Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

New Heuristic Algorithms for the Windy Rural Postman Problem

[EN] In this paper we deal with the windy rural postman problem. This problem generalizes several important arc routing problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a scatter search algorithm for the windy rural postman problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented. (c) 2004 Elsevier Ltd. All rights reserved.Benavent, E.; Corberán, A.; Piñana, E.; Plana. I.; Sanchís Llopis, JM. (2005). New Heuristic Algorithms for the Windy Rural Postman Problem. Computers & Operations Research. 32(12):3111-3128. doi:10.1016/j.cor.2004.04.007S31113128321

A branch-and-cut algorithm for the multidepot rural postman problem

This paper considers the Multidepot Rural Postman Problem, an extension of the classical Rural Postman Problem in which there are several depots instead of only one. The aim is to construct a minimum cost set of routes traversing each required edge of the graph, where each route starts and ends at the same depot. The paper makes the following scientific contributions: (i) It presents optimality conditions and a worst case analysis for the problem; (ii) It proposes a compact integer linear programming formulation containing only binary variables, as well as a polyhedral analysis; (iii) It develops a branch-and-cut algorithm that includes several new exact and heuristic separation procedures. Instances involving up to four depots, 744 vertices, and 1,315 edges are solved to optimality. These instances contain up to 140 required components and 1,000 required edges.Peer ReviewedPostprint (author's final draft

Algoritmos e formulações matemáticas para problemas de roteamento em arcos

Orientador: Fábio Luiz UsbertiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de roteamento em arcos têm por objetivo determinar rotas de custo mínimo que visitam um subconjunto de arcos de um grafo, com uma ou mais restrições adicionais. Esta tese estuda três problemas NP-difíceis de roteamento em arcos: (1) o problema de roteamento em arcos capacitado (CARP); (2) o problema de roteamento em arcos capacitado e aberto (OCARP); e (3) o problema do carteiro chinês com cobertura (CCPP). Apresentamos formulações matemáticas e métodos exatos e heurísticos para tratar computacionalmente esses problemas: (i) uma heurística construtiva gulosa e randomizada é proposta para o CARP; (ii) uma metaheurística de algoritmos genéticos híbrido e dois métodos de limitantes inferiores por programação linear inteira, um branch-and-cut e um baseado em redes de fluxos, são propostos para o OCARP; e (iii) um método exato branch-and-cut com desigualdades válidas e uma heurística construtiva são propostos para o CCPP. Extensivos experimentos computacionais utilizando instâncias de benchmark foram executados para demonstrar o desempenho dos métodos propostos em relação aos métodos da literatura, considerando tanto a qualidade das soluções obtidas quanto o tempo de processamento. Nossos resultados mostram que os métodos propostos são estado da arte. Os problemas estudados apresentam aplicações práticas relevantes: o CARP tem aplicações em coleta de lixo urbano e remoção de neve de estradas; o OCARP tem aplicações em roteamento de leituristas e na definição de caminhos de corte em chapas metálicas; e o CCPP tem aplicações em roteamento de leituristas com o uso de tecnologia wireless. A solução desses problemas remete à diminuição de custos logísticos, melhorando a competitividade das empresasAbstract: Arc routing problems aim to find minimum cost routes that visit a subset of arcs of a graph, with one or more side constraints. This thesis studies three NP-hard arc routing problems: (1) the capacitated arc routing problem (CARP); (2) the open capacitated arc routing problem (OCARP); and (3) the covering Chinese postman problem (CCPP). We present mathematical formulations and heuristic and exact methods to computationally solve these problems: (i) a greedy and randomized constructive heuristic is proposed for the CARP; (ii) a hybrid genetic algorithm metaheuristic and two linear integer programming lower bound methods, one based on branch-and-cut and one based on flow networks, are proposed for the OCARP; and (iii) an exact branch-and-cut method with valid inequalities and a constructive heuristic are proposed for the CCPP. Extensive computational experiments using benchmark instances were performed to demonstrate the performance of the proposed methods in comparison to the previous methods, regarding both quality of solutions and processing time. Our results show that the proposed methods are state-of-the-art. The studied problems have many relevant practical applications: the CARP has applications on urban waste collection and snow removal; the OCARP has applications on the routing of meter readers and the cutting of metal sheets; and last, the CCPP has applications on automated meter readers routing. The solution of these problems leads to the reduction of logistics costs, improving businesses competitivenessDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2016/00315-0FAPES

An updated annotated bibliography on arc routing problems

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.info:eu-repo/semantics/publishedVersio

Investigating edge-reordering procedures in a tabu search algorithm for the capacitated arc routing problem

This paper presents two ideas to guide a tabu search algorithm for the Capacitated Arc Routing Problem to a promising region of the solution space. Both ideas involve edge-reordering, although they work in different ways. One of them aims to directly tackle deadheading cycles, and the other tries to reorder edges with the aim of extending a scope of solutions that can be reached from a given solution. Experiments were performed on 134 benchmark instances of various sizes, and the two ideas were shown to have an ability to guide the search to good solutions. Possible issues that may arise when implementing these ideas are also discussed

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

The Team Orienteering Arc Routing Problem

The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers that maximize the total profit collected while satisfying the given time limit for each vehicle. In this paper we propose a formulation for this problem and study a relaxation of its associated polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational experiments are run on a large set of benchmark instances.The authors thank the reviewers for their comments that helped to provide an improved and clearer version of this paper. Angel Corberan, Isaac Plana, and Jose M. Sanchis wish to thank the Ministerio de Ciencia e Innovacion [Project MTM2009-14039-C06-02] and the Ministerio of Economia y Competitividad [Project MTM2012-36163-C06-02] of Spain for their support.Archetti, C.; Speranza, MG.; Corberan, A.; Sanchís Llopis, JM.; Plana, I. (2014). The Team Orienteering Arc Routing Problem. Transportation Science. 48(3):442-457. https://doi.org/10.1287/trsc.2013.0484S44245748

The generalized arc routing problem

The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-017-0437-4This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed.Peer ReviewedPostprint (author's final draft