Genetic Algorithm Design Research For Solving Fucntion Optimization Problems

Genetic algorithm(GA) is a computation model which mimicks natural selection of Darwinian evolution and evolution mechanism of genetic mechanism and is a algorithm for searching the global optimal silution. It is applied to solve many practical optimization problems by many engineers. GA has two shortcomings, one shortcoming is that GA has weak local searching ability, another shortcoming is that GA is apt to premature stagnate. To overcome the two shortcomings, this paper does four aspects of research work for function optimization problems as following:1.For the defect that GA has weak local searching ability, This paper applies the golden section method and fitness sharing method to GA and proposes a improved genetic algorithm based on mountain-climbing operator and fitness sharing. The golden section method enhances the local searching ability of GA. This paper tests some classical function optimization problems, Numerical results show that the algorithm is superior to FSGA and HX-NUM in both accuracy and convergence rate.2.For function optimization problems which aren’t differentiable, this paper proposes the search method of steepest direction. The method not only overcome the weakness of the first kind of traditional optimization method that the objective function can be derived, but also can obtain high-precision local optimal solution. This paper inserts the method into genetic algorithm based on fitness sharing method and proposes a improved genetic algorithm based on the search algorithm of steepest direction. Numerical results show that the algorithm is superior to StGA, FEP, HSOGA and LEA in accuracy.3.For the defect that GA is apt to premature stagnate, The strategy of dual population is presented to maintian the population diversity. The paper improves a dual-population genetic algorithm for adaptive diversity control and proposes a genetic algorithm based on the classification of the auxiliary group. The improved algorithm classifies auxiliary population into several classes with priori knowledge and maintains the auxiliary population diversity. Numerical results show that the algorithm is superior to FSGA and DPGA.4.In some dual-population genetic algorithms, the radius parameter changes too quickly, making auxiliary population out of control. For the defect, This paper describes the change of the radius parameter with cosine function and proposes a dual-population genetic algorithm based on periodic slow change of radius parameter. The improved algorithm not only maintains the population diversity, but also enhances the local searching ability. This paper proposes the concept of the distance between an individual and the main group firstly, and takes the maximum distance between an individual and the main group as the maximum value of radius parameter. Numerical results show the effectiveness of the algorithm.