解非线性方程组的拟牛顿混合遗传算法  

Quasi-Newton hybrid genetic algorithm for solving nonlinear system of equations

作　　者：何俊红[1] 赵天绪[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《西北大学学报（自然科学版）》2015年第3期352-356,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11371291);陕西省教育厅科研计划基金资助项目(11JK0506);宝鸡文理学院校级重点科研计划基金资助项目(ZK12044)

摘　　要：利用熵函数将非线性方程组转化为一个极小值优化问题。结合拟牛顿法和遗传算法的优缺点,提出了一种求解非线性方程组的拟牛顿混合遗传优化算法。该方法不仅有效发挥了遗传算法在进化初期的群搜索能力,而且利用了拟牛顿法的局部精搜索性能,克服了遗传算法在后期易陷入局部收敛的缺陷,提高了算法整体寻优效率。计算机仿真表明,该算法对非线性方程组的求解具有较好的稳定性和较高的收敛精度。First, the nonlinear system of equations was transformed into a minimum optimal problem by using an entropy function. And combining the Quasi-Newton method with the genetic algorithm, a Quasi-Newton hy- brid genetic algorithm for solving the nonlinear system of equations is proposed. The proposed algorithm can not only utilize the swarm search ability of genetic algorithm in the initial evolution stage, but also take advan- tage of the local search property of the Quasi-Newton, and these have made the proposed algorithm overcome the local convergence of genetic algorithm in the later evolution stage and improved the overall search ability of the proposed algorithm. The computer simulations demonstrate the proposed algorithm has good stability and convergence precision in solving the nonlinear system of equations.

关 键 词：非线性方程组 拟牛顿法 遗传算法 熵函数 

分 类 号：O224[理学—运筹学与控制论] TP301.6[理学—数学]