Research Of Genetic Algorithm And Its Application In Numerical Computation

Genetic Algorithms is a random searching method, which is in virtue of the biological mechanism of natural selection and heredity and leveraging colony searching technology. It searched the global optimal solution by imitating the process of the species evolution. The characteristic of the algorithm is the information exchange of individuals and population selection. And the algorithm isn't affected by the gradient information. It can be used efficiently to solve complex problems and non-liner problems. With 20 years development, Genetic Algorithms has been widely used in many fields such as data mining, production management, function optimization, machine learning, planning design and other fields. And it has become a research hotspot of the 21th century's intelligent computation. Genetic Algorithms has been widely used in the engineering research, and the application of which on tradition mathematics should be improved. Genetic Algorithms has two superiorities: (1) Genetic Algorithms searches in the global space, and it focus on the high efficient part, so it can heighten efficiency. (2) Genetic Algorithms has inherent parellelism, and it can be easily done by dealing with a lot of patterns. In this paper we researched how to use Genetic Algorithms in traditional mathematics. The major tasks in this paper include: (1) Improvement in the lower bound of max eigenvalue of the positive matrix. (2) Using the Genetic Algorithm to solve a difficult problem –searching the eigenvalue and the eigenvector of a matrix. (3) Solved the nonlinear Least square problem based on Genetic Algorithms. (4) Solved the Least Absolute Deviation based on Genetic Simulated Annealing Algorithm. By a lot of tests, we found that Genetic Algorithms is a good method to solve traditional mathematics problems.