Research On Differential Evolution Algorithm And Its Applications

Differential Evolution (DE) is proposed by Storn & Price in 1996. As a novel Evolutionary Algorithm (EA), DE has attracted more attention in recent years. The crucial idea behind DE is a scheme for generating trial vectors. DE generates new vectors by adding the scaled difference of two randomly selected population vectors to a third randomly selected population vector, and mixing the target vector with the generated vector. In the selection stage, the trial vector competes against the target vector to produce the new generation Compared with other EAs, DE is capable of optimizing high dimension, nonlinear, nond ifferentiable, multimodal objective functions and multiobjective optimization problems. It has been applied to many areas successfully. However, like other EAs, DE still suffer from the problem of slow and premature convergence. In addition, the control parameters involved in DE is highly dependent on the problems under consideration and is not easy to properly set. In this dissertation, some improved DE algorithms are proposed and applied in the fields of fuzzy clustering analysis, agent coalition formation and adaptive equalization. The main contributions of this dissertation are described as follows:(1) In order to speed up the convergence of DE and to avoid the algorithm falling into a local optimal solution, a modified DE algorithm, called DocDE, is presented, in which two trial vectors are created by crossover operation as candidates of the next generation The experimental results on benchmark functions show that the proposed algorithm is good at adaptability, stability and global search ability. Especially, for high-dimensional complicated functions, DocDE can expand the search space to find the optimal solution quickly. A novel method for adaptive equalization is presented, which using DocDE instead of gradient descent to adjust the coefficients of the equalizer. The experimental results show that the novel algorithm speeds up the convergence rate and improves the convergence precision through the evolution of multi-gene ration in the situation of a short training set. Compared with the traditional LMS and original DE, the novel algorithm achieves the lower misadjustment and the less symbol error rate.(2) For solving control parameters selected problem of DE, a self-adaptive differential evolution algorithm, called SelfDE, is presented. The improved algorithm uses self-adaptive mechanisms to adjust scale factor F and crossover rate CR in DE. It not only reduces the control parameters of DE required to be selected by hand , but also speeds up the algorithm convergence rate. Experimental results on different benchmark functions show that SelfDE is superior to the other related algorithms such as jDE, FADE, DESAP and SaDE algorithms on the quality of solution for most benchmark functions. A new fuzzy clustering algorithm based on SelfDE (FCBADE) is presented, which can be used for optimizing clustering criterion function and generating appropriate partitioning of the dataset. In the algorithm, the weighted sum validity function (WSVF) is improved as a dynamic weighted sum validity function(DWSVF). Several experiments have been implemented to show the effectiveness of FCBADE. In comparison with other genetic clustering algorithms, FCBADE can consistently and efficiently converge to the best-known optimum corresponding to the given data in concurrence with the convergence result. The experiments also found that DWSVF is generally able to improve the confidence of clustering solutions and achieve more accurate and robust results.(3) In multi-agent systems, forming agent coalition is a combinatorial optimization problem. In order to apply DE which is suitable for solving optimization problems mainly in continuous spaces to solve the combined optimization problems in discrete spaces, a novel binary-encoding differential evolution (BinDE) algorithm, which combined with forming agent coalition, is presented. The experimental results show that the new algorithm is feasible and efficient. It is superior to other related methods such as GA and ACA both on the quality of solution and on the convergence rate.