# Efficient Large-scale Road Inspection Routing

### Yujie Chen, Peter Cowling, Stephen Remde, Fiona Polack

#### Abstract

Gaist Solutions Ltd. carries out large scale surveys for UK road inspection. To estimate the total distance that vehicles travel, we model routing as a Chinese Postman Problem. We propose a novel graph reduction approach that dramatically speeds up the calculation of the Chinese Postman Tour for large-scale road networks. Because the analysis of large road-network graphs is now possible, planners can explore the effects of changes to traditional inspection techniques and scheduling. Case studies of road networks from six UK cities and the county of Norfolk are tested. The graph reduction process is also analysed on ten randomly generated road networks with different characteristics, to show its ability and give advice for suitable use.

#### References

- Blitzstein, J. and Diaconis, P. (2011). A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Internet Mathematics, 6(4):489-522.
- Chartrand, G. and Oellermann, O. (1993). Graph Minors. In Applied and Algorithmic Graph Theory, pages 277- 281. McGraw-Hill.
- Corberán, Í. and Laporte, G. (2015). Arc routing: problems, methods, and applications. SIAM.
- Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1):269- 271.
- Edmonds, J. (1965). Paths, trees, and flowers. Canadian Journal of mathematics, 17(3):449-467.
- Edmonds, J. and Johnson, E. L. (1973). Matching, Euler tours and the Chinese postman. Mathematical programming, 5(1):88-124.
- Fleury, M. (1883). Deux problemes de geometrie de situation. Journal de mathematiques elementaires, 2(2):257-261.
- Floyd, R. W. (1962). Algorithm 97: Shortest Path. Communications of the ACM, 5(6):345.
- Fredman, M. L. and Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34(3):596-615.
- Gabow, H. N. (1990). Data structures for weighted matching and nearest common ancestors with linking. In Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 434-443. Society for Industrial and Applied Mathematics.
- Guan, M. (1962). Graphic programming using odd or even points. Chinese Math, 1(273-277):110.
- Hierholzer, C. and Wiener, C. (1873). Ueber die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Mathematische Annalen, 6(1):30-32.
- Irnich, S. (2008). Solution of real-world postman problems. European Journal of Operational Research, 190(1):52-67.
- Kolmogorov, V. (2009). Blossom V: a new implementation of a minimum cost perfect matching algorithm. Mathematical Programming Computation, 1(1):43-67.
- Kurtzberg, J. M. (1962). On approximation methods for the assignment problem. Journal of the ACM (JACM), 9(4):419-439.
- Laporte, G. (1997). Modeling and solving several classes of arc routing problems as traveling salesman problems. Computers & operations research, 24(11):1057-1061.
- Lovász, L. (2006). Graph minor theory. Bulletin of the American Mathematical Society, 43(1):75-86.
- Reingold, E. M. and Tarjan, R. E. (1981). On a greedy heuristic for complete matching. SIAM Journal on Computing, 10(4):676-681.
- Thimbleby, H. (2003). The directed Chinese Postman Problem. Software Practice and Experience, 33(11):1081- 1096.

#### Paper Citation

#### in Harvard Style

Chen Y., Cowling P., Remde S. and Polack F. (2016). **Efficient Large-scale Road Inspection Routing** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 304-312. DOI: 10.5220/0005749203040312

#### in Bibtex Style

@conference{icores16,

author={Yujie Chen and Peter Cowling and Stephen Remde and Fiona Polack},

title={Efficient Large-scale Road Inspection Routing},

booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2016},

pages={304-312},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005749203040312},

isbn={978-989-758-171-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Efficient Large-scale Road Inspection Routing

SN - 978-989-758-171-7

AU - Chen Y.

AU - Cowling P.

AU - Remde S.

AU - Polack F.

PY - 2016

SP - 304

EP - 312

DO - 10.5220/0005749203040312