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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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.
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.
E. Benavent, V. Campos, A. Corberán, and E. Mota. The Capacitated Arc Routing Problem: Lower Bounds. Networks, 22:669–690, 1992.
N. Christofides. The Optimum Traversal of a Graph. Omega, 1:719–732, 1973.
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.
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.
A. Corberán and J.M. Sanchis. A polyhedral approach to the rural postman problem. European Journal of Operational Research, 79:95–114, 1994.
M. Dror. Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers, 2000.
J. Edmonds and E. L. Johnson. Matching, Euler Tours and the Chinese Postman. Mathematical Programming, 5:88–124, 1973.
H. A. Eiselt, M. Gendreau, and G. Laporte. Arc routing problems I: The Chinese Postman Problem. Operations Research, 43(2):231–242, 1995.
H. A. Eiselt, M. Gendreau, and G. Laporte. Arc routing problems II: The Rural Postman Problem. Operations Research, 43(3):399–414, 1995.
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.
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.
B. L. Golden and R.T. Wong. Capacitated arc routing problems. Networks, 11:305–315, 1981.
T. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoretical Computer Science, 38:293–306, 1985.
M. Guan. Graphic Programming using odd and even points. Chinese Mathematics, 1:273–277, 1962.
A. Hertz, G. Laporte, and M. Mittaz. A Tabu Search Heuristic for the Capacitated Arc Routing Problem. Operations Research, 48(1):129–135, 2000.
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.
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.
L.Y. O. Li. Vehicle Routeing for Winter Gritting. PhD thesis, Department of Management Science, Lancaster University, 1992.
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.
W. L. Pearn. Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4):241–244, 1994.
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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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