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A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

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Abstract

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.

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References

  • Amberg, A., Domschke, W., Voß, S.: Multiple center capacitated arc routing problems: a tabu search algorithm using capacitated trees. Eur. J. Oper. Res. 124, 360–376 (2000)

    Article  MATH  Google Scholar 

  • Assad, A., Golden, B.: Arc routing methods and applications. In: Ball, M., et al. (eds.) Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 375–483 (1995)

  • Baldacci, R., Maniezzo, V.: Exact methods based on node routing formulations for arc routing problems. Networks 47, 52–60 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer, J.M., Benavent, E.: The capacitated arc routing problem: valid inequalities and facets. Comput. Optim. Appl. 10(2), 165–187 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer, J.M., Benavent, E.: A cutting plane algorithm for the capacitated arc routing problem. Comput. Oper. Res. 30(5), 705–728 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer, J.M., Benavent, E., Cognata, F.: A metaheuristic for the capacitated arc routing problem. Unpublished manuscript, University of Valencia, Spain 11, pp. 305–315 (1997)

  • Belenguer, J.M., Benavent, E., Lacomme, P., Prins, C.: Lower and upper bounds for the mixed capacitated arc routing problem. Comput. Oper. Res. 33(12), 3363–3383 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Beullens, P., Muyldermans, L., Cattrysse, D., Van Oudheusden, D.: A guided local search heuristic for the capacitated arc routing problem. Eur. J. Oper. Res. 147, 629–643 (2003)

    Article  MATH  Google Scholar 

  • Brandao, J., Eglese, R.: A deterministic tabu search algorithm for the capacitated arc routing problem. Comput. Oper. Res. 35(4), 1112–1126 (2008)

    Article  MATH  Google Scholar 

  • Bräysy, O.: A reactive variable neighborhood search for the vehicle-routing problem with time windows. INFORMS J. Comput. 15(4), 347–368 (2003)

    Article  MathSciNet  Google Scholar 

  • Chu, F., Labadi, N., Prins, C.: A scatter search for the periodic capacitated arc routing problem. Eur. J. Oper. Res. 169(2), 586–605 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Dror, M.: ARC ROUTING: Theory, Solutions and Applications. Kluwer Academic, Dordrecht (2000)

    MATH  Google Scholar 

  • Dueck, G., Scheuer, T.: Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90, 161–175 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Eglese, R.W.: Routing Winter gritting vehicles. Discrete Appl. Math. 48(3), 231–244 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Fleury, G., Lacomme, P., Prins, C.: Evolutionary algorithms for stochastic arc routing problems. In: Proceedings of the EvoWorkshops 2004, pp. 501–512 (2004)

  • Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP Completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  • Ghiani, G., Improta, G., Laporte, G.: The capacitated arc routing problem with intermediate facilities. Networks 37, 134–143 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Ghiani, G., Guerriero, F., Laporte, G., Musmanno, R.: Tabu search heuristics for the arc routing problem with intermediate facilities under capacity and length restrictions. J. Math. Model. Algorithms 3, 209–223 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Golden, B.L., Wong, R.T.: Capacitated arc routing problems. Networks 11, 305–315 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • Greistorfer, P.: A tabu scatter search metaheuristic for the arc routing problem. Comput. Ind. Eng. 44(2), 249–266 (2003)

    Article  Google Scholar 

  • Hansen, P., Mladenović, N.: An introduction to variable neighborhood search. In: Voss, S. (ed.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic, Boston (1999)

    Google Scholar 

  • Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)

    Article  MATH  Google Scholar 

  • Hertz, A., Laporte, G., Mittaz, M.: A tabu search heuristic for the capacitated arc routing problem. Oper. Res. 48, 129–135 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Hertz, A., Laporte, G., Mittaz, M.: A variable neighborhood descent algorithm for the undirected capacitated arc routing problem. Transp. Sci. 35, 425–434 (2001)

