A basic consideration of an optimizer based on piecewise rotational chaos system

We consider an optimization method that updates multi searching points based on piecewise rotational chaos system. In previous, some optimization methods utilizing chaos dynamics have been proposed. The considered method is simpler than these methods because it has two system parameters and the searching points are governed by single dynamics. We compared the performance of the considered method for 27 benchmark functions with particle swarm optimization and a previous proposed chaos-based method. The considered method obtains the best performance for 16 functions and tie for 2 functions. The Friedman test shows that the considered method obtains significancy better than both methods.

[1]  L. Coelho,et al.  A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch , 2009 .

[2]  Andries Petrus Engelbrecht,et al.  A generalized theoretical deterministic particle swarm model , 2014, Swarm Intelligence.

[3]  Takashi Okamoto,et al.  Global optimization using a synchronization of multiple search Points autonomously driven by a chaotic dynamic model , 2008, J. Glob. Optim..

[4]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[5]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[6]  Masafumi Miyatake,et al.  Maximum Power Point Tracking of Multiple Photovoltaic Arrays: A PSO Approach , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Jacek M. Zurada,et al.  An approach to multimodal biomedical image registration utilizing particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[8]  Jiang Chuanwen,et al.  A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation , 2005, Math. Comput. Simul..

[9]  E. Aiyoshi,et al.  Particle swarm optimization: a numerical stability analysis and parameter adjustment based on swarm activity , 2008 .

[10]  Manifold Piecewise Linear Chaotic System on Cylinder and Super Expanding Chaos , 2014 .

[11]  Andries Petrus Engelbrecht,et al.  A study of particle swarm optimization particle trajectories , 2006, Inf. Sci..

[12]  Yoshikazu Yamanaka,et al.  An optimizer using swarm of chaotic dynamical particles , 2015 .

[13]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[14]  Russell C. Eberhart,et al.  Human tremor analysis using particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[15]  Shiyuan Yang,et al.  Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm , 2007, Inf. Process. Lett..

[16]  R. A. Groeneveld,et al.  Practical Nonparametric Statistics (2nd ed). , 1981 .

[17]  Mohamed E. El-Hawary,et al.  A Survey of Particle Swarm Optimization Applications in Electric Power Systems , 2009, IEEE Transactions on Evolutionary Computation.

[18]  Zengqiang Chen,et al.  New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process , 2007, IEEE Transactions on Neural Networks.

[19]  Bo Liu,et al.  Improved particle swarm optimization combined with chaos , 2005 .

[20]  Ettore Francesco Bompard,et al.  A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment , 2005 .

[21]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[22]  Xin-She Yang,et al.  Chaos-enhanced accelerated particle swarm optimization , 2013, Commun. Nonlinear Sci. Numer. Simul..

[23]  B. Alatas,et al.  Chaotically encoded particle swarm optimization algorithm and its applications , 2009 .

[24]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[25]  H. Yoshida,et al.  A particle swarm optimization for reactive power and voltage control considering voltage security assessment , 1999, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[26]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[27]  Visakan Kadirkamanathan,et al.  Stability analysis of the particle dynamics in particle swarm optimizer , 2006, IEEE Transactions on Evolutionary Computation.

[28]  Tadashi Tsubone,et al.  Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator , 2009, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[29]  Lixiang Li,et al.  CHAOTIC PARTICLE SWARM OPTIMIZATION FOR ECONOMIC DISPATCH CONSIDERING THE GENERATOR CONSTRAINTS , 2007 .