Differential Evolution Algorithm With Greedy Strategy And Its Applications

As optimization problems exist widely in all domains of scientific research and engineering application, research on optimization methods is of great theoretical significance and practical value. Differential evolution ( DE )algorithm is a kind of evolutionary algorithm derived from the natural biological evolution. Biological evolution means members more fit with environment survive while other less fit members are going to disappear as generation increases. DE has the ability to handle non-differentiable, nonlinear and multimodal cost functions, it is also easy to use, robust, and has excellent global convergence properties. However, as the search of DE algorithm is of some blindness, its local search ability and the whole search efficiency is limited, the convergence rate during the latter part of search is slow. As a result, the convergence rate of DE in optimizing a computationally expensive objective function still does not meet all our requirements.Based on analysis of the principle and the shortcoming of DE, firstly the parameter effects on the algorithm were studied, then the basic DE was modified to improve its search efficiency and form three differential evolution algorithms with greedy strategy, finally the modified DE was applied in clustering analysis and design of digital filters to verify the validity and practicability.The main contents and research contributions of this dissertation are as follows:1. The reasonable range of mutation factor, crossover factor and population size was studied by the method of statistic analysis and phase portraits. The principle for parameter selection was also concluded by studying parameter effects on the convergence speed and optimization performace.2. As the local search ability of DE is weak, and the convergence speed is slow during the latter part of the search. Based on analysis of search mechanism of DE, a modified DE with local enhanced operator was proposed, which makes some individuals of the population search around the current best individual, and turn to careful seaching as generation increases. Simulation results show that the local search ability and the convergence speed of the modified algorithm are enhanced effectively.3. Based on analysis of advantages and disadvantages of optimization strategies for DE, two modified differential evolution algorithms with hybrid optimization strategy were proposed, and the dynamic updating of the hybrid factor was also studied. The main idea of hybrid optimization is to optimize by grouping or giving a second optimization chance. It is observed that the search efficiency of the hybrid algorithm is significantly improved.4. As the mutation operation of DE is completely stochastic and blind, the greedy mutation operation was proposed and embedded into the dynamic differential evolution algorithm. The greedy mutation operation ensures that the fitness of base vector is superior to the average fitness of population, which accelerates generating of better offspring. Simulation results show that the iterations needed for convergence are significantly reduced as well as the high search success rate is ensured.5. The modified algorithm proposed in this dissertation was applied to partitional clustering analysis and optimization design of digital filters. Simulation results show that the clustering algorithm based on DE is superior compared to the typical K-means algorithm, both with respect to precision as well as robustness of the results. It is also observed that the optimization design of digital filters with DE is more quick and precise than other methods.