We propose a stochastic programming approach for a static origin–destination (OD) reconstruction problem. We focus on the reconstruction of route flows such that the likelihood function of route flows is maximized. The route volumes are assumed to follow exponential families that are known or estimated in advance. The consideration of the joint distribution function of route flows eliminates the route selection from the model, as the route choice patterns are embedded in the distribution of the route flows. We assume that additional information regarding the traffic counts (i.e., node counts, link counts, and turn counts) is available.

Finally, solution methodologies for different stochastic programmings are proposed: barrier method and Primal-dual interior point method for Quadratic Programming and Convex Programming respectively. We compared the proposed stochastic models with the entropy approach. Experimental results indicate that the inclusion of traffic-count information in the stochastic model significantly improves the accuracy of OD reconstruction if we can predict the correct distribution of route flows. Meanwhile the entropy approach requires the inclusion of the additional information on the true volumes of route flows to achieve a similar level of performance. We apply the proposed algorithm to the bus transit system of Seoul, Korea using bus-card data. Compared with the real OD volumes, the reconstruction is fairly accurate.

我们为静态原点-目的地（OD）重建问题提出了一种随机编程方法。我们专注于路径流量的重构，以使路径流量的似然函数最大化。假定路线量遵循事先已知或估计的指数族。路径流的联合分布函数的考虑消除了模型中的路径选择，因为路径选择模式嵌入了路径流的分布中。我们假定有关流量计数（即节点计数，链接计数和转弯计数）的其他信息可用。

最后，提出了针对不同随机规划的求解方法：分别用于二次规划和凸规划的势垒法和原始对偶内点法。我们将所提出的随机模型与熵方法进行了比较。实验结果表明，如果我们能够预测路线流的正确分布，则将交通量信息包含在随机模型中将显着提高OD重建的准确性。同时，熵方法要求在路由流的真实数量上包括附加信息，以实现类似的性能水平。我们使用公交卡数据将所提出的算法应用于韩国首尔的公交系统。与实际OD量相比，重建是相当准确的。