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On a two-phase solution approach for the bi-objective k-dissimilar vehicle routing problem

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Abstract

In the k-dissimilar vehicle routing problem, a set of k dissimilar alternatives for a Capacitated Vehicle Routing Problem (CVRP) has to be determined for a single instance. The tradeoff between minimizing the longest routing and maximizing the minimum dissimilarity between two routings is investigated. Here, spatial dissimilarity is considered. Since short routings tend to be similar to each other, an objective conflict arises. The developed heuristic approach approximates the Pareto-set with respect to this tradeoff. This paper focuses on the generation of a high-quality candidate set of routings from which k routings are extracted with respect to a spatial as well as to an edge-based dissimilarity metric. In particular two algorithmic variants are suggested which differ in generating dissimilar routings. They are further compared to each other as well as to a naive approach. The method is tested on benchmark instances of the CVRP and findings are reported for both metrics. Taking the hypervolume as a quality criterion, it could be shown that the approach provides a good approximation of the Pareto-set for both metrics. An additional comparison to the results of Talarico et al. (Eur J Oper Res 244(1):129–140, 2015) proves its competitive ability.

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References

  • Akgün, V., Erkut, E., Batta, R.: On finding dissimilar paths. Eur. J. Oper. Res. 121(2), 232–246 (2000)

    Article  MATH  Google Scholar 

  • Augerat, P., Belenguer, J., Benavent, E., Corberán, A., Naddef, D., Rinaldi, G. (1998) Computational results with a branch-and-cut code for the capacitated vehicle routing problem. Tech. Rep. RR. 949-M, Université Joseph Fourier, Grenoble, France

  • Caramia, M., Giordani, S., Iovanella, A.: On the selection of \(k\) routes in multiobjective hazmat route planning. IMA J. Manag. Math. 21, 239–251 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Christofides, N.: Combinatorial Optimization. John Wiley and Sons Canada Limited, New York (1979)

    MATH  Google Scholar 

  • Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964)

    Article  Google Scholar 

  • Croes, G.A.: A method for solving traveling salesman problems. Oper. Res. 6, 791–812 (1958)

    Article  MathSciNet  Google Scholar 

  • Dantzig, G., Fulkerson, R., Johnson, S.: Solution of a large-scale traveling-salesman problem. Oper. Res. 2, 393–410 (1954)

    MathSciNet  Google Scholar 

  • Dell’Olmo, P., Gentili, M., Scozzari, A.: On finding dissimilar Pareto-optimal paths. Eur. J. Oper. Res. 162(1), 70–82 (2005)

    Article  MATH  Google Scholar 

  • Fisher, M.: Optimal solution of vehicle routing problems using minimum \(k\)-trees. Oper. Res. 42(4), 626–642 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Geiger, M.J.: Fast approximation heuristics for multi-objective vehicle routing problems. In: Chio, C., Brabazon, A., Caro, G.A., Ebner, M., Farooq, M., Fink, A., Grahl, J., Greenfield, G., Machado, P., O’Neill, M., Tarantino, E., Urquhart, N. (eds.) Applications of Evolutionary Computation. Lect Notes Comput Sc, vol. 6025, pp. 441–450. Springer, Berlin (2010)

    Chapter  Google Scholar 

  • Johnson, P., Joy, D., Clarke, D.: HIGHWAY 3.01 – An enhancement routing model: Program, description, methodology and revised user’s manual. Tech. rep., Oak Ridge National Laboratories, Washington, D.C. (1992)

  • Kuby, M., Zhongyi, X., Xiaodong, X.: A minimax method for finding the \(k\) best “differentiated” paths. Geogr. Anal. 29(4), 298–313 (1997)

    Article  Google Scholar 

  • Laporte, G.: The vehicle routing problem: An overview of exact and approximate algorithms. Eur. J. Oper. Res. 59(3), 345–358 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Lei, H., Laporte, G., Guo, B.: A generalized variable neighborhood search heuristic for the capacitated vehicle routing problem with stochastic service times. TOP 20(1), 99–118 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Levenshtein, V.: Binary codes capable of correcting deletions, insertions, and reversals. Sov. Phys. Dokl. 10, 707–710 (1966)

