基于遗传算法的最大似然参数优化估计

用最大似然法进行参数优化估计时，为了避免常规优化算法由于受迭代初值的影响不易收敛到全局最优解的缺点，文中采用遗传算法，不再需要估计优化变量的初始值即可获得全局近似最优解。建立以似然函数为目标，求其极大值点即可确定参数最优解的优化模型。为了更好地确保遗传算法获得全局最优解，在传统遗传算法的基础上采用尺度变换适应度函数、并行操作、保留最优个体等方法，进一步保证方程解的精度。最后以威布尔分布为例进行参数估计，结果表明，改进的遗传算法可以在求解效率和收敛性能上达到较好的平衡，能更好地将优化方法与最大似然估计法相结合。

OPTIMIZATION METHOD OF MAXIMUM LIKELIHOOD ESTIMATION PARAMETER ESTIMATION BASED ON GENETIC ALGORITHMS

In order to avoid computing complex derivate for maximum likelihood estimation (MLE) parameter estimation, an optimization method of MLE functions as the optimization objection was established. Genetic algorithms (GA) was utilized to obtain optimization solution, compared with conventional optimization algorithms, this method can solve MLE parameter estimation problem without estimating initialization of optimization variable. The main contribution of this paper is to propose some practical methods and improvements of using scale transform fitness, parallel operation and preserving excellence individual for dealing with the shortcoming of traditional GA. A special parameter estimation case of Weibull distribution was presented, through computer simulation, the result shows that the optimization method of MLE parameter estimation is feasible, and demonstrates that the improvement GA has high efficiency and convergence to find global optimal solution. Accordingly, it is better than traditional optimization method for parameter estimation.