Research & Application On Some Key Problems In Bayesian Optimization Algorithm

Estimation of distribution algorithms (EDAs) are a class of innovative stochastic optimization algorithms. EDAs acquire solutions by statistically learning and sampling the probability distribution of the best individuals of the population at each iteration cycle of the algorithms. Bayesian optimization algorithm (BOA) is a kind of estimation of distribution algorithms in which Bayesian Network is used as probabilistic model to capture the (inter)dependencies among the decision variables of the optimization problem. Although Bayesian optimization algorithm has experienced some progresses since it was fist proposed, there are still many gaps in current knowledge base, such as theory analysis, algorithm designs and applications, etc. Based on characteristics of Bayesian optimization algorithm, theory analysis on algorithm convergence is systematically discussed, selection strategy and algorithm design are deeply researched to improve algorithm efficiency, and applications in the field of image process are innovated in the dissertation. The main contributions of this dissertation are as follows:1. It is discovered the convergence of Bayesian optimization algorithm. The ideal mathematic model of Bayesian optimization algorithm is set up based on probability analysis. Then it is found that the algorithm will converge to the global optimum. Furthermore, considering probabilistic model error in Bayesian optimization algorithm, and it is found that in given situation of the dissertation the algorithm will converge to the global optimum too. The convergence theory of Bayesian optimization algorithm is developed by the probability anlaysis in this dissertation. The sufficient condition of convergency of Bayesian optimization algorithm is gotten. It is no need to depend on the necessary condition of Genetic algorithm anymore.2. The best selection strategy and replacement strategy of Bayesian optimization algorithm is discussed in detail. Tournament selection and full replacement are found to be the best operand of Bayesian optimization algorithm in tests. It is also confirmed based on analysis on individual copy, loss of population diversity, correct building block searching and probabilistic model setting up. The operand selection difference between Bayesian optimization algorithm and Genetic algorithm is discovered by the analysis in the dissertation.The study provides guide of Bayesian optimization algorithm operand selection.3. A new Bayesian optimization algorithm by refined BIC metric is proposed in the dissertation. Based the analysis on simplified BIC metric, BIC metric gain is found to be in linear relationship with tournament size. A penalty function in tournament size is added in BIC metric. As a result, the number of setting up Bayesian model is reduced; further, the calculation of the algorithms is also reduced. So Bayesian optimization algorithm based this refined BIC metric proposed in this dissertation is proved to outperform in evolution speed. The proposed algorithm utilizes the current Baysian probability model as reference model to set up a new one. The reference model is used as prior knowledge will reduce calculation and promote model accurrence. The idea to design a more fast and precise algorithm is thus realized.4. The application of Bayesian optimization algorithm in the field of image process is discussed in the dissertation. First in image segmentation, Bayesian optimization algorithm aiming to search the optimal threshold is proposed. In the algorithm the ratio of variance is considered as the objection. Tests show that Bayesian optimization algorithm validly found optimal threshold in image segmentation. The second application is a content-based image retrieval to find the best match attributed graph after shot change detection and key frame extraction. The study extends Bayesian optimization algorithm application to the field of image process. The tests show that Bayesian optimization algorithms have better result than Genetic algorithms. The proposed Bayesian optimization algorithms applied in image process solve how to express and code the optimal objective. The method provides a new way to deal with the image process.This dissertation has proved that Bayesian optimization algorithm converges in ideal situation and in considering some error. Studies show that the algorithm will converge to the global optimum. The best selection strategy and replacement strategy of Bayesian optimization algorithm are achieved by numerical simulations. Detailed analysis is provided to confirm the test results. The study conclusion provides guidance of Bayesian optimization algorithm operand selection. Improvement of Bayesian optimization algorithm by refined BIC metric is also provided in the dissertation. The refined Bayesian optimization algorithm reduces calculation and accelerates the convergence. At last, Bayesian optimization algorithm is applied in image process. The test result shows that the performance of Bayesian optimization algorithm and refined Bayesian optimization algorithm are better than that of Genetic algorithms.The study extends the application field of Bayesian opitimization algorithm to image process.