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Bag of local landscape features for fitness landscape analysis

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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.

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Notes

  1. The term “landscape” or “fitness landscape” in this paper conceptually denotes the shape of search space, e.g., ridges, valleys, plateaus, and basins, and is formally defined by the tuple of objective function, candidate solutions, and distance function (see Sect. 3.1 for details).

  2. Evolvability can be also formulated by the expected evaluation value or the quantile of the neighbors.

  3. It might be able to reduce the computational cost by using the fast nearest neighbor search methods such as k-dimensional tree.

  4. https://cran.r-project.org/web/packages/flacco/index.html.

  5. http://coco.gforge.inria.fr/doku.php?id=bbob-2013.

  6. http://coco.gforge.inria.fr/doku.php?id=bbob-2013-results.

References

  • Altenberg L (1994) The evolution of evolvability in genetic programming. In: Kinnear KE Jr (ed) Advances in genetic programming. MIT Press, Cambridge, pp 47–74

    Google Scholar 

  • 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 1–22

  • 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

  • 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):765–781

    Article  Google Scholar 

  • 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):1863–1880

    Article  Google Scholar 

  • 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 184–192

  • 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):321–347

    Article  Google Scholar 

  • 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 1177–1184

  • 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 477–484

  • 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 1440–1447

  • Malan KM, Engelbrecht AP (2013) A survey of techniques for characterising fitness landscapes and some possible ways forward. Inf Sci 241:148–163

    Article  Google Scholar 

  • 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 1071–1077

  • 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 829–836

  • Merz P (2004) Advanced fitness landscape analysis and the performance of memetic algorithms. Evolut Comput 12(3):303–325

    Article  MathSciNet  Google Scholar 

  • 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 1377–1388

  • 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 407–416

  • 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):456–461

  • 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 2685–2692

  • 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 294–303

  • 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 226–235

  • 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 317:224–245

    Article  Google Scholar 

  • Murphy KP (2012) Machine learning: a probabilistic perspective. The MIT Press, Cambridge

    MATH  Google Scholar 

  • 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 582–585

  • 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 973–974

  • 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 973–974

  • Pietikäinen M, Hadid A, Zhao G, Ahonen T (2011) Computer vision using local binary patterns, computational imaging and vision, vol 40. Springer, Berlin

    Book  Google Scholar 

  • 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 161–191

  • 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 467–478

  • Smith T, Husbands P, Layzell P, O’Shea M (2002) Fitness landscapes and evolvability. Evolut Comput 10(1):1–34

    Article  Google Scholar 

  • 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 1–8

  • 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 319–328

  • Tang H, Yin B, Sun Y, Hu Y (2013) 3D face recognition using local binary patterns. Signal Process 93(8):2190–2198

  • 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 178–189

  • Weinberger E (1990) Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol Cybern 63(5):325–336

    Article  MATH  Google Scholar 

  • Zhao Y, Huang DS, Jia W (2012) Completed local binary count for rotation invariant texture classification. IEEE Trans Image Process 21(10):4492–4497

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Shinichi Shirakawa

  2. Faculty of Environment and Information Sciences, Yokohama National University, 79-7, Tokiwadai Hodogaya-ku, Yokohama, Kanagawa, 240-8501, Japan

    Tomoharu Nagao

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  1. Shinichi Shirakawa
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  2. Tomoharu Nagao
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Correspondence to Shinichi Shirakawa.

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The authors declare that they have no conflict of interest.

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Communicated by B. Xue and A. G. Chen.

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Shirakawa, S., Nagao, T. Bag of local landscape features for fitness landscape analysis. Soft Comput 20, 3787–3802 (2016). https://doi.org/10.1007/s00500-016-2091-4

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