Arc-routing for winter road maintenance

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Jiří Fink , Martin Loebl , Petra Pelikánová
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引用次数: 1

Abstract

The winter road maintenance arc-routing is recognized as a notoriously hard problem not only from the algorithmic point of view. This paper lays down foundations of theoretical understanding of our new winter road maintenance optimization for the Plzeň region of the Czech Republic which has been implemented by the regional authorities since the winter of 2019–20. Our approach is not, contrary to most of existing work, based on the integer and linear programming machinery. We concentrate on studying arc-routing on trees. This is practical since routes of single vehicles can be well represented by trees, and allows algorithms and complementary hardness results. We then extend the approach to the bounded tree width graphs. This leads to considering planar graphs which well abstract the realistic road networks. We formalize important aspects of the winter road maintenance problem which were not formalized before, e.g., public complaints. The number of complaints from public against the winter road maintenance is a quantitative measure of the quality of the service which is focused on, e.g., in media or in election campaigns. A fear of ’complaints’ is a fact every optimizer must deal with. Hence, a formal model of public complaints and its inclusion in the optimization is vital. Our formalization of the winter road maintenance is robust in the sense that it relates to well-known extensively studied concepts of discrete mathematics like graph cutting and splitting of necklaces.

冬季道路养护的弧形路线
冬季道路养护的弧形路线不仅从算法的角度来看是一个众所周知的难题。本文为我们自2019-20年冬季以来在捷克共和国普列泽普地区实施的新的冬季道路养护优化奠定了理论基础。与大多数现有工作相反,我们的方法不是基于整数和线性规划机制。我们专注于研究树木的弧形路径。这是实用的,因为单个车辆的路线可以很好地用树表示,并且允许算法和互补的硬度结果。然后,我们将该方法扩展到有界树宽度图。这导致考虑平面图,它很好地抽象了现实的道路网络。我们将冬季道路养护问题的重要方面正式化,这些问题以前没有正式化,例如公众投诉。公众对冬季道路维修的投诉数量是对服务质量的一种定量衡量,例如在媒体或竞选活动中。对“抱怨”的恐惧是每个优化人员必须面对的一个事实。因此,建立一个正式的公众投诉模型并将其纳入优化是至关重要的。我们对冬季道路维护的形式化在某种意义上是稳健的,因为它涉及到众所周知的广泛研究的离散数学概念,如图形切割和项链分割。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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