Researches On Hybrid Genetic Algorithm Based On Conjugate Gradient Algorithm

Nonlinear optimization computational method is a cross-cutting researching area of operational research and computational mathematics. Intelligent optimization method is an active research in recent years. These two methods have a wide range of applications in many real sectors, such as the national defense, economic, engineering and so on. They have an important theoretical significance especially in unconstrained and superlinear optimization problems.In this paper, I do some researches on multiple hump function optimization problems. A hybrid genetic algorithm based on nonlinear conjugate gradient algorithm is proposed.The background and the research actuality of CGA and GA are presented in introduction. Then, the organizational of this paper is offered briefly.In Chapter 1, we first propose some conjugate gradient algorithm theories and review the details of SGA. Some mild conditions are given in this Chapter, which ensure the global convergence of these methods.In Chapter 2, we emphases research on a new hybrid genetic algorithm which can solve the multiple hump functions optimization problem better. A new hybrid genetic algorithm which combines the good property of global search of the genetic algorithm and the good property of regional search of the conjugate gradient approach is proposed. To ensure global convergence and superlinear convergence rate of the conjugate gradient algorithm, we introduce the n+1 step return method. It can ensure that the each step is descent direction. Then, we put forward Gray coded not binary-coded to avoid hamming cliff. In order to ensure the diversity of population and improve the velocity of convergence and efficiency, the niche skill is brought out, by which the best operator is better shared and the function is strengthened. It exceeds standard genetic algorithm (SGA) on the ability of local searching and premature convergence.The hybrid genetic algorithm by defining an additional operation which is designed as CG operator and act to the best individual in the evolution processes of GA. After selection, crossover and mutation operator, then the optimation of hybrid algorithm is realized. The conclusion of global convergence is also shown.In Chapter 3, we propose some numerical experiment, and the results show the feasibility and efficiency of the method. Experiments indicate that the hybrid algorithm is better than SGA and CGA alone. It is proved in the experiments that the scheme not only could strengthen searching ability but also could accelerate the convergent speed of optimization.In the last Chapter, we sum up the research efforts in this thesis and give prospects of the further research in the fields.