中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (1): 9-13.

• 研究论文 • 上一篇    下一篇

基于改进遗传算法的非线性方程组求解

燕乐纬1,陈树辉2
  

  1. (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 )
  • 收稿日期:2010-03-02 修回日期:1900-01-01 出版日期:2011-01-25 发布日期:2011-01-25
  • 通讯作者: 陈树辉

Solving Nonlinear Equations Based on Improved Genetic Algorithm

YAN Lewei1, CHEN Shuhui2
  

  1. (1.Department of Engineering Mechanics,Guangzhou University,Guangzhou 510006,China;2.Department of Applied Mechanics and Engineering, School of Engineering, Sun Yatsen University, Guangzhou 510275, China)
  • Received:2010-03-02 Revised:1900-01-01 Online:2011-01-25 Published:2011-01-25

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〖JP2〗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。

关键词: 非线性方程组, 遗传算法, 异种机制, 自适应随机变异

Abstract: 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.

Key words: Nonlinear equations, genetic algorithm, heterogeneous strategy, adaptive random mutation

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