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

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

## Abstract

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.

## Keywords

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

## Notes

### Acknowledgements

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.

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## Authors and Affiliations

• Ángel Corberán
• 1
• Isaac Plana
• 2
• Miguel Reula
• 1
• José M. Sanchis
• 3
1. 1.Dept. d’Estadística i Investigació OperativaUniversitat de ValènciaValenciaSpain
2. 2.Dept. de Matemáticas para la Economía y la EmpresaUniversitat de ValènciaValenciaSpain