Abstract
Differential evolution is one of the great family of evolutionary algorithms. As well as all evolutionary algorithms differential evolution uses pseudorandom numbers generators in many steps of algorithm. In this paper we will compare pseudorandom numbers generators as Mersenne Twister, Crypto Random, Random number generator in Microsoft .NET System.Random class, Visual Studio 2010, Multiply-with-carry, Xorshift and chaotic numbers generators as Logistic map, Arnold Cat Map and Sinai. The main goal of this paper is compare these pseudorandom numbers generators and chaotic numbers generators from the view of differential evolution convergence’s speed to the global minimum.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zelinka, I., Celikovsky, S., Richter, H., Chen, G., et al. (eds.): Evolutionary Algorithms and Chaotic Systems. SCI, vol. 267. Springer, Heidelberg (2010)
Senkerik, R., et al.: Chaos driven evolutionary algorithm: A new approach for evolutionary optimization. International Journal of Mathematics and Computers in Simulation 7, 363–368 (2013)
Pluhacek, M., et al.: On the behavior and performance of chaos driven PSO algorithm with inertia weight. Computers & Mathematics with Applications 66, 122–134 (2013)
Pluhacek, M., et al.: Chaos PSO Algorithm Driven Alternately by two Different Chaotic Maps - an Initial Study. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 2444–2449 (2013)
Zelinka, I., et al.: Do Evolutionary Algorithms Indeed Require Randomness? In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 2283–2289 (2013)
Senkerik, R., et al.: Investigation on the Differential Evolution Driven by Selected Six Chaotic Systems in the Task of Reactor Geometry Optimization. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 3087–3094 (2013)
Senkerik, R., Davendra, D., Zelinka, I., Pluhacek, M., Kominkova Oplatkova, Z.: Chaos Driven Differential Evolution with Lozi Map in the Task of Chemical Reactor Optimization. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 56–66. Springer, Heidelberg (2013)
Pluhacek, M., Senkerik, R., Zelinka, I.: Impact of Various Chaotic Maps on the Performance of Chaos Enhanced PSO Algorithm with Inertia Weight – An Initial Study. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 153–166. Springer, Heidelberg (2013)
Tsai, J.T.: Optimized weights of document keywords for auto-reply accuracy. Neurocomputing 124, 43–56 (2014)
Kong, X.Y., et al.: A prediction-based adaptive grouping differential evolution algorithm for constrained numerical optimization. Soft Computing 17, 2293–2309 (2013)
Zou, D.X., et al.: A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120, 469–481 (2013)
Matsumoto, M., Nishimura, T.: Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator. ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation 8, 3–30 (1998)
Bonato, V., et al.: A Mersenne Twister Hardware Implementation for the Monte Carlo Localization Algorithm. Journal of Signal Processing Systems for Signal Image and Video Technology 70, 75–85 (2013)
Saito, M., Matsumoto, M.: Variants of Mersenne Twister Suitable for Graphic Processors. ACM Transactions on Mathematical Software 39 (2013), doi:10.1145/2427023.2427029
Manssen, M., et al.: Random number generators for massively parallel simulations on GPU. European Physical Journal-Special Topics 210, 53–71 (2012), doi:10.1140/epjst/e2012-01637-8
Leiserson, C.E., et al.: Deterministic Parallel Random-Number Generation for Dynamic-Multithreading Platforms. ACM Sigplan Notices 47, 193–204 (2012), doi:10.1145/2370036.2145841
http://msdn.microsoft.com/en-us/library/system.random%28v=vs.110%29.aspx
Knuth, D.E.: Art of Computer Programming. The: Generating All Trees, History of Combinatorial Generation, vol. 4, Fascicle 4. Pearson Education, Inc. (2006)
http://thinketg.com/how-to-generate-better-random-numbers-in-c-net-2/
Zeng, G., et al.: Improvement of one type Xorshift random number generators. In: Proceedings of the First International Symposium on Data, Privacy, and E-Commerce, pp. 472–474 (2007)
