Abstract
We propose a new exact method for bi-objective vehicle routing problems where edges are associated with two costs. The method generates the minimum complete Pareto front of the problem by combining the scalarization of the objective function and the column generation technique. The aggregated objective allows to apply the exact algorithm for the mono-objective vehicle routing problem of Baldacci et al. (2008). The algorithm is applied to a bi-objective VRP with time-windows. Computational results are compared with a classical bi-objective technique. The results show the pertinence of the new method, especially for clustered instances.
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References
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80–91 (1959)
Jozefowiez, N., Semet, F., Talbi, E.G.: Multi-objective vehicle routing problems. Eur. J. Oper. Res. 189(2), 293–309 (2008)
Parragh, S.N., Tricoire, F.: Branch-and-bound for bi-objective integer programming. Optimization Online (2015)
Boland, N., Charkhgard, H., Savelsbergh, M.: The triangle splitting method for biobjective mixed integer programming. In: Lee, J., Vygen, J. (eds.) IPCO 2014. LNCS, vol. 8494, pp. 162–173. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07557-0_14
Moradi, S., Raith, A., Ehrgott, M.: A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem. Eur. J. Oper. Res. 244(2), 369–378 (2015)
Bérubé, J.F., Gendreau, M., Potvin, J.Y.: An exact \(\epsilon \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur. J. Oper. Res. 194(1), 39–50 (2009)
Özlen, M., Azizoğlu, M.: Multi-objective integer programming: a general approach for generating all non-dominated solutions. Eur. J. Oper. Res. 199(1), 25–35 (2009)
Boland, N., Charkhgard, H., Savelsbergh, M.: A criterion space search algorithm for biobjective integer programming: the balanced box method. INFORMS J. Comput. 27(4), 735–754 (2015)
Dai, R., Charkhgard, H.: A two-stage approach for bi-objective integer linear programming. Oper. Res. Lett. 46(1), 81–87 (2018)
Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Oper. Res. 12(2), 300–304 (1964)
Baldacci, R., Christofides, N., Mingozzi, A.: An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math. Program. 115(2), 351–385 (2008)
Ehrgott, M.: Multicriteria Optimization, vol. 491. Springer Science & Business Media, Heidelberg (2005)
Ulungu, E., Teghem, J.: The two phases method: an efficient procedure to solve bi-objective combinatorial optimization problems. Found. Comput. Dec. Sci. 20(2), 149–165 (1995)
Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22(3), 618–630 (1968)
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Glize, E., Jozefowiez, N., Ngueveu, S.U. (2018). An Exact Column Generation-Based Algorithm for Bi-objective Vehicle Routing Problems. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_18
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