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A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem

  • Ángel Corberán
  • Isaac Plana
  • Miguel ReulaEmail author
  • José M. Sanchis
Original Paper


The Close-Enough Arc Routing Problem, also called Generalized Directed Rural Postman Problem, is an arc routing problem with interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets within a certain distance of a meter, the receiver is able to record the gas, water, or electricity consumption. Therefore, the vehicle does not need to traverse every street, but only a few, in order to be close enough to each meter. In this paper we deal with an extension of this problem, the Distance-Constrained Generalized Directed Rural Postman Problem or Distance-Constrained Close Enough Arc Routing Problem, in which a fleet of vehicles is available. The vehicles have to leave from and return to a common vertex, the depot, and the length of their routes must not exceed a maximum distance (or time). For solving this problem we propose a matheuristic that incorporates an effective exact procedure to optimize the routes obtained. Extensive computational experiments have been performed on a set of benchmark instances and the results are compared with those obtained with an exact procedure proposed in the literature.


Close-Enough Arc Routing Problem Generalized directed Rural Postman Problem Distance constraints Matheuristic multi-start 



This work was supported by the Spanish Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER) through Project MTM2015-68097-P (MINECO/FEDER). Authors want to thank two anonymous referees for their suggestions and comments that have contributed to improve the paper.


  1. Aráoz J, Fernández E, Franquesa C (2017) The generalized arc routing problem. TOP 25:497–525CrossRefGoogle Scholar
  2. Ávila T, Corberán Á, Plana I, Sanchis JM (2016) A new branch-and-cut algorithm for the generalized directed rural postman problem. Transportation Science 50:750–761CrossRefGoogle Scholar
  3. Ávila T, Corberán Á, Plana I, Sanchis JM (2017) Formulations and exact algorithms for the distance-constrained generalized directed rural postman problem. EURO Journal on Computational Optimization 5:339–365CrossRefGoogle Scholar
  4. Cerrone C, Cerulli R, Golden B, Pentangelo R (2017) A flow formulation for the close-enough arc routing problem. In Sforza A. and Sterle C., editors, Optimization and Decision Science: Methodologies and Applications. ODS 2017., volume 217 of Springer Proceedings in Mathematics & Statistics, pages 539–546Google Scholar
  5. Corberán Á, Laporte G (editors) (2014) Arc Routing: Problems,Methods, and Applications. MOS-SIAM Series on Optimization,PhiladelphiaGoogle Scholar
  6. Corberán Á, Plana I, Sanchis J.M (2007) Arc routing problems: data instances.
  7. Drexl M (2007) On some generalized routing problems. PhD thesis, Rheinisch-Westfälische Technische Hochschule, Aachen UniversityGoogle Scholar
  8. Drexl M (2014) On the generalized directed rural postman problem. Journal of the Operational Research Society 65:1143–1154CrossRefGoogle Scholar
  9. Gendreau M, Laporte G, Semet F (1997) The covering tour problem. Operations Research 45:568–576CrossRefGoogle Scholar
  10. Hà M-H, Bostel N, Langevin A, Rousseau L-M (2014) Solving the close enough arc routing problem. Networks 63:107–118CrossRefGoogle Scholar
  11. Mourão MC, Pinto LS (2017) An updated annotated bibliography on arc routing problems. Networks 70:144–194CrossRefGoogle Scholar
  12. Renaud A, Absi N, Feillet D (2017) The stochastic close-enough arc routing problem. Networks 69:205–221CrossRefGoogle Scholar
  13. Shuttleworth R, Golden BL, Smith S, Wasil EA (2008) Advances in meter reading: Heuristic solution of the close enough traveling salesman problem over a street network. In: Golden BL, Raghavan S, Wasil EA (eds) The Vehicle Routing Problem: Lastest Advances and New Challenges. Springer, pp 487–501Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Dept. d’Estadística i Investigació OperativaUniversitat de ValènciaValenciaSpain
  2. 2.Dept. de Matemáticas para la Economía y la EmpresaUniversitat de ValènciaValenciaSpain
  3. 3.Dept. de Matemática AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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