Abstract: In this paper, the grey constrained nonlinear programming problems were investigated. With the help of mean, this paper firstly transformed the original grey optimization problem into a determinate constrained nonlinear programming problem. Then, based on the estimation of distribution algorithm, a stochastic search method was developed to solve the determinate constrained nonlinear programming problem. The key technique of the proposed method was explained in detail and the steps of the proposed method were described concretely. Finally, the elementary numerical examples show the proposed stochastic search method is feasible and effective.

Key words: grey nonlinear programming, mean-whitenization model, Estimation of Distribution Algorithm (EDA), (approximate) optimal solution, Monte Carlo simulation

摘要： 对带约束条件的灰色非线性规划问题进行了探讨，首先将原灰色约束非线性规划问题进行均值白化处理，转化成一个确定型的带约束条件的非线性规划问题，对该确定型的非线性约束规划问题提出一个基于分布估计算法的随机搜索方法，对所提出的求解方法的关键技术作了详细的说明并给出了具体的算法步骤。 初步的数值算例表明所提出的方法是可行有效的

关键词: 灰色非线性规划, 均值白化模型, 分布估计算法, (近似)最优解, 蒙特卡罗模拟