解非线性优化问题GM（1,1）模型的多子群遗传算法

针对非线性优化问题约束条件中待定参数的时间序列数据,首先使用GM(1,1)方法进行建模预测得到参数的预测值,进而将参数预测值代入原问题中提出一个确定型的非线性优化问题。对该确定型问题设计了一个多子种群并行进化的遗传算法进行求解,在分析所提算法的收敛性的基础上,给出了初步的数值算例。数值算例实验结果表明:该算法能够较为精确地获得预测型非线性优化问题的(近似)全局最优解。

A Multi-subgroup Genetic Algorithm for Solving GM (1, 1) Model of Nonlinear Optimization Problem

According to the historical data of the time series of the constraints parameters in the nonlinear optimization prob-lem, the values of the constraints parameters are modeled and predicted using GM(1,1) method. Substituting the predicted values of the parameters into the grey nonlinear optimization problem, we obtain a determinate nonlinear optimization problem. Then, we design a multi-subgroup genetic algorithm genetic algorithm to solve the resulting problem. Moreover, we analyze the convergence of our method and develop preliminary the numerical experiment which shows that the ( approximated) global optimal solution of the predicted nonlinear optimization problem can be found using the proposed method.