Abstract The purpose of this paper is to develop a data-driven matheuristic for the Commodity-Split Multi-Compartment Capacitated Arc Routing Problem (CSMC-CARP). This problem arises in curbside waste collection, where there are different recyclable waste types called fractions. The CSMC-CARP is defined on an undirected graph with a limited heterogeneous fleet of multi-compartment vehicle types based at a depot, where each compartment’s capacity can vary depending on the waste fraction assigned to it and on the compression factor of that fraction in that vehicle type. The aim is to determine a set of least-cost routes starting and ending at the depot, such that the demand of each edge for each waste fraction is collected exactly once by one vehicle, without violating the capacity of any compartment. The CSMC-CARP consists of three decision levels: selecting the number of vehicles of each type, assigning waste fractions to the compartments of each selected vehicle, and routing the vehicles. Our three-phase algorithm decomposes the problem into incomplete solution representations and heuristically solves one or more decision levels at a time. The first phase selects a subset of attractive compartment assignments from all assignments of all vehicle types. The second phase solves the CSMC-CARP with an unlimited fleet of the selected assignments. This is done by our C-split tour splitting algorithm, which can simultaneously split a giant tour of required edges into feasible routes while making decisions on the fractions that are collected by each route. The third phase selects the set of best routes servicing all fractions of all required edges without exceeding the number of vehicles available of each type. The algorithm is applied to real-life instances arising from recyclable waste collection operations in Denmark, with graph sizes up to 6,149 nodes and 3,797 required edges, the waste sorted in three to six fractions, and four to six vehicle types with one to four compartments. Computational results show that the generated solutions favor combining different fractions together in vehicles with higher numbers of compartments, and that the algorithm adapts well to the characteristics of the data, in terms of the graph, vehicle types, degree of sorting, and to skewness in demand among waste fractions.

中文翻译：

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商品分割多室电容电弧路由问题

摘要 本文的目的是为商品拆分多隔室电容电弧路由问题 (CSMC-CARP) 开发一种数据驱动的数学算法。这个问题出现在路边垃圾收集中，那里有不同的可回收垃圾类型，称为碎片。CSMC-CARP 是在一个无向图上定义的，其中包含基于一个仓库的有限的多舱车辆类型的异构车队，其中每个舱的容量可以根据分配给它的废物比例以及该比例的压缩系数而变化车辆类型。目的是确定一组在仓库开始和结束的成本最低的路线，以便每个边缘对每个废物部分的需求被一辆车辆恰好收集一次，而不会影响任何车厢的容量。CSMC-CARP 包括三个决策层：选择每种类型的车辆数量，将废物部分分配给每个选定车辆的车厢，并对车辆进行路由。我们的三阶段算法将问题分解为不完整的解决方案表示，并一次启发式地解决一个或多个决策级别。第一阶段从所有车辆类型的所有分配中选择有吸引力的车厢分配子集。第二阶段使用无限数量的选定任务解决 CSMC-CARP。这是通过我们的 C-split 旅行分割算法完成的，该算法可以同时将所需边的巨大旅行分割成可行的路线，同时对每条路线收集的分数做出决定。第三阶段选择一组最佳路线，在不超过每种类型可用车辆数量的情况下，为所有所需边的所有部分提供服务。该算法应用于丹麦可回收垃圾收集操作产生的现实生活实例，图形大小高达 6,149 个节点和 3,797 条所需边，垃圾分为三到六个部分，以及四到六种车辆类型，一到四个隔间. 计算结果表明，生成的解决方案有利于在车厢数量较多的车辆中将不同的分数组合在一起，并且该算法在图形、车辆类型、排序程度和偏度方面很好地适应了数据的特征。废物馏分之间的需求。该算法应用于丹麦可回收垃圾收集操作产生的现实生活实例，图形大小高达 6,149 个节点和 3,797 个所需边，垃圾分为三到六个部分，以及四到六种车辆类型，一到四个隔间. 计算结果表明，生成的解决方案有利于在车厢数量较多的车辆中将不同的分数组合在一起，并且该算法在图形、车辆类型、排序程度和偏度方面很好地适应了数据的特征。废物馏分之间的需求。该算法应用于丹麦可回收垃圾收集操作产生的现实生活实例，图形大小高达 6,149 个节点和 3,797 个所需边，垃圾分为三到六个部分，以及四到六种车辆类型，一到四个隔间. 计算结果表明，生成的解决方案有利于在车厢数量较多的车辆中将不同的分数组合在一起，并且该算法在图形、车辆类型、排序程度和偏度方面很好地适应了数据的特征。废物馏分之间的需求。