Some Key Problems In Evolutionary Computation And Wavelet Analysis

Evolutionary Computation is a kind of effective bionic algorithms, which simulates and researches the intelligence of biology from life evolutionary principle. It develops the classical computation method and shows a new direction to complex optimization problem. Because of its intelligence, universality, robustness , global search ability and parallelism, Evolutionary computation has been used in many fields, such as engineer optimization, machine learning, fuzzy systems, data mining and neural network.Since Y. Meyer and S. Mallat have proposed a new method to construct wavelet basis: multiresolution analysis. Wavelet analysis has become research focus of mathematician and engineering. Because of its local characteristic in time domain and frequency domain, wavelet analysis has been used successfully in numerical analysis, function approximate, signal processing, image processing and singularity detection.Supported by the National Natural Science Foundation of China, and the Natural Science Foundation of Henan Province, the attention of dissertation is focused on some issues concerning Evolutionary Computation and Wavelets analysis, which are two focuses in current research fields. The main work can be summarized as follows:1. The convergence of evolutionary algorithms is studied. Firstly the abstract evolution and selection operators, and some characteristic parameters related these two operators are defined, at the same time the relation of these parameters is analyzed. Based on the abstract evolution and selection operators, then the abstract evolutionary algorithm is defined and convergent conditions of the algorithm are analyzed. Lastly a special abstract evolutionary algorithm is proposed, and the characteristic of transition matrix is studied, at the same time the special algorithm is proved to be convergent, and the convergent speed is estimated.2. Based on multi-agent system, genetic algorithm and orthogonal experimental design, a novel hybrid evolutionary algorithm, Orthogonal multi-agent genetic algorithm (OMAGA), is proposed. Based on the inter-action between the agents and their abilities of local perceptivity and self-learning, the global searching ability and the convergent speed is improved; a large store memory was needed in generating an initial population with orthogonal design, to overcome this problem, a method called subspace partition was proposed, so that the store memory is one tenth that of original one; to evaluate performance of the algorithm, the statistic disciplinarian is introduced; the algorithm is proved to be convergent. The experimental result showthat the algorithm have a strong global searching ability , a fast convergent speed and good robustness.3. Three improved particle swarm optimization algorithms are proposed. In the first algorithm, which is called multi-agent particle swarm optimization, common particle swarm considered as an agent or the particle swarms with memory, communication ability, feedback, self-learning and local perception, and based the ability of memory and self-learning, the next particle swarms are generated., through updating of the velocity and location, death, rebirth and self study. The experimental result shows the first algorithm is better than standard classical particle swarm optimization; based on the orthogonal experimental design and particle swarm optimization, an orthogonal particle swarm optimization is proposed; based on orthogonal experimental design and multi-agent particle swarm optimization, an orthogonal multi-agent particle swarm optimization algorithm is proposed. Because of uniformity and choiceness of orthogonal experimental design, the performance of the last two algorithms is improved much.4. A novel particle swarm optimization algorithm based on the clone selection is proposed. The clone selection and agent system are used in construction optimization proposed. The clone operation, rebirth operation and clone selection are used in the new optimization al...