基于飞蛾火焰优化算法的改进GM(1,1)模型

A modified GM (1,1) model based on moth flame optimization algorithm

飞蛾火焰优化(MFO)算法是受飞蛾在自然界中的横向定位导航方法启发而提出的一种新的元启发式算法。初值是影响灰色模型预测精度的主要因素之一,针对由辨识参数和初值引起的GM(1,1)模型误差,本文提出一种基于飞蛾火焰优化算法改进的GM(1,1)模型——MFOGM(1,1)。以最小化平均绝对相对误差为目标函数,利用飞蛾火焰优化算法优化GM(1,1)模型的参数,同时在连续区间[x;(1),x;(n)]中搜索最优初值。分别用基本GM(1,1)模型,初值为x;(n)的GM(1,1)模型,MFOGM(1,1)模型对绝缘电阻历史数据进行模拟,三个模型的平均绝对百分比误差MAPE分别是4.30%, 4.60%, 3.74%。实例结果展示,改进的MFOGM(1,1)模型的精度得到了改善,在三个模型中是最好的,表明了所改进的模型的有效性和可行性。

The Moth flame optimization(MFO) algorithm is a novel meta-heuristic algorithm inspired by the navigation method for moths in nature called transverse orientation. Initial value is one of the main factors affecting prediction accuracy of the Grey Model. Aiming at errors of fitting value of GM(1,1) model caused by identification parameters and initial value, a modified GM(1,1) model based on moth flame optimization algorithm abbreviated MFOGM(1,1) is presented. The GM(1,1) model based on moth flame optimization algorithm abbreviated MFOGM(1,1) is proposed. The objective function is to minimize the mean absolute relative error. The parameters of the model are optimized by using the moth flame optimization algorithm, and at the same time the optimal initial value is searched in the continuous interval [x;(1), x;(n)]. The historical data of insulation resistance are simulated by using the basic GM(1,1) model, the GM(1,1) model with the initial value of x;(n), and the MFOGM(1,1) model, respectively. The mean absolute percentage errors(MAPE) of the three models are 4.30%, 4.60% and 3.74%, respectively. The results of example exhibit that the accuracy of modified GM(1,1) model is the best among the three models, showing the effectiveness and feasibility of the proposed model.