基于蚁群算法的GM(1,1)幂模型参数优化

Parameter optimization of GM(1,1)power model based on ant colony algorithm

为了提高GM(1,1)幂模型的精度,将平均相对误差函数和偏差平方和误差函数分别看成是幂指数、发展系数、灰作用量以及初值的函数,通过蚁群算法进行参数辨识.根据两类误差函数最小化原则得到两组参数估计值,再利用这两组参数估计值的凸组合优化模型的参数,通过最大相对误差最小化确定凸组合权系数.实例表明,基于蚁群算法和参数估计凸组合优化改进的GM(1,1)幂模型,其建模精度高于传统GM(1,1)幂模型,同时也说明该优化方法是有效的和可行的.

In order to improve the accuracy of GM（1,1）power model,the average relative error function and sum of square of deviations are regarded as the functions of power exponent,development coefficient,grey action quantity and initial value.Based on the minimization of the average relative error function and the sum of square of deviations,the estimate parameters of two models are solved using ant colony algorithm.The convex combination of the estimate parameter values of two models is as the optimized parameters of GM（1,1）power model,and the combination weight factors are determined according to the minimization of maximum relative error.Finally,one example shows that the precision of the modified GM（1,1）power model with parameter identification based on ant colony algorithm and convex combination is higher than that of traditional GM（1,1）power model.So this method is feasible and effective.