Improve Real-coded Genetic Algorithm Solving Numerical Solution Of Differential Equation

Genetic algorithm is a computational model which simulates the nature evolution procedures. Since 1960s', GA has been rapidly developed in theory and application. The paper discusses the basic principle and process of basic genetic algorithm, and address the problem of binary coding error and slow convergence rate, and real coded genetic algorithm suited complex great research space but yet it has the problem of inefficiency and slowly converging in the later period. An improved real coded genetic algorithm is proposed.Its main operators include deterministic ranking selecting operator, numerical cross operator, multiple gauss mutation operator, adopting elites to keep the tactics and immigration and depopulation operator. The improved real coded genetic algorithm, which can quicken the convergence velocity and be proved the convergence theoretically, can be applied to suitable second-order two-point boundary-value problems numerical solution and linear and nonlinear problems as well. To accelerate the running speed, other rapid method which using real coded genetic algorithm can solve the numerical solution of the second-order two-point boundary-value problem, is proposed. The methods apply to improve real-coded algorithm many times which successive allocation the calculation area from coarse to fine. It reduces the running time for the variables which aren't large each time and easy to come into being parallel algorithm. And the new method, whose availability can be proved by numerical examples, can be applied to numerical solution of Laplace equation and Poisson equation. The real-coded genetic algorithm provides a new available method to solve numerical solution of differential equation for the engineering field.