Abstract
It is commonly known that evolutionary algorithms use pseudorandom numbers generators. They need them for example to generate the first population, they are necessary in crossing or perturbation process etc. In this paper chaos attractors Arnold Cat Map and Sinai are used as chaotic numbers generators. The main goal was to investigate if they are usable as chaotic numbers generators and their influence on the cost functions convergence’s speed. Next goal was to compare reached values of Arnold Cat Map and Sinai and assess which attractor is better from the view of cost function convergence’s speed.
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References
Koloseni, D., et al.: Differential evolution based nearest prototype classifier with optimized distance measures for the features in the data sets. Expert Systems with Applications 40, 4075–4082 (2013), doi:10.1016/j.eswa.2013.01.040
Tasgetiren, M.F., et al.: A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem. Computers & Operations Research 40, 1729–1743 (2013), doi:10.1016/j.cor.2013.01.005
De Melo, V.V., Carosio, G.L.C.: Investigating Multi-View Differential Evolution for solving constrained engineering design problems. Expert Systems with Applications 40, 3370–3377 (2013), doi:10.1016/j.eswa.2012.12.045
Depolli, M., et al.: Asynchronous Master-Slave Parallelization of Differential Evolution for Multi-Objective Optimization. Evolutionary Computation 21, 261–291 (2013)
Maione, G., Punzi, A.: Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers. Mathematical and Computer Modelling of Dynamical Systems 19, 277–299 (2013), doi:10.1080/13873954.2012.745006
Senkerik, R.: On the Evolutionary Optimization of Chaos Control - A Brief Survey. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 35–48. Springer, Heidelberg (2013)
Senkerik, R., Oplatkova, Z., Zelinka, I.: Evolutionary Synthesis of Control Rules by Means of Analytic Programming for the Purpose of High Order Oscillations Stabilization of Evolutionary Synthesized Chaotic System. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 191–201. Springer, Heidelberg (2013)
Zelinka, I., et al.: An Ivestigation on Evolutionary Reconstruction of Continuous Chaotic Systems. Mathematical and Computer Modelling 57, 2–15 (2013), doi:10.1016/j.mcm.2011.06.034
Nguyen, T.D., Zelinka, I.: Using Method of Artificial Intelligence to Estimate Parameters of Chaotic Synchronization Systems. In: Mendel 2011-17th International Conference on Soft Computing, Mendel, pp. 22–29 (2011)
Umeno, K., Sato, A.H.: Chaotic Method for Generating q-Gaussian Random Variables. IEEE Transactions on Information Theory 59, 3199–3209 (2013), doi:10.1109/TIT.2013.2241174
Wang, H., et al.: Gaussian Bare-Bones Differential Evolution. IEEE Transactions on Cybernetics 43, 634–647 (2013), doi:10.1109/TSMCB.2012.2213808
Caamano, P., et al.: Evolutionary algorithm characterization in real parameter optimization problems. Applied Soft Computing 13, 1902–1921 (2013), doi:10.1016/j.asoc.2013.01.002
Senkerik, R., et al.: Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming. Mathematical and Computer Modelling 57, 57–67 (2013), doi:10.1016/j.mcm.2011.05.030
Hasselblatt, B., Katok, A.: A First Course in Dynamics: With a Panorama of Recent Developments. Cambridge University Press (2003) ISBN 0-521-58750-6
Vellekoop, M., Berlund, R.: Om Intervals, Transitivity = Chaos, vol. 101, pp. 353–355. The American Mathematical Monthly, JSTOR (1994)
Liu, C.: A novel chaotic attractor. Chaos, Solitons & Fractals 39, 1037–1045 (2009)
Grebogi, C., et al.: Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics. In: Non-Linear Physics for Begginers: Fractals, Chaos, Pattern Formation, Solutions, Cellular Automata and Complex Systems, pp. 111–117. Word Scientific Publishing Co. Pte. Ltd. (1998)
Chen, F., et al.: Period Distribution of the Generalized Discrete Arnold Cat Map for N=2(e). IEEE Transactions on Information Theory 59, 3249–3255 (2013), doi:10.1109/TIT.2012.2235907
Bao, J.H., Yang, Q.G.: Period of the discrete Arnold cat map and general cat map. Nonlinear Dynamics 70, 1365–1375 (2012), doi:10.1007/s11071-012-0539-3
Kanso, A., Ghebleh, M.: A novel image encryption algorithm based on a 3D chaotic map. Communications in Nonlinear Science and Numerical Simulation 17, 2943–2959 (2012), doi:10.1016/j.cnsns.2011.11.030
Yang, R., et al.: Harnessing quantum transport by transient chaos. CHAOS 23 (March 2013), doi:10.1063/1.4790863
Pecora, L.M., et al.: Regularization of Tunneling Rates with Quantum Chaos. International Journal of Bifurcation and Chaos 22 (October 2012), doi:10.1142/S0218127412502471
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Skanderova, L., Zelinka, I. (2014). Arnold Cat Map and Sinai as Chaotic Numbers Generators in Evolutionary Algorithms. In: Zelinka, I., Duy, V., Cha, J. (eds) AETA 2013: Recent Advances in Electrical Engineering and Related Sciences. Lecture Notes in Electrical Engineering, vol 282. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41968-3_39
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DOI: https://doi.org/10.1007/978-3-642-41968-3_39
Publisher Name: Springer, Berlin, Heidelberg
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