In this paper, we study the elastic-demand bi-criteria traffic assignment problem under the continuously distributed value of time, referred to as the ED-CBiTA problem for simplicity. Specifically, the origin and destination (O–D) demand of ED-CBiTA is endogenously guided by the expected generalized travel time aggregated from all efficient paths, and the consideration of user heterogeneity regarding the tradeoff between time and toll is accomplished by incorporating a continuously distributed value of time. We present a variable demand formulation and an equivalent excess demand reformulation for the ED-CBiTA problem. Based on two types of Gauss–Seidel decomposition schemes, we propose a novel two-stage gradient projection (TSGP) algorithm, which implicitly delivers visual interpretations to depict the interplay of supply and demand interactions. The first stage, called demand equilibration, aims to adjust O–D demand and all efficient path flows “vertically upward or downward” based on the level of network congestion. The second stage, namely boundary equilibration, is to perform the boundary movements and adjust adjacent efficient flows “horizontally forward or backward”, to achieve exact positions along the Pareto frontier. Numerical results on a small network show TSGP’s features and confirm that TSGP significantly outperforms two link-based benchmark algorithms. For instances of practical network size, TSGP consistently promises to obtain high-quality solutions with a rather smaller CPU time.

中文翻译：

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时间连续分布值下的弹性需求双标准流量分配：具有图形解释的两阶段梯度投影算法

在本文中，我们研究时间连续分布值下的弹性需求双标准流量分配问题，为简单起见，称为 ED-CBiTA 问题。具体来说，ED-CBiTA 的出发地和目的地 (O-D) 需求是由所有有效路径聚合的预期广义出行时间内生地引导的，并且通过不断合并一个连续的模型来实现对时间和通行费之间权衡的用户异质性的考虑。时间的分配价值。我们针对 ED-CBiTA 问题提出了可变需求公式和等效超额需求重新公式。基于两种类型的高斯-塞德尔分解方案，我们提出了一种新颖的两阶段梯度投影（TSGP）算法，该算法隐式地提供视觉解释来描述供给和需求相互作用的相互作用。第一阶段称为需求均衡，旨在根据网络拥塞程度“垂直向上或向下”调整 O-D 需求和所有有效路径流量。第二阶段，即边界平衡，是执行边界运动并“水平向前或向后”调整相邻的有效流，以获得沿帕累托边界的精确位置。小型网络上的数值结果显示了 TSGP 的特性，并证实 TSGP 显着优于两种基于链路的基准算法。对于实际网络规模的实例，TSGP始终承诺以相当小的CPU时间获得高质量的解决方案。