    Article  MATH  Google Scholar 

  • Hirabayashi, R., Saruwatari, Y., Nishida, N.: Tour construction algorithm for the capacitated arc routing problems. Asia Pac. J. Oper. Res. 9(2), 155–175 (1992)

    MATH  MathSciNet  Google Scholar 

  • Lacomme, P., Prins, C., Ramdane-Cherif, W.: A genetic algorithm for the capacitated routing problem and its extensions. In: Boers, E.J.W., et al. (eds.) Proceedings of the EvoWorkshops 2001, pp. 473–483 (2001)

  • Lacomme, P., Prins, C., Ramdane-Cherif, W.: Competitive memetic algorithms for arc routing problems. Ann. Oper. Res. 131, 159–185 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Lacomme, P., Prins, C., Ramdane-Cherif, W.: Evolutionary algorithms for periodic arc routing problems. Eur. J. Oper. Res. 165(2), 535–553 (2005)

    Article  MATH  Google Scholar 

  • Maniezzo, V.: Metaheuristics for large directed CARP instances: urban solid waste collection operational support. Technical Report UBLCS-2004-16, Dept. Computer Science, University of Bologna (2004)

  • Maniezzo, V., Baldacci, R.: Exact solutions of mixed CARP instances. In: Proceedings of the Odysseus 2006, Altea, Spain (2006)

  • Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Polacek, M., Hartl, R.F., Doerner, K.F., Reimann, M.: A variable neighborhood search for the multi depot vehicle routing problem with time windows. J. Heuristics 10(6), 613–627 (2004)

    Article  Google Scholar 

  • Polacek, M., Doerner, K.F., Hartl, R.F., Kiechle, G., Reimann, M.: Scheduling periodic customer visits for a traveling salesperson. Eur. J. Oper. Res. 179(3), 823–837 (2007)

    Article  MATH  Google Scholar 

  • Snizek, J., Bodin, L., Levy, L., Ball, M.: Capacitated arc routing problem with vehicle-site dependencies: the Philadelphia experience. In: Toth, P. (ed.) The Vehicle Routing Problem, pp. 287–308. SIAM, Philadelphia (2002)

    Google Scholar 

  • Taillard, E.D., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.Y.: A tabu search heuristic for the vehicle routing problem with soft time windows. Transp. Sci. 31, 170–186 (1997)

    Article  MATH  Google Scholar 

  • Ulusoy, G.: The fleet size and mix problem for capacitated arc routing. Eur. J. Oper. Res. 22, 329–337 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  • Wirasinghe, C., Waters, N.M.: An approximate procedure for determining the number, capacities and locations of solid waste transfer-stations in an urban region. Eur. J. Oper. Res. 12, 105–111 (1983)

    Article  MATH  Google Scholar 

  • Wøhlk, S.: New lower bound for the capacitated arc routing problem. Comput. Oper. Res. 33(12), 3458–3472 (2006)

    Article  MathSciNet  Google Scholar 

  • Xin, X.: Hanblen SWRoute: A GIS Based Spatial Decision Support System for Designing Solid Waste Collection Routes in Rural Countries. The University of Tennessee, Knoxville (2000)

    Google Scholar 

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Authors and Affiliations

  1. Department of Business Administration, University of Vienna, Bruenner Strasse 72, 1210, Vienna, Austria

    Michael Polacek, Karl F. Doerner & Richard F. Hartl

  2. Department of Computer Science, University of Bologna, Mura Anteo Zamboni, 7, 40100, Bologna, Italy

    Vittorio Maniezzo

Authors
  1. Michael Polacek
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  2. Karl F. Doerner
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  3. Richard F. Hartl
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  4. Vittorio Maniezzo
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Correspondence to Karl F. Doerner.

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Polacek, M., Doerner, K.F., Hartl, R.F. et al. A variable neighborhood search for the capacitated arc routing problem with intermediate facilities. J Heuristics 14, 405–423 (2008). https://doi.org/10.1007/s10732-007-9050-2

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  • DOI: https://doi.org/10.1007/s10732-007-9050-2

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