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New Heuristics and Lower Bounds for the Min-Max k-Chinese Postman Problem

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Algorithms — ESA 2002 (ESA 2002)

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Abstract

Given an undirected edge-weighted graph and a depot node, postman problems are generally concerned with traversing the edges of the graph (starting and ending at the depot node) while minimizing the distance traveled. For the Min-Max k-Chinese Postman Problem (MM k- CPP) we have k > 1 postmen and want to minimize the longest of the k tours. We present two new heuristics and improvement procedures for the MM k-CPP. Furthermore, we give three new lower bounds in order to assess the quality of the heuristics. Extensive computational results show that our algorithms outperform the heuristic of Frederickson et al. [12].

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References

  1. D. Applegate, W. Cook, S. Dash, and A. Rohe. Solution of a Min-Max Vehicle Routing Problem. INFORMS Journal on Computing, 14(2):132–143, 2002.

    Article  MathSciNet  Google Scholar 

  2. A.A. Assad and B. L. Golden. Arc Routing Methods and Applications. In M.G. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, editors, Network Routing, volume 8 of Handbooks in Operations Research and Management Science, chapter 5, pages 375–483. Elsevier, 1995.

    Google Scholar 

  3. E. Benavent, V. Campos, A. Corberán, and E. Mota. The Capacitated Arc Routing Problem: Lower Bounds. Networks, 22:669–690, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  4. N. Christofides. The Optimum Traversal of a Graph. Omega, 1:719–732, 1973.

    Article  Google Scholar 

  5. N. Christofides, V. Campos, A. Corberán, and E. Mota. An Algorithm for the Rural Postman Problem. Technical Report I.C.O.R. 81.5, Imperial College, 1981.

    Google Scholar 

  6. A. Corberán, A. Letchford, and J.M. Sanchis. A Cutting Plane Algorithm for the General Routing Problem. Mathematical Programming Series A, 90(2):291–316, 2001.

    Article  MATH  Google Scholar 

  7. A. Corberán and J.M. Sanchis. A polyhedral approach to the rural postman problem. European Journal of Operational Research, 79:95–114, 1994.

    Article  MATH  Google Scholar 

  8. M. Dror. Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers, 2000.

    Google Scholar 

  9. J. Edmonds and E. L. Johnson. Matching, Euler Tours and the Chinese Postman. Mathematical Programming, 5:88–124, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. A. Eiselt, M. Gendreau, and G. Laporte. Arc routing problems I: The Chinese Postman Problem. Operations Research, 43(2):231–242, 1995.

    MATH  MathSciNet  Google Scholar 

  11. H. A. Eiselt, M. Gendreau, and G. Laporte. Arc routing problems II: The Rural Postman Problem. Operations Research, 43(3):399–414, 1995.

    MATH  MathSciNet  Google Scholar 

  12. G.N. Frederickson, M. S. Hecht, and C. E. Kim. Approximation Algorithms for some routing problems. SIAM Journal on Computing, 7(2):178–193, May 1978.

    Article  MathSciNet  Google Scholar 

  13. B. L. Golden, J. S. DeArmon, and E.K. Baker. Computational experiments with algorithms for a class of routing problems. Computers & Operations Research, 10(1):47–59, 1983.

    Article  MathSciNet  Google Scholar 

  14. B. L. Golden and R.T. Wong. Capacitated arc routing problems. Networks, 11:305–315, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  15. T. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoretical Computer Science, 38:293–306, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Guan. Graphic Programming using odd and even points. Chinese Mathematics, 1:273–277, 1962.

    Google Scholar 

  17. A. Hertz, G. Laporte, and M. Mittaz. A Tabu Search Heuristic for the Capacitated Arc Routing Problem. Operations Research, 48(1):129–135, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Hertz, G. Laporte, and P. Nanchen Hugo. Improvement Procedures for the Undirected Rural Postman Problem. INFORMS Journal on Computing, 11(1):53–62, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  19. A. Hertz and M. Mittaz. Heuristic Algorithms. In M. Dror, editor, Arc Routing: Theory, Solutions and Applications, chapter 9, pages 327–386. Kluwer Academic Publishers, 2000.

    Google Scholar 

  20. L.Y. O. Li. Vehicle Routeing for Winter Gritting. PhD thesis, Department of Management Science, Lancaster University, 1992.

    Google Scholar 

  21. L.Y.O. Li and R.W. Eglese. An Interactive Algorithm for Vehicle Routeing for Winter-Gritting. Journal of the Operational Research Society, 47:217–228, 1996.

    Article  Google Scholar 

  22. W. L. Pearn. Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4):241–244, 1994.

    Article  MATH  MathSciNet  Google Scholar 

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Ahr, D., Reinelt, G. (2002). New Heuristics and Lower Bounds for the Min-Max k-Chinese Postman Problem. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_10

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  • DOI: https://doi.org/10.1007/3-540-45749-6_10

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  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

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