基于灰色自适应粒子群LSSVM的铁路货运量预测

为了提高铁路货运量的预测精度及建模速度,将灰色预测模型(GM(1,1))、最小二乘支持向量机(LSSVM)和自适应粒子群优化(APSO)算法相融合,建立了灰色自适应粒子群最小二乘支持向量机(GM-APSO-LSSVM)预测模型.通过灰色预测模型中的灰色序列算子,弱化原始数列随机性,挖掘数列中蕴含的规律,利用最小二乘支持向量机计算简便、求解速度快、非线性映射能力强的特点进行预测,并采用自适应粒子群算法优化选择LSSVM参数.对我国铁路货运量的实例分析表明:用该模型得到的评价指标RMSE、MAE、MPE和Theil不等系数分别为0.062 8、0.052 3、0.016 2和0.010 7,均小于其它模型,预测性能好;用APSO算法搜索LSSVM最优参数的时间为55.656 s,比传统交叉验证法减少了10.462 s;2006～2009年的预测相对误差分别为0.39%、-1.67%、1.44%和4.75%,适用于铁路货运量的短期预测.

Prediction of Railway Freight Volumes Based on Grey Adaptive Particle Swarm Least Squares Support Vector Machine Model

In order to improve the forecasting accuracy and the modeling speed for railway freight volumes,the grey forecasting model GM(1,1) and the adaptive particle swarm optimization(APSO) were both introduced into the least squares support vector machines(LSSVMs).Thus,a new model,the grey APSO least squares support vector machine(GM-APSO-LSSVM) model,was built.The new model weakens the stochastic factor in the original sequence and exploits the regularity of data using the grey sequence operator of the grey model in the first stage.Then,the new data are forecasted with the LSSVM featured by simple calculation,fast solving speed,and powerful non-linear mapping ability.At the same time,the parameters of LSSVM are optimized by the APSO.An empirical analysis was performed to verify the proposed model using the freight volumes data in China.The results show that the proposed model has a superior prediction performance to the existing models,and its performance indices RMSE,MAE,MPE,and Theil are 0.062 8,0.052 3,0.016 2,and 0.010 7,respectively,all less than those of the other models.The searching time for the optimal LSSVM parameters using the APSO is 55.656 s,which is 10.462 s less than the time spent by the conventional cross-validation method.The relative prediction errors of the model in predicting the railway freight volumes from 2006 to 2009 are 0.39%,-1.67%,1.44% and 4.75%,respectively;therefore,the proposed model is more suitable for short-term railway freight volumes forecasting.