Abstract
This paper proposes a new memetic approach to address the problem of obtaining the optimal set of individual Self-Similar Contractive Functions (SSCF) for the reconstruction of self-similar binary IFS fractal images, the so-called SSCF problem. This memetic approach is based on the hybridization of the modified cuckoo search method for global optimization with a new strategy for the Lévy flight step size (MMCS) and the adaptive step size random search (ASSRS) heuristics for local search. This new method is applied to some illustrative examples of self-similar fractal images with satisfactory graphical and numerical results. Our approach represents a substantial improvement with respect to a previous method based on the original cuckoo search algorithm for all contractive functions of the examples in this paper.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Barnsley, M.F.: Fractals Everywhere, 2nd edn. Academic Press, San Diego (1993)
Falconer, K.: Fractal Geometry: Mathematical Foundations and Applications, 2nd edn. Wiley, Chichester, England (2003)
Gálvez, A.: IFS Matlab generator: a computer tool for displaying IFS fractals. In: Proceedings of ICCSA 2009, pp. 132–142. IEEE CS Press, Los Alamitos, CA (2009)
Gálvez, A., Iglesias, A.: Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting. Sci. World J. 2014, 11 (2014). Article ID 138760
Gálvez, A., Iglesias, A., Takato, S.: Matlab-based KETpic add-on for generating and rendering IFS fractals. CCIS 56, 334–341 (2009)
Gálvez, A., Iglesias, A., Takato, S.: KETpic Matlab binding for efficient handling of fractal images. Int. J. Future Gener. Comm. Networ. 3(2), 1–14 (2010)
Gálvez, A., Kitahara, K., Kaneko, M.: IFSGen4LaTeX : Interactive graphical user interface for generation and visualization of iterated function systems in LaTeX. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 554–561. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44199-2_84
Gutiérrez, J.M., Iglesias, A.: A mathematica package for the analysis and control of chaos in nonlinear systems. Comput. Phys. 12(6), 608–619 (1998)
Gutiérrez, J.M., Iglesias, A., Rodríguez, M.A.: A multifractal analysis of IFSP invariant measures with application to fractal image generation. Fractals 4(1), 17–27 (1996)
Gutiérrez, J.M., Iglesias, A., Rodríguez, M.A., Burgos, J.D., Moreno, P.A.: Analyzing the multifractal structure of DNA nucleotide sequences. In: Chaos and Noise in Biology and Medicine, vol. 7, pp. 315–319. World Scientific, Singapore (1998)
Hutchinson, J.E.: Fractals and self similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
Iglesias, A., Gálvez, A.: Cuckoo search with Lévy flights for reconstruction of outline curves of computer fonts with rational Bézier curves. In: Proceedings of Congress on Evolutionary Computation, CEC 2016. IEEE CS Press, Los Alamitos, CA (2016)
Quirce, J., Gálvez, A., Iglesias, A.: Computing self-similar contractive functions for the IFS inverse problem through the cuckoo search algorithm. In: Del Ser, J. (ed.) ICHSA 2017. AISC, vol. 514, pp. 333–342. Springer, Singapore (2017). https://doi.org/10.1007/978-981-10-3728-3_33
Marsaglia, G.: Choosing a point from the surface of a sphere. Annal. Math. Stat. 43(2), 645–646 (1972)
Mlakar, U., Fister Jr., I., Fister, I.: Hybrid self-adaptive cuckoo search optimization. Swarm Evol. Comput. 29, 47–72 (2016)
Schumer, M.A., Steiglitz, K.: Adaptive step size random search. IEEE Trans. Autom. Control 13(3), 270–276 (1968)
Walton, S., Hassan, O., Morgan, K., Brown, M.R.: Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons Fractals 44, 710–718 (2011)
Yang, X.-S.: Nature-Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press, Frome, UK (2010)
Yang, X.S., Deb, S.: Cuckoo search via Lévy flights. In: Proceedings of World Congress on Nature & Biologically Inspired Computing (NaBIC), pp. 210–214. IEEE Press, New York (2009)
Yang, X.S., Deb, S.: Engineering optimization by cuckoo search. Int. J. Math. Model. Numer. Optim. 1(4), 330–343 (2010)
Acknowledgements
This research is supported by the project PDE-GIR of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 778035, the Spanish Ministry of Economy and Competitiveness under grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE), the project #JU12, of SODERCAN and European Funds FEDER (SODERCAN/FEDER UE) and the project EMAITEK of the Basque Government.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Gálvez, A., Iglesias, A., Fister, I., Fister, I., Osaba, E., Del Ser, J. (2018). Memetic Modified Cuckoo Search Algorithm with ASSRS for the SSCF Problem in Self-Similar Fractal Image Reconstruction. In: de Cos Juez, F., et al. Hybrid Artificial Intelligent Systems. HAIS 2018. Lecture Notes in Computer Science(), vol 10870. Springer, Cham. https://doi.org/10.1007/978-3-319-92639-1_55
Download citation
DOI: https://doi.org/10.1007/978-3-319-92639-1_55
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92638-4
Online ISBN: 978-3-319-92639-1
eBook Packages: Computer ScienceComputer Science (R0)