi L, Tomassini M, Collard P, Vérel S (2006) Negative slope coefficient: a measure to characterize genetic programming fitness landscapes. In: Collet P, Tomassini M, Ebner M, Gustafson S, Ekárt A (eds) Proceedings of the 9th European conference on genetic programming (EuroGP 2006), lecture notes in computer science, vol 3905. Springer, Berlin, Heidelberg, pp 178–189Google Scholar
  34. Weinberger E (1990) Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol Cybern 63(5):325–336CrossRefMATHGoogle Scholar
  35. Zhao Y, Huang DS, Jia W (2012) Completed local binary count for rotation invariant texture classification. IEEE Trans Image Process 21(10):4492–4497MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan
  2. 2.Faculty of Environment and Information SciencesYokohama National UniversityYokohamaJapan

Personalised recommendations