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Recent Algorithmic Advances for Arc Routing Problems

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Operations Research/Management Science at Work

Abstract

This article reports on some recent algorithmic development for the Rural Postman Problem (CPP) and for the Capacitated Arc Routing Problem (CARP). Heuristics are described for the RPP and for the CARP. A branch-and-cut algorithm is described for the RPP.

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References

  • Anily, S., Gendreau, M. and Laporte, G. Optimal sequencing of tasks on a tree shaped structure. Ricerca Operativa 2000; 29:3–14

    Google Scholar 

  • Assad, A.A. and Golden, B.L. “Arc routing methods and applications”. In M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser, Network Routing, Handbooks in Operations Research and Management Science, Amsterdam: North-Holland, 1995.

    Google Scholar 

  • Barahona, F. and Grötschel, M. On the cycle polytope of a binary matroid. Journal of Combinatorial Theory, Series B 1986; 40:40–62

    Article  Google Scholar 

  • Beltrami, E.L. and Bodin, L.D. Networks and vehicle routing for municipal waste collection. Networks 1974; 4:65-94

    Article  Google Scholar 

  • Benavent, E.fttp://indurain.estadi.uv.es/pub/CARP.1997

  • Christofides, N. The optimum traversal of a graph. Omega 1973; 1:719–732

    Article  Google Scholar 

  • Christofides, N. Worst-case analysis of a new heuristic for the traveling salesman problem. Report No 388, Graduate School of Industrial Administration, Pittsburgh, PA, Carnegie Mellon University, 1976.

    Google Scholar 

  • Christofides, N., Campos, V., Corberán, A. and Mota, E. An algorithm for the rural postman problem. Imperial College Report I C.O.R. 81.5, London, 1981.

    Google Scholar 

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

    Article  Google Scholar 

  • Croes, G.A. A method for solving traveling-salesman problems. Operations Research 1958; 6:791–812

    Article  Google Scholar 

  • DeArmon, J.S. A comparison of heuristics for the capacitated Chinese postman problem. Master’s Thesis, University of Maryland, College Park, MD, 1981.

    Google Scholar 

  • Edmonds, J. and Johnson, E.L. Matching, Euler tours and the Chinese postman problem. Mathematical Programming 1973; 5:88–124

    Article  Google Scholar 

  • Eiselt, H.A., Gendreau, M. and Laporte, G. Arc routing problems, part I: The Chinese postman problem. Operations Research 1995a; 43:231–242

    Article  Google Scholar 

  • Eiselt, H.A., Gendreau, M. and Laporte, G. Arc routing problems, part II: The rural postman problem. Operations Research 1995b; 43:399–414

    Article  Google Scholar 

  • Euler, L. Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientarum Petropolitanae 1736; 8:128–140

    Google Scholar 

  • Fleischner, H. Eulerian Graphs and Related Topics (Part I, Volume I), Annals of Discrete Mathematics 45, Amsterdam: North-Holland, 1990.

    Google Scholar 

  • Ford, L.R. and Fulkerson, D.R. Flows in Networks. Princeton, NJ.: Princeton University Press, 1962.

    Google Scholar 

  • Frederickson, G.N. Approximation algorithms for some postman problems. SIAM Journal on Computing 1979; 7:179–193

    Google Scholar 

  • Gendreau, M., Hertz, A. and Laporte, G. A tabu search heuristic for the vehicle routing problem. Management Science 1994; 40:1276–1290

    Article  Google Scholar 

  • Ghiani, G. and Improta, G. Optimizing laser-plotter beam movement. Journal of the Operational Research Society 2001, forthcoming.

    Google Scholar 

  • Ghiani, G. and Laporte, G. Eulerian location problems. Networks 1999; 34:291–302

    Article  Google Scholar 

  • Ghiani, G. and Laporte, G. A branch-and-cut algorithm for the undirected rural postman problem. Mathematical Programming 2000; 87:467–481

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Greistorfer, P. Computational experiments with heuristics for a capacitated arc routing problem. Working Paper 32, Department of Business, University of Graz, Austria, 1994.

    Google Scholar 

  • Grötschel, M. and Holland, O. Solution of large-scale symmetric traveling salesman problems. Mathematical Programming 1991; 51:141–202

    Article  Google Scholar 

  • Guan, M. Graphic programming using odd and even points. Chinese Mathematics 1962; 1:273–277

    Google Scholar 

  • Hertz, A., Laporte, G. and Mittaz, M. A tabu search heuristic for the capacitated arc routing problem. Operations Research 2000; 48:129–135

    Article  Google Scholar 

  • Hertz, A., Laporte, G. and Nanchen-Hugo, P. Improvement procedures for the undirected rural postman problem. INFORMS Journal on Computing 1999; 11:53–62

    Article  Google Scholar 

  • Hierholzer Uber die Möglichkeit einen Linienzug ohne Widerholung und ohne Unterbrechung zu umfahren. Mathematische Annalen 1873; VI:30–32

    Google Scholar 

  • Jünger, M., Reinelt, G. and Rinaldi, G. The traveling salesman problem. In Network Models, Handbooks in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser (eds), Amsterdam: North-Holland, 1995.

    Google Scholar 

  • Lenstra, J.K. and Rinnooy Kan, A.H.G. On general routing problems. Networks 1976; 6:273–280

    Article  Google Scholar 

  • Letchford, A.N. Polyhedral results for some constrained arc-routing problems, Ph.D. Thesis, Department of Management Science, Lancaster University, United Kingdom, 1996

    Google Scholar 

  • Mittaz, M. Problèmes de cheminements optimaux dans des réseaux avec contraintes associées aux arcs, Ph.D. Thesis, Department of Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland, 1999.

    Google Scholar 

  • Mladenović, N. and Hansen, P. Variable neighbourhood search. Computers & Operations Research 1997; 34:1097–1100

    Article  Google Scholar 

  • Nobert, Y. and Picard, J.-C. An optimal algorithm for the mixed Chinese postman problem. Networks 1996; 27:95–108

    Article  Google Scholar 

  • Orloff, C.S. A fundamental problem in vehicle routing. Networks 1974; 4:35–64

    Article  Google Scholar 

  • Padberg, M.W. and Rinaldi, G. A branch and cut algorithm for the resolution of large-scale symmetric traveling salesman problem. SIAM Review 1991; 33:60–100

    Article  Google Scholar 

  • Pearn, W.-L. Approximate solutions for the capacitated arc routing problem. Computers & Operations Research 1989; 16:589–600

    Article  Google Scholar 

  • van Aardenne-Ehrenfest, T. and de Bruijn, N.G. Circuits and trees in oriented linear graphs. Simon Stevin 1951; 28:203–217

    Google Scholar 

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Erhan Kozan Azuma Ohuchi

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Ghiani, G., Hertz, A., Laporte, G. (2002). Recent Algorithmic Advances for Arc Routing Problems. In: Kozan, E., Ohuchi, A. (eds) Operations Research/Management Science at Work. International Series in Operations Research & Management Science, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0819-9_1

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  • DOI: https://doi.org/10.1007/978-1-4615-0819-9_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5254-9

  • Online ISBN: 978-1-4615-0819-9

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