Solutions Of Diverse Optimizing Problems Based On Chaos

This thesis is concerned with problems of chaos and chaotic optimization.In this paper, the advantage and disadvantages of traditional optimization algorithms are analyses. A phenomenon-chaos, which only exists in the nonlinear system, then, is discussed.The chaotic system's outstanding character, ergodicity, is noticed. Chaotic variables can approach to every value in its defining range, so they can find the global optimal solution. Based on this feature, chaotic optimization algorithm is presented. In the simulation with chaotic optimization algorithm, the defect is found, and the nature of this method is discovered after carefully thinking. Chaotic variables have not uniform distribution, and it is worse that chaotic variables are very sensitive to the change of initial value and the defining range of variable; therefore it is uncertain that the optimal solution can be found. All those shortcomings above bring numerous problems in the process of optimization.The author combined chaotic optimization algorithm with traditional optimization methods. This combination helps the traditional optimization methods approach to die global optimal solution and shortens the searching time of chaotic optimization algorithm. After training the neural network and Fuzzy Inference System with the method named Gauss Newton Levenberg-Marquard, we optimize these two systems with chaoticoptimization method. Simulated Annealing Algorithm and Genetic Algorithm can find the better solution, with the help of chaotic optimization method. This combined method can not only prevent form falling into the trap of local minimum but also prompt the process of chaotic optimization.There are many faults in the chaotic optimization algorithm. To solve these problems, a new method named "bisection-interpolation approach" is put forward. It has numerous advantages such as ergodicity, uniform distribution, not sensitive to the change of initial value, not sensitive to the defining range of variable, not requiring the continuation and not requiring differential of the optimized object. In the simulation of functions, this method performs better than chaotic optimization algorithm. With the combination of bisection-interpolation approach and Gauss Newton Levenberg-Marquardt method, we optimize neural network and Fuzzy Inference System. Taking advantage of bisection-interpolation approach, Simulated Annealing Algorithm and Genetic Algorithm find the better solution than chaotic combination method.