The mixed capacitated arc routing problem with non-overlapping routes

Constantino, Miguel; Gouveia, Luís; Mourão, Maria Cândida; Nunes, Ana Catarina

doi:10.1016/j.ejor.2015.01.042

Cited by 31 publications

(23 citation statements)

References 34 publications

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“…The value of VA can be 1; in practice, its value is usually less than 0.5. The first set of multiroute metrics was proposed by Constantino et al in [8]. The authors give three metrics.…”

Section: Compactness and Separation Of Routesmentioning

confidence: 99%

“…Last-minute adjustments to a route can be made without significantly disturbing the routes of other drivers. Second, the visual preferences can serve as a source for new metrics that can help quantify the visual appeal of a route more precisely [8,20,22,[25][26][27]. These new metrics may be used as alternatives to, or penalties in, the overall objective function.…”

Section: Introductionmentioning

confidence: 99%

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Partitioning a street network into compact, balanced, and visually appealing routes

et al. 2017

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In practice, it is often desirable for the routes of vehicles to be compact and separate. A set of routes is compact if the streets serviced by each route are geographically clustered, and separated if the routes overlap minimally. We consider the Min-Max K Windy Rural Postman Problem (MMKWRPP), in which the objective is to route a homogeneous fleet of K vehicles such that the cost of the longest route is minimized. We develop a heuristic that is algorithmically simple, produces solutions that are comparable in quality to those produced by an existing approach, and performs well with respect to metrics that quantify compactness and separation. Our heuristic uses a partitioning scheme in which the weight of a vertex includes contributions from both incident streets requiring service and the distance needed to travel to a vertex. We present computational results for a set of instances that we generate from real-world street networks and for a set of artificial instances. Our code is part of the Open-source Arc Routing Library (OAR Lib) at https://github.com/Olibear/ArcRoutingLibrary.

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“…The value of VA can be 1; in practice, its value is usually less than 0.5. The first set of multiroute metrics was proposed by Constantino et al in [8]. The authors give three metrics.…”

Section: Compactness and Separation Of Routesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Partitioning a street network into compact, balanced, and visually appealing routes

et al. 2017

View full text Add to dashboard Cite

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“…Of all the metrics shown in Table , in this paper we consider two of them. The first one is the Routes Overlapping Index (ROI), proposed by Constantino et al , which counts the number of nodes that are visited by more than one route:

ROI = \frac{N O - | V |}{{(\sqrt{K} + \sqrt{| V |} - 1)}^{2} - | V |},

where node overlap (NO) is

NO = \sum_{i \in V} \sum_{k = 1}^{K} n_{i}^{k}

, where

n_{i}^{k}

takes value 1 if vertex i belongs to route k . The second measure we will study, also proposed in , is the average task distance (ATD):

ATD = \frac{1}{K} \sum_{k = 1}^{K} \frac{\sum_{e_{1}, e_{2} \in E_{R} served by k} d_{e_{1} e_{2}}}{| t a s k p a i r s |},

where

d_{e_{1} e_{2}}

is the minimum length of the shortest paths between the end nodes of required edges e 1 and e 2 , and

| t a s k p a i r s | = \frac{| E_{R} | * (| E_{R} | - K)}{2 K}

is an estimate of the average number of pairs of required edges in a single route.…”

Section: The Problemmentioning

confidence: 99%

“…Of all the metrics shown in Table 1, in this paper we consider two of them. The first one is the Routes Overlapping Index (ROI), proposed by Constantino et al [10], which counts the number of nodes that are visited by more than one [13,24] CLP The crossing length percentage. Crossing points within the context of a single route are identified.…”

Section: The Problemmentioning

confidence: 99%

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Aesthetic considerations for the min‐max K‐Windy Rural Postman Problem

et al. 2017

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The aesthetic quality of routes is a feature of route planning that is of practical importance, but receives relatively little attention in the literature. Several practitioners have pointed out that the visual appeal of a proposed set of routes can have a strong influence on the willingness of a client to accept or reject a specific routing plan. While some work has analyzed algorithmic performance relative to traditional min‐sum or min‐max objective functions and aesthetic objective functions, we are not aware of any work that has considered a multi‐objective approach. This work considers a multi‐objective variant of the Min‐Max K‐Vehicles Windy Rural Postman Problem, discusses several formulations of the problem, and presents computational experiments with a heuristic algorithm. After exploring several formulations, we choose to study the problem with a bi‐objective function that includes contributions from the route overlap index and average task distance aesthetic measures. The heuristic extends the cluster‐first procedure presented in Lum et al. (Networks 69 (2017), 290–303) by incorporating the new objective function into the improvement phase and adding a perturbation routine. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 216–232 2017

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An updated annotated bibliography on arc routing problems

Mourão

Pinto

2017

Networks

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The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post‐disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 144–194 2017

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The mixed capacitated arc routing problem with non-overlapping routes

Cited by 31 publications

References 34 publications

Partitioning a street network into compact, balanced, and visually appealing routes

Partitioning a street network into compact, balanced, and visually appealing routes

Aesthetic considerations for the min‐max K‐Windy Rural Postman Problem

An updated annotated bibliography on arc routing problems

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