Arnold Cat Map and Sinai as Chaotic Numbers Generators in Evolutionary Algorithms

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.

[1]  Vinicius Veloso de Melo,et al.  Investigating Multi-View Differential Evolution for solving constrained engineering design problems , 2013, Expert Syst. Appl..

[2]  A. Kanso,et al.  A novel image encryption algorithm based on a 3D chaotic map , 2012 .

[3]  Roman Senkerik,et al.  Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming , 2013, Math. Comput. Model..

[4]  Qigui Yang,et al.  Period of the discrete Arnold cat map and general cat map , 2012 .

[5]  Hui Wang,et al.  Gaussian Bare-Bones Differential Evolution , 2013, IEEE Transactions on Cybernetics.

[6]  Guido Maione,et al.  Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers , 2013 .

[7]  Boris Hasselblatt,et al.  A First Course in Dynamics: with a Panorama of Recent Developments , 2003 .

[8]  Matjaz Depolli,et al.  Asynchronous Master-Slave Parallelization of Differential Evolution for Multi-Objective Optimization , 2013, Evolutionary Computation.

[9]  Emilio Corchado,et al.  Nostradamus: Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems, Nostradamus conference 2012, Ostrava, Czech Republic, September 2012 , 2013, NOSTRADAMUS.

[10]  Jouni Lampinen,et al.  Differential evolution based nearest prototype classifier with optimized distance measures for the features in the data sets , 2013, Expert Syst. Appl..

[11]  Louis M. Pecora,et al.  Regularization of Tunneling Rates with Quantum Chaos , 2012, Int. J. Bifurc. Chaos.

[12]  Chongxin Liu.  A novel chaotic attractor , 2009 .

[13]  Kwok-Wo Wong,et al.  Period Distribution of the Generalized Discrete Arnold Cat Map for $N = 2^{e}$ , 2013, IEEE Transactions on Information Theory.

[14]  Roman Senkerik,et al.  On the Evolutionary Optimization of Chaos Control - A Brief Survey , 2012, NOSTRADAMUS.

[15]  Roman Senkerik,et al.  Evolutionary Synthesis of Control Rules by Means of Analytic Programming for the Purpose of High Order Oscillations Stabilization of Evolutionary Synthesized Chaotic System , 2012, NOSTRADAMUS.

[16]  Mehmet Fatih Tasgetiren,et al.  A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem , 2013, Comput. Oper. Res..

[17]  Richard J. Duro,et al.  Evolutionary algorithm characterization in real parameter optimization problems , 2013, Appl. Soft Comput..

[18]  Y. Lai,et al.  Harnessing quantum transport by transient chaos. , 2013, Chaos.

[19]  J. Yorke,et al.  Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics , 1987, Science.

[20]  Ken Umeno,et al.  Chaotic Method for Generating q-Gaussian Random Variables , 2012, IEEE Transactions on Information Theory.

[21]  Roman Senkerik,et al.  An investigation on evolutionary reconstruction of continuous chaotic systems , 2013, Math. Comput. Model..