Traffic assignment is an important stage in the task of modeling a transportation system. Several methods for solving the traffic assignment problem (TAP) were proposed, mostly based on iterative procedures. However, little was done in the direction of analyzing the difficulty of such procedures. For instance, why is it that some networks require orders of magnitude more iterations than others? What matters in this task? Clearly, the topology of the network can only give hints up to a certain level; the assignment task is fundamentally tied to how the demand is distributed (among other characteristics of the problem). This means that methods to estimate the complexity of a network (e.g. those based on centrality measures) can only help up to a certain level. The motivation for this work is to, a priori, estimate how hard will the effort underlying solving the TAP be (i.e. without doing the actual assignment). It arose from the fact that after performing assignment in several different networks, we noted that finding the solution for the problem was much easier for some networks than for others. Specifically, the more complex the network, the more difficulty it is to setup the parameters underlying the procedure for solving the TAP. In this work, we propose a new measure of how coupled routes in a network are, based on an estimation of the demand distribution. Our approach involves three main steps: (i) sampling the universe of all possible assignments, (ii) creating a model that gives the incentive a road user has for changing routes, as well as the asymptotic distribution of preference for routes, and (iii) computing the entropy of this distribution. This approach is experimentally validated using several networks of different natures. We then solve the TAP by letting road users use reinforcement learning to learn the user equilibrium. With this, we are able to make important relationships between the entropy values and how hard are the learning tasks. Results suggest that it is possible to use both the entropy values as well as the asymptotic distribution of preferences of the road users to gain important information that guides the traffic expert. For instance, the higher the entropy, the higher the indication that more than one route is perceived as preferable and, hence, the more difficult the learning task.

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代理商学习用户平衡有多难？用熵来表征交通网络

交通分配是交通系统建模任务中的一个重要阶段。提出了几种解决交通分配问题（TAP）的方法，主要是基于迭代过程。然而，在分析此类程序的难度方面做得很少。例如，为什么某些网络需要比其他网络多几个数量级的迭代？这项任务的重点是什么？显然，网络的拓扑只能给出一定程度的提示；分配任务从根本上与需求的分配方式（以及问题的其他特征）相关联。这意味着估计网络复杂性的方法（例如基于中心性度量的方法）只能在一定程度上有所帮助。这项工作的动机是先验地，估计解决 TAP 的工作难度（即不进行实际分配）。这是因为在几个不同的网络中执行分配后，我们注意到对于某些网络来说找到问题的解决方案比其他网络容易得多。具体来说，网络越复杂，设置用于求解 TAP 的过程的参数就越困难。在这项工作中，我们基于对需求分布的估计，提出了一种新的衡量网络中路由耦合程度的方法。我们的方法包括三个主要步骤：（i）对所有可能的分配进行抽样，（ii）创建一个模型，该模型给出道路使用者改变路线的动机，以及路线偏好的渐近分布，(iii) 计算该分布的熵。这种方法使用几个不同性质的网络进行了实验验证。然后，我们通过让道路使用者使用强化学习来学习用户平衡来解决 TAP。有了这个，我们能够在熵值和学习任务的难度之间建立重要的关系。结果表明，可以同时使用熵值以及道路使用者偏好的渐近分布来获得指导交通专家的重要信息。例如，熵越高，表明不止一条路线被认为是可取的指示就越高，因此，学习任务就越困难。然后，我们通过让道路使用者使用强化学习来学习用户平衡来解决 TAP。有了这个，我们能够在熵值和学习任务的难度之间建立重要的关系。结果表明，可以同时使用熵值以及道路使用者偏好的渐近分布来获得指导交通专家的重要信息。例如，熵越高，表明不止一条路线被认为是可取的指示就越高，因此，学习任务就越困难。然后，我们通过让道路使用者使用强化学习来学习用户平衡来解决 TAP。有了这个，我们能够在熵值和学习任务的难度之间建立重要的关系。结果表明，可以同时使用熵值以及道路使用者偏好的渐近分布来获得指导交通专家的重要信息。例如，熵越高，表明不止一条路线被认为是可取的指示就越高，因此，学习任务就越困难。结果表明，可以同时使用熵值以及道路使用者偏好的渐近分布来获得指导交通专家的重要信息。例如，熵越高，表明不止一条路线被认为是可取的指示就越高，因此，学习任务就越困难。结果表明，可以同时使用熵值以及道路使用者偏好的渐近分布来获得指导交通专家的重要信息。例如，熵越高，表明不止一条路线被认为是可取的指示就越高，因此，学习任务就越困难。