Solving Problems in Chaos Control though an Differential Evolution Algorithm with Region Zooming

In this paper, a novel scheme is propose to solve the problems in chaos control via a nonnegative multi–modal nonlinear optimization, which finds the unstable periodic orbits and best parameters of chaos system such that the objective function is minimized. The novel scheme embeds with a differential evolution algorithm consisting of techniques in three aspects: uniform design to the initial population, deflection and stretching to the objective functions, and the region zooming self–adaptively, which result in a much more effective searching mechanism with fine equilibrium between exploitation and exploration. To exhibit the new scheme’s performance, the experiments done to Hénon, Chen and Lü system are given, and the simulations done show that the method has better adaptability, dependability and robustness.

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COMPUTING TWO LINCHPINS OF TOPOLOGICAL DEGREE BY A NOVEL DIFFERENTIAL EVOLUTION ALGORITHM

International Journal of Computational Intelligence and Applications ◽

10.1142/s1469026805001647 ◽

2005 ◽

Vol 05 (03) ◽

pp. 335-350 ◽

Cited By ~ 8

Author(s):

FEI GAO ◽

HENG-QING TONG

Keyword(s):

Differential Evolution ◽

Topological Degree ◽

Large Scale ◽

Uniform Design ◽

Lipschitz Constant ◽

Differential Evolution Algorithm ◽

Initial Point ◽

Benchmark Problems ◽

Initial Population ◽

Evolution Algorithm

How to detect the topological degree (TD) of a function is of vital importance in investigating the existence and the number of zero values in the function, which is a topic of major significance in the theory of nonlinear scientific fields. Usually a sufficient refinement of the boundary of the polyhedron decided by Boult and Sikorski algorithm (BS) is needed as prerequisite when the well known method of Stenger and Kearfott is chosen for computing TD. However two linchpins are indispensable to BS, the parameter δ on the boundary of the polyhedron and an estimation of the Lipschitz constant K of the function, whose computations are analytically difficult. In this paper, through an appropriate scheme that transforms the problems of computing δ and K into searching optimums of two non-differentiable functions, a novel differential evolution algorithm (DE) combined with established techniques is proposed as an alternative method to computing δ and K. Firstly it uses uniform design method to generate the initial population in feasible field so as to have the property of large scale convergence, without better approximation of the unknown parameter as iterative initial point. Secondly, it restrains the normal DE's local convergence limitation virtually through deflection and stretching of objective function. The main advantages of the put algorithm are its simplicity and its ability to work by using function values solely. Finally, details of applying the proposed method into computing δ and K are given, and experimental results on two benchmark problems in contrast to the results reported have demonstrated the promising performance of the proposed algorithm in different scenarios.

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Optimal Power Flow with Four Objective Functions using Improved Differential Evolution Algorithm: Case Study IEEE 57-bus power system

10.1109/ciem52821.2021.9614925 ◽

2021 ◽

Author(s):

Murtadha Al-Kaabi ◽

Layth Al-Bahrani ◽

Virgil Dumbrava ◽

Mircea Eremia

Keyword(s):

Power System ◽

Differential Evolution ◽

Power Flow ◽

Optimal Power Flow ◽

Differential Evolution Algorithm ◽

Objective Functions ◽

Optimal Power ◽

Evolution Algorithm ◽

Improved Differential Evolution Algorithm

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Adaptive Constrained Differential Evolution Algorithm by Using Generalized Opposition-Based Learning

Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University ◽

10.1051/jnwpu/20193751000 ◽

2019 ◽

Vol 37 (5) ◽

pp. 1000-1010

Author(s):

Wenhai Wu ◽

Xiaofeng Guo ◽

Siyu Zhou ◽

Jintao Liu

Keyword(s):

Differential Evolution ◽

Optimization Problem ◽

Simple Structure ◽

Differential Evolution Algorithm ◽

Initial Population ◽

Mutation Operator ◽

Competition Mechanism ◽

Opposition Based Learning ◽

Adaptive Differential Evolution ◽

Evolution Algorithm

Differential evolution is a global optimization algorithm based on greedy competition mechanism, which has the advantages of simple structure, less control parameters, higher reliability and convergence. Combining with the constraint-handling techniques, the constraint optimization problem can be efficiently solved. An adaptive differential evolution algorithm is proposed by using generalized opposition-based learning (GOBL-ACDE), in which the generalized opposition-based learning is used to generate initial population and executes the generation jumping. And the adaptive trade-off model is utilized to handle the constraints as the improved adaptive ranking mutation operator is adopted to generate new population. The experimental results show that the algorithm has better performance in accuracy and convergence speed comparing with CDE, DDE, A-DDE and. And the effect of the generalized opposition-based learning and improved adaptive ranking mutation operator of the GOBL-ACDE have been analyzed and evaluated as well.

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Color Image Quantization Algorithm Based on Self-Adaptive Differential Evolution

Computational Intelligence and Neuroscience ◽

10.1155/2013/231916 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 15

Author(s):

Qinghua Su ◽

Zhongbo Hu

Keyword(s):

Differential Evolution ◽

Color Image ◽

Differential Evolution Algorithm ◽

Optimization Methods ◽

Particle Swarm Algorithm ◽

The Novel ◽

Image Quantization ◽

Adaptive Differential Evolution ◽

Evolution Algorithm ◽

Self Adaptive

Differential evolution algorithm (DE) is one of the novel stochastic optimization methods. It has a better performance in the problem of the color image quantization, but it is difficult to set the parameters of DE for users. This paper proposes a color image quantization algorithm based on self-adaptive DE. In the proposed algorithm, a self-adaptive mechanic is used to automatically adjust the parameters of DE during the evolution, and a mixed mechanic of DE andK-means is applied to strengthen the local search. The numerical experimental results, on a set of commonly used test images, show that the proposed algorithm is a practicable quantization method and is more competitive thanK-means and particle swarm algorithm (PSO) for the color image quantization.

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