出行分布矩阵的极大熵估计法比较研究

Compare of the Estimation Method of Matrix Based on Maximum Entropy Model

摘要: 极大熵方法是用于估计起讫点间出行分布矩阵的一种高效简便的方法。在介绍基础极大熵公式的形式和原理后，应用Stirling近似公式和对数近似公式简化基本极大熵公式，得出六个改进的极大熵公式，在总出行需求固定或可变、先验OD矩阵可行或不可行、节点流连续条件满足或不满足的三种不同的情况下在两个网络上测试七个极大熵公式，对其特征进行比较。结果表明七个目标函数在寻优时表现出一致性，但是在一些特定的情况下，有几个公式产生较大误差，使得其在实际使用中受到限制。

Abstract: Maximum Entropy model is an efficient and simple model to estimate origin destination matrix. After introducing the formation and principle of basic maximum entropy model, this article uses Stirling approximate formula and log sum approximate formula to simplify basic model and obtains six improved models. Then it tests seven models in two networks under three different conditions, namely the total demand is fixed or unfixed, the prior matrix is feasible or unfeasible and the node continuity condition is satisfied or unsatisfied and compare the properties of these models. The results show that they show uniform in searching for optimum solutions. However, several formations produce large errors under some circumstances, which restrict their applications in reality.