    MathSciNet  MATH  Google Scholar 

  • Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • Løkketangen, A., Oppen, J., Oyola, J., Woodruff, D.L.: An attribute based similarity function for VRP decision support. DMMS 6(2), 65–83 (2012)

    Article  MATH  Google Scholar 

  • Lombard, K., Church, R.L.: The gateway shortest path problem: Generating alternative routes for a corridor location problem. Geogr. Syst. 1, 25–45 (1993)

    Google Scholar 

  • Martí, R., González Velarde, J.L., Duarte, A.: Heuristics for the bi-objective path dissimilarity problem. Comput. Oper. Res. 36(11), 2905–2912 (2009)

    Article  MATH  Google Scholar 

  • Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Ngueveu, S.U., Prins, C., Wolfler Calvo, R.: A hybrid tabu search for the \(m\)-peripatetic vehicle routing problem. In: Maniezzo, V., Stützle, T., Voß, S. (eds.) Matheuristics, Annals of Information Systems, vol. 10, pp. 253–266. Springer, Boston (2010)

    Google Scholar 

  • Potvin, J.Y., Rousseau, J.M.: An exchange heuristic for routeing problems with time windows. J. Oper. Res. Soc. 46(12), 1433–1446 (1995)

    Article  MATH  Google Scholar 

  • Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Savelsbergh, M.W.P.: The vehicle routing problem with time windows: minimizing route duration. INFORMS J. Comput. 4, 146–154 (1992)

    Article  MATH  Google Scholar 

  • Sörensen, K.: Route stability in vehicle routing decisions: a bi-objective approach using metaheuristics. Cent. Europ. J. Oper. Re. 14(2), 193–207 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Suurballe, J.W.: Disjoint paths in a network. Networks 4(2), 125–145 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Taillard, E.: Parallel iterative search methods for vehicle routing problems. Networks 23(8), 661–673 (1993)

    Article  MATH  Google Scholar 

  • Talarico, L., Sörensen, K., Springael, J.: The \(k\)-dissimilar vehicle routing problem. Eur. J. Oper. Res. 244(1), 129–140 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Toth, P., Vigo, D.: The granular tabu search and its application to the vehicle routing problem. INFORMS J. Comput. 15(4), 333–346 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Uchoa, E., Pecin, D., Pessoa, A., Poggi, M., Vidal, T., Subramanian, A.: New benchmark instances for the capacitated vehicle routing problem. Eur. J. Oper. Res. 257(3), 845–858 (2017)

    Article  MathSciNet  Google Scholar 

  • Wolfler Calvo, R., Cordone, R.: A heuristic approach to the overnight security service problem. Comput. Oper. Res. 30(9), 1269–1287 (2003)

    Article  MATH  Google Scholar 

  • Yen, J.Y.: Finding the \(k\) shortest loopless paths in a network. Manage. Sci. 17(11), 712–716 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • Zajac, S.: The bi-objective \(k\)-dissimilar vehicle routing problem. In: Paias, A., Ruthmair, M., Voß, S. (eds.) Computational Logistics. Lect Notes Comput Sc, vol. 9855, pp. 306–320. Springer International Publishing (2016)

  • Zitzler, E.: Thiele L (1998) Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.P. (eds.) Parallel Problem Solving from Nature - PPSN V. Lect Notes Comput Sc, vol. 1498, pp. 292–301. Springer, Berlin (1998)

    Chapter  Google Scholar 

  • Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the Strength Pareto approach. IEEE Trans. Evolut. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

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  1. Helmut Schmidt University Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany

    Sandra Zajac

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  1. Sandra Zajac
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Zajac, S. On a two-phase solution approach for the bi-objective k-dissimilar vehicle routing problem. J Heuristics 24, 515–550 (2018). https://doi.org/10.1007/s10732-017-9341-1

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  • DOI: https://doi.org/10.1007/s10732-017-9341-1

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