Leong, P.H.W., et al.: A comment on the implementation of the Ziggurat method. Journal of Statistical Software 7, 1–4 (2005)
Marsaglia, G.: Xorshift RNGs. Journal of Statistical Software (2003)
de Oliveira, T., Marranghello, N.: Design of a reconfigurable pseudorandom number generator for use in intelligent systems. Neurocomputing 74(10), 1510–1519 (2011)
Marsaglia, G., Tsang, W.W.: The Monty Python method for generating random variables. ACM Transactions on Mathematical Software 24(3), 341–350 (1998)
Li, X., et al.: Chaotic Differential Evolution Algorithm Based on Competitive Coevolution and Its Application to Dynamic Optimizzation of Chemical Processes. Intelligent Automation and Soft Computing, 85–98 (February 2013), doi:10.1080/10798587.2013.771437
Zelinka, I.: On Evolutionary Synthesis of Chaotic Systems. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 29–34. Springer, Heidelberg (2013)
Brandejsky, T., Zelinka, I.: Specific Behaviour of GPA-ES Evolutionary System Observed in Deterministic Chaos Regression. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 73–81. Springer, Heidelberg (2013)
Chadli, M., Zelinka, I.: Chaos Synchronization Based on Unknown Inputs Takagi-Sugeno Fuzzy Observer. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 83–92. Springer, Heidelberg (2013)
Pluhacek, M., Budikova, V., Senkerik, R., Oplatkova, Z., Zelinka, I.: Extended Initial Study on the Performance of Enhanced PSO Algorithm with Lozi Chaotic Map. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 167–177. Springer, Heidelberg (2013)
Ma, Z.S.: Chaotic populations in genetic algorithms. Applied Soft Computing 12, 2409–2424 (2012), doi:10.1016/j.asoc.2012.03.001
Alligood, K., Sauer, T.D., Yorke, J.A.: CHaos - an introduction to dynamical systems. Textbooks in Mathematical Sciences, p. 1197. Springer - Verlag New York, Inc. (1996) ISBN 0- 987-94677-2
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)
Arun Fera, M., Jaganathan, S.: Securing DICOM Format Image Archives Using Improved Chaotic Cat Map Method. In: Meghanathan, N., Nagamalai, D., Chaki, N. (eds.) Advances in Computing & Inform. Technology. AISC, vol. 177, pp. 319–328. Springer, Heidelberg (2012)
Taneja, N., et al.: Chaos based cryptosystem for still visual data. Multimedia Tools and Applications 61, 281–298 (2012)
Fu, C., et al.: An efficient and secure medical image protection scheme based on chaotic maps. Computers in Biology and Medicine 43, 1000–1010 (2013)
Chen, Y.L., et al.: A Maximum Entropy-Based Chaotic Time-Variant Fragile Watermarking Scheme for Image Tampering Detection. Entropy 15, 3170–3185 (2013)
Anishchenko, V.S., et al.: Statistics of Poincare recurrences in local and global approaches. Communications in Nonlinear Science and Numerical Simulation 18, 3423–3435 (2013)
Iida, H., et al.: Entropy production in classical Yang-Mills theory from glasma initial conditions. Physical Review D 88 (November 12, 2013)
Green, J.R., et al.: Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium. Proceedings of the National Academy of Sciences of the United States of America 110, 16339–16343 (2013)
Blakely, J.N., Corron, N.J.: Correlation properties of exactly solvable chaotic oscillators. Physical Review E 88 (August 12, 2013)
Pecora, L.M., et al.: Regularization of Tunneling Rates with Quantum Chaos. International Journal of Bifurcation and Chaos 22 (October 2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Skanderova, L., Řehoř, A. (2014). Comparison of Pseudorandom Numbers Generators and Chaotic Numbers Generators used in Differential Evolution. In: Zelinka, I., Suganthan, P., Chen, G., Snasel, V., Abraham, A., Rössler, O. (eds) Nostradamus 2014: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 289. Springer, Cham. https://doi.org/10.1007/978-3-319-07401-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-07401-6_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07400-9
Online ISBN: 978-3-319-07401-6
eBook Packages: EngineeringEngineering (R0)