The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution as a representative, is often used to address the challenge. Built on a recently proposed day-to-day (DTD) discrete-time dynamical model called cumulative logit (CULO), this study provides a new behavioral underpinning for the maximum-entropy UE (MEUE) route flow. It has been proven that CULO can reach a UE state without presuming travelers are perfectly rational. Here, we further establish that CULO always converges to the MEUE route flow if (i) travelers have zero prior information about routes and thus are forced to give all routes an equal choice probability, or (ii) all travelers gather information from the same source such that the so-called general proportionality condition is satisfied. Thus, CULO may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CULO model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them to CULO. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments.

翻译：交通分配中用户均衡（UE）路径流的非唯一性给诸多交通应用带来了重大挑战。最大熵原理主张始终选择最可能解作为代表性结果，常被用于应对这一挑战。本研究基于近期提出的名为累积逻辑模型（CULO）的逐日离散时间动态模型，为最大熵用户均衡（MEUE）路径流提供了新的行为基础。已有研究证明，CULO无需假设出行者完全理性即可达到UE状态。本文进一步确立：当满足以下任一条件时，CULO始终收敛至MEUE路径流：（i）出行者对路径无先验信息，因而被迫对所有路径赋予相等选择概率；（ii）所有出行者通过同一信息源获取信息，从而满足所谓的广义比例条件。因此，CULO可作为MEUE问题的实用求解算法。为实现这一构想，我们提出通过迭代路径发现方案消除原始CULO模型的路径枚举需求。此外，本文考察了四种经典连续时间动态模型的离散时间版本，并与CULO进行比较分析。结果表明，复制者动态是唯一具有规律性收敛至MEUE解潜力的模型。数值实验验证了理论分析结果。