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Math. Comput. Appl. 2010, 15(5), 866-871; doi:10.3390/mca15050866

Controlling Chaos by an Improved Estimation of Distribution Algorithm

1
Department of Computer Science & Technology Tsinghua University, 100084, Beijing, P. R. China
2
Center for Forecasting Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, 100190, Beijing, P. R. China
*
Author to whom correspondence should be addressed.
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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Abstract

Control and synchronization of chaotic systems are important issues in nonlinear sciences. This paper proposes an effective estimation of distribution algorithm (EDA)-based memetic algorithm (MA) to direct the orbits of discrete chaotic dynamical systems as well as to synchronize chaotic systems, which could be formulated as complex multi-modal numerical optimization problems. In EDA-based MA (EDAMA), both EDA-based searching operators and simulated annealing (SA)–based local searching operators are designed to balance the exploration and exploitation abilities. On the other hand, global information provided by EDA is combined with local information from SA to create better solutions. In particular, to enrich the searching behaviors and to avoid premature convergence, SA-based local search is designed and incorporated into EDAMA. To balance the exploration and exploitation abilities, after the standard EDA-based searching operation, SA-based local search is probabilistically applied to some good solutions selected by using a roulette wheel mechanism with a specified probability. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of EDAMA, and the effects of some parameters are investigated as well.
Keywords: Estimation of Distribution Algorithm; Chaotic dynamics Estimation of Distribution Algorithm; Chaotic dynamics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Huang, X.; Jia, P.; Liu, B. Controlling Chaos by an Improved Estimation of Distribution Algorithm. Math. Comput. Appl. 2010, 15, 866-871.

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