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为了提高OD矩阵的估计精度,提出了一种基于贝叶斯方法的分层优化OD矩阵估计模型,该模型将OD矩阵估计分为三个最优化问题:(1)Wardrop最小方差优化模型,用以得到路径选择概率;(2)最小二乘优化问题,用以获得OD样本数据;(3)最大似然优化问题,用以进行参数估计。利用Nguyen-Dupuis网络对本方法进行了实例验证和对比分析,为了对比先验信息与观测样本信息对OD估计精度影响程度的不同,设计了3种不同权重进行比较,结果表明观测样本信息对OD估计精度的影响更大。最后,将本算法与双层规划模型进行对比分析,结果表明本文提出的分层优化模型的均方根误差比双层规划模型降低了43.1%,模型精度得到显著提高。
In order to improve the estimation accuracy of OD matrices, a hierarchical optimization OD matrix estimation model based on Bayesian method is proposed, which divides OD matrix estimation into three optimization problems: (1) Wardrop minimum variance optimization model To get the path selection probability; (2) least square optimization problem, to obtain the OD sample data; (3) maximum likelihood optimization problem for parameter estimation. This method is validated and contrasted by using Nguyen-Dupuis network. In order to compare the difference between the priori information and observed sample information on the accuracy of OD estimation, three different weights are compared and the results show that ODN The impact of accuracy is even greater. Finally, the proposed algorithm is compared with the bilevel programming model. The results show that the root mean square error of the proposed hierarchical optimization model is reduced by 43.1% compared with the bilevel programming model, and the accuracy of the model is significantly improved.