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TRANSMax Ⅱ: Designing a flexible model for transit route optimization

机译：TransmaxⅡ：设计一个用于运输路线优化的灵活模型

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Covering path problems date from the pioneering work of Current et al. (1984, 1985). Two basic forms were defined in their work: the shortest covering path problem and the maximal covering shortest path problem. These two problems differ in that one requires complete coverage by the defined path and the other involves determining path alternatives which cover as much as possible while keeping the path length as short as possible. The latter of these two problems, the maximal covering shortest path problem, embodies the two major goals in transit planning: that is, finding efficient paths which serve as many people as possible. Often transit routes are restricted to major road segments, and when that occurs, routes do not compete with one another unless they overlap along a street segment or at an intersection. In addition, coverage distances can be quite small, barely extending to other streets. Given this type of situation, Curtin and Biba (2011) developed a model called TRANSMax (Transit Route Arc-Node Service Maximization), which maximizes node and arc service, where service coverage is defined for only those street and node segments that are part of a route. They based their model on a structure first proposed by Vajda (1961) in formulating and solving the traveling salesman problem. Because of this structure, we demonstrate that it is possible that a route generated by their original TRANSMax model may not be Pareto optimal with respect to both distance and access. In this paper, we develop a flexible TRANSMax model formulation that finds Pareto Optimal solutions when the original form does not. We also present computational experience in solving this new model on the same street network of Curtin and Biba involving Richardson, Texas. This application allows us to make comparisons between this work and the original work of Curtin and Biba. Overall, we show that this new model can identify new, improved routes over the existing TRANSMax model.
机译：从Current等人的开创性工作中覆盖路径问题日期。 （1984年，1985年）。在其工作中定义了两个基本形式：最短的覆盖路径问题和最大覆盖最短路径问题。这两个问题的不同之处在于，一个人需要完全覆盖所定义的路径，另一个问题包括确定尽可能短地保持路径长度的路径替代方案。这两个问题的后者，最大涵盖了最短的路径问题，体现了过境规划中的两个主要目标：即找到有效的路径，尽可能多的人。经常过境路线仅限于主要道路段，当发生这种情况时，除非沿着街道段或交叉点重叠，否则路线不会竞争。此外，覆盖距离可以很小，几乎没有延伸到其他街道。考虑到这种情况，Curtin和Biba（2011）开发了一种名为Transmax（Transit Route Arc-Node Service Service Service Maximization）的模型，最大化节点和弧服务，其中仅为那些部分的街道和节点段定义了服务覆盖范围一条路线。他们基于他们在vajda（1961）提出的结构上制定和解决旅行推销员问题的结构模型。由于这种结构，我们证明了由其原始变送模型产生的路线可能在距离和访问中可能不是Pareto。在本文中，我们开发了一种灵活的传输模型配方，当原始形式没有时，找到帕累托最佳解决方案。我们还提出了在德克萨斯州德克萨斯州的德克萨斯州的Curtin和Biba的同一个街道网络上解决了这个新模型的计算经验。此申请允许我们在这项工作与杂皮饼和BIBA的原始工作之间进行比较。总的来说，我们表明，这个新模型可以通过现有的传输模型来识别新的，改进的路由。

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