The Study On Modern Optimization Algorithms And Their Applications In The Bilevel Nonlinear Programming

The paper improves and perfects a modern optimization algorithm proposed in the resent years----chaos optimization algorithm. Then make use of the chaos optimization algorithm and particle swarm optimization algorithm to get the global solution of the bilevel nonlinear programming.After the study, the paper point out the disadvantage in the existing chaos optimization algorithm. Then the paper gives an improved chaos optimization algorithm----successive approximation chaos optimization method. Numerical experiments show the method's effectiveness. The paper proves that this method is almost sure convergence.It is very difficult to determine the bilevel nonlinear programming's solution. It can't be solved with the analytic methods in the most situations. And the present numerical methods for the bilevel nonlinear programming have many disadvantages too. So the paper give a new train of though based on the modern optimization algorithms to solve this programming. At the same time, the paper give the detailed method step by step for using the chaos optimization algorithm and the particle swarm optimization algorithm to solve it. Numerical experiments show the tow method's effectiveness.This paper is divided in five sections, as follows:Chapter 1 gives an introduction to the background, the aims and the importance of the problem in the paper. Then we give a simple survey on the chaos optimization algorithm, the particle swarm optimization algorithm and the bilevel nonlinear programming. At last, we give the new ideas of this paper.Chapter 2 is an introduction to the general knowledge of the chaos optimization algorithm and the particle swarm optimization algorithm. Chapter 3 is an introduction to the general knowledge of the bilevel nonlinear programming and the present methods that can solve this programming.Chapter 4 points the disadvantage of the present chaos optimization algorithm. Then a new one which local searching space can be decided under a self-adaptive control strategy is proposed. The method keeps multiple better searching points at present searching space to decide its local searching space later. By this way the method have a self-adaptive on different functions and deferent times the search has carried out before. Simulation results show that the algorithm can improve the chaos optimization algorithm's performance effectively as well as make the chaos optimization more practical. The global convergence of the algorithm is proved.Chapter 5 points the disadvantages of the existing numerical methods when they are used to solve the bilevel nonlinear programming, a new train of thought is give. Then the paper gives tow detailed algorithms and the flowcharts for making use of the chaos optimization algorithm and the particle swarm optimization algorithm to solve this problem. The global convergence proof of the method base on chaos optimization algorithm is given. Numerical experiments show that the tow proposed methods can give the better solution of this programming.