# AN EXACT ALGORITHM FOR THE CLOSE ENOUGH TRAVELING SALESMAN PROBLEM WITH ARC COVERING CONSTRAINTS

### Minh Hoang Ha, Nathalie Bostel, André Langevin, Louis-Martin Rousseau

#### Abstract

In this paper, we consider a problem still seldom studied in the literature, the Close Enough Traveling Salesman problem with covering constraints on the arcs. This problem arises in the context of utility companies that use automated meter reading (AMR) with radio frequency identification (RFID) technology to read meters from a distance. The contribution of this paper is to introduce a new mathematical formulation and to propose a first exact algorithm for this problem. Computational results show that our algorithm is capable of solving to optimality instances of realistic size, such as those introduced in (Golden et al., 2008), with 1000 arcs and 9000 customers in less than 2 hours.

#### References

- Dong, J., Yang, N., and Chen, M. (2007). Extending the Horizons: Advances in Computing, Optimisation, and Decision Technologies, chapter Heuristic Approaches for a TSP Variant: The Automatic Meter Reading Shortest Tour Problem, pages 145-163. Springer Verlag.
- Gendreau, M., Laporte, G., and Semet, F. (1997). The covering tour problem. Operations Research, 45:568- 576.
- Golden, B., Raghavan, S., and Wasil, E. (2008). The Vehicle Routing Problem: Lastest Avances and New Challenges, chapter Advances in Meter Reading: Heuristic Solution of the Close Enough Traveling Salesman Problem over a Street Network, pages 487-501. Springer.
- Gulczynski, D., Heath, J., and Price, C. (2006). Perspectives in Operations Research: Papers in Honor of Saul Gass 80th Birthday, chapter The Close Enough Traveling Salesman Problem: A Discussion of Several Heuristics, pages 271-283. Springer Verlag.

#### Paper Citation

#### in Harvard Style

Hoang Ha M., Bostel N., Langevin A. and Rousseau L. (2012). **AN EXACT ALGORITHM FOR THE CLOSE ENOUGH TRAVELING SALESMAN PROBLEM WITH ARC COVERING CONSTRAINTS** . In *Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-8425-97-3, pages 233-238. DOI: 10.5220/0003698702330238

#### in Bibtex Style

@conference{icores12,

author={Minh Hoang Ha and Nathalie Bostel and André Langevin and Louis-Martin Rousseau},

title={AN EXACT ALGORITHM FOR THE CLOSE ENOUGH TRAVELING SALESMAN PROBLEM WITH ARC COVERING CONSTRAINTS},

booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2012},

pages={233-238},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003698702330238},

isbn={978-989-8425-97-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - AN EXACT ALGORITHM FOR THE CLOSE ENOUGH TRAVELING SALESMAN PROBLEM WITH ARC COVERING CONSTRAINTS

SN - 978-989-8425-97-3

AU - Hoang Ha M.

AU - Bostel N.

AU - Langevin A.

AU - Rousseau L.

PY - 2012

SP - 233

EP - 238

DO - 10.5220/0003698702330238