Researches On Hybrid Genetic Algorithm For Nonlinear Problems

For solve the nonlinear numerical problems, the traditional optimization and genetic algorithm will be combined for proposing a new hybrid genetic algorithm. Numerical experiments show that this algorithm has highly precision and reliable convergent resulting.In Chapter 1, we review the basic theory of genetic algorithm, introduce the research state and advances of hybrid genetic algorithm.In Chapter 2, we analyze some basic methods for solving the nonlinear equations. And introduce three methods for solving the nonlinear equations.In Chapter 3, we propose a hybrid genetic algorithm for solving nonlinear complement-tarity problems (denoted by NCP). At first, we transform NCP into the equivalent optimization problems.Then taking advantage of excellence of the floating genetic algorithms, we gain the superior results which close to precise solutions quickly, and then taking the results as the initial values of Newton or quasi-Newton iterations, which has strong ability in locally converging to precise solution, we obtain satisfactory approximation solution. The hybrid genetic algorithm absorbs fully the merits of the floating genetic algorithm and the Newton-type'methods.Some numerical results show that this method is effective.In Chapter 4, we discuss a method that transform the problems of solving nonlinear equations into an unconstrained optimization problem.Then taking advantage of excellence of the floating genetice algorithms,we obtain the superior results which close to precise solution quickly,and then taking the results as the initial values of Newton or quasi-Newton interations.This algorithm absorbs fully the merits of the Newton methods and overcome the limitations of initial values. The numerical results show the effectiveness of the algorithm.