基于改进遗传算法的非线性方程组求解  

Solving Nonlinear Equations Based on Improved Genetic Algorithm

作　　者：燕乐纬[1] 陈树辉[2] 

机构地区：[1]广州大学工程力学系,广东广州510006 [2]中山大学应用力学与工程系,广东广州510275

出　　处：《中山大学学报（自然科学版）》2011年第1期9-13,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10972240)

摘　　要：采用种群隔离机制、最优保持策略、算术杂交、自适应随机变异和异种机制等方法对遗传算法进行了改进。在保持遗传算法仅需目标函数值信息即可求解这一优点的基础上,这一改进方法增强了遗传算法的局部搜索能力。将该方法应用于非线性方程组的求解。数值算例表明,该方法能够求解以非线性方程为等式约束的最优化问题。此外,异种机制的引入加快了遗传算法的收敛效率,有效提高了遗传算法收敛于全局最优解的概率。Some methods such as population isolation mechanism,optimum reserved strategy,arithmetic crossover,adaptive random mutation and heterogeneous strategy are used to improve genetic algorithm.Besides the advantage that the optimal solution can be found only by the value of objective function,the local searching capability is enhanced in this improve genetic algorithm.This algorithm is applied to solve nonlinear equations.Numerical examples demonstrated that this algorithm can solve the optimization problem which has nonlinear equality constraint.Furthermore,the heterogeneous strategy speeds up the process of convergence and raises the convergence probability of global optimal solution.

关 键 词：非线性方程组 遗传算法 异种机制 自适应随机变异 

分 类 号：TU375[建筑科学—结构工程] O241.7[理学—计算数学]