Entropy maximization is a standard approach to consistently selecting a unique class-specific solution for multi-class traffic assignment. Here, we show the conventional maximum entropy formulation fails to strictly observe the multi-class bi-criteria user equilibrium condition, because a class-specific solution matching the total equilibrium link flow may violate the equilibrium condition. We propose to fix the problem by requiring the class-specific solution, in addition to matching the total equilibrium link flow, also match the objective function value at the equilibrium. This leads to a new formulation that is solved using an exact algorithm based on dualizing the hard, equilibrium-related constraints. Our numerical experiments highlight the superior stability of the maximum entropy solution, in that it is affected by a perturbation in inputs much less than an untreated benchmark multi-class assignment solution. In addition to instability, the benchmark solution also exhibits varying degrees of arbitrariness, potentially rendering it unsuitable for assessing distributional effects across different groups, a capability crucial in applications concerning vertical equity and environmental justice. The proposed formulation and algorithm offer a practical remedy for these shortcomings.

中文翻译：

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多类流量分配中的熵最大化


熵最大化是一种标准方法，用于为多类流量分配一致地选择唯一的类特定解决方案。在这里，我们展示了常规的最大熵公式未能严格遵守多类双标准用户均衡条件，因为与总平衡链接流匹配的类特定解可能会违反均衡条件。我们建议通过要求特定于类的解来解决这个问题，除了匹配总均衡链接流外，还要匹配均衡时的目标函数值。这导致了一个新的公式，该公式使用基于对硬均衡相关约束进行对偶化的精确算法进行求解。我们的数值实验强调了最大熵解的卓越稳定性，因为它受输入扰动的影响远小于未经处理的基准多类赋值解。除了不稳定性之外，基准解决方案还表现出不同程度的任意性，可能使其不适合评估不同群体之间的分布效应，而这一能力在涉及垂直公平和环境正义的应用中至关重要。所提出的公式和算法为这些缺点提供了实用的补救措施。