Estimation Of Distribution Algorithms And Its Application In IIR Digital Filter Design

Estimation of distribution algorithms (EDAs) are a novel calss of probabilistic model-building evolutionary algorithms, which combine the statistic theory with evolutionary shcemes. In each interation, the best individuals of current population are selected according to their fitness, and the probability distribution of the selected individuals are esimated in order to guide the new generation. In recently years, EDAs have become a hot topic in field of evolutionary computation, which attract a large number of scholars carried on the theoretical research and application of optimization about them. There are amany problems about EDAs that need further research owing to the short development time. Based on the characteristics of EDAs, we maily focus our study on the perofrmance enhancement of EDAs and the applications of EDA to optimization design of IIR digital filter, through improving the probabilistic model and its construction method of EDAs. The main research work of this paper are as follows:1. Improved the probability model modeling method of EDA based on evolutionary mechanism analysis. In this paper, the probabilistic modeling method of EDA has been improved according to changes in the characteristics of probability models in the evolutionary process. In order to improve the performance of EDAs, We use the winning individuals as the center of the probability model, called Multi-center probability estimation of distribution algorithms, which replaces the traditional EDAs sample of individuals as the center to build a probabilistic model modeling approach.2. Probability model on the estimation of distribution algorithm has been improved through the introduction of multiple probability distribution. Classical estimation of distribution algorithms generally use the Gaussian distribution model as a probability estimation of distribution algorithms in solving continuous optimization problems. Although Gaussian distribution mode is helpful to EDAs for searching more excellent solutions around the field of superior individual, but but the Gaussian distribution tail narrow, with a smaller transition, the ability of global optimization is not strong enough. Is there any other probability mode which can make the algorithm with stronger global search ability? For this puprose, we introduce the Cauchy probability model with a wider tail to enhance the global search ability of EDAs. We propose a combination of probabilistic model estimation of distribution algorithms by combining the Gaussian and Cauchy distribution, whose performance has been proven through a large number of numerical experiments.3. The application of EDAs in IIR digital filters optimal design is studied in this paper. We obtain a group of better performance of the IIR digtial filter than the related literature by taking the combination of probabilistic model EDA to optimimal design. This work is supported by the National Natural Science Foundation of China (61170016), the program for New Century Excellent Talents in university (NCET-11-0715) and the project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.