求解一类随机规划的Monte Carlo模拟方法

通过对目标函数和约束函数同时抽样,提出了基于Monte Carlo模拟的遗传算法,通过逐步增加样本容量和遗传进化代数以得到满足精度要求的近似最优解,并且通过统计方法讨论样本容量的迭代终止条件,以减少Monte Carlo随机模拟的盲目性;同时给出了最优解的表达形式以及算法的迭代终止条件;数值实验证明了方法的有效性。

Monte Carlo Simulation for Solving a Class of Stochastic Programming

The Genetic Algorithm based on Monte Carlo simulation by sampling both of objective and constraint function is presented for solving a class of stochastic programming.We can get the approximate optimal solution satisfying the requriement of accuracy through gradually increasing sample size and genetix evolutionary generations,discuss stopping crierion for iteration of the sample size to reduce the blindness of Monte Carlo stochastic simulationby statstical method,and give stopping crierion for iteration of the algorithm and the expressions of optimal solution.Numerical example is employed to demonstrate the effectiveness of the presented algorithm.