Abstract
We consider a complex variant of the Container Loading Problem arising from a real-world industrial application. It includes several features such as multiple containers, box rotation, and bearable weight, which are of importance in many practical situations. In addition, it also considers the situation in which boxes have to be delivered to different destinations (multi-drop).
Our solution technique is based on local search metaheuristics. Local search works on the space of sequences of boxes to be loaded, while the actual load is obtained by invoking, at each iteration, a specialized procedure called loader. The loader inserts the boxes in the container using a deterministic heuristic which produces a load that is feasible according to the constraints.
We test our solver on real-world instances provided by our industrial partner, showing a clear improvement on the previous heuristic solution. In addition, we compare our solver on benchmarks from the literature on the basic container loading problems. The outcome is that the results are in some cases in-line with the best ones in the literature and for other cases they also improve upon the best known ones. All instances and solutions are made available on the web for future comparisons.
Similar content being viewed by others
References
Aarts, E.H., Korst, J., van Laarhoven, P.J.: Simulated annealing. In: Aarts, E.H., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization. Wiley, Chichester (1997)
Bischoff, E.: Three-dimensional packing of items with limited load bearing strength. J. Oper. Res. 168(3), 952–966 (2006)
Bischoff, E.E., Ratcliff, M.S.W.: Issues in the development of approaches to container loading. Omega 23(4), 377–390 (1995)
Bischoff, E.E., Janetz, F., Ratcliff, M.S.W.: Loading pallets with non-identical items. Eur. J. Oper. Res. 84(3), 681–692 (1995)
Bortfeldt, A.: A heuristic for multiple container loading problems. OR Spektrum 22, 239–261 (2000). In German
Bortfeldt, A., Gehring, H.: A tabu search algorithm weakly heterogeneous container loading problem. OR Spektrum 20, 237–250 (1998). In German
Bortfeldt, A., Gehring, H.: A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131(1), 143–161 (2001)
Bortfeldt, A., Homberger, J.: Packing first, routing second—a heuristic for the vehicle routing and loading problem. In: Bortfeldt, A., Homberger, J., Kopfer, H., Pankratz, G., Strangmeier, R. (eds.) Intelligent Decision Support—Current Challenges and Approaches, Intelligente Entscheidungsunterstützung—Aktuelle Herausforderungen und LösungsansätzeIntelligent Decision Support, pp. 91–113. Deutscher Universitäts-Verlag, Wiesbaden (2008). In German
Bortfeldt, A., Gehring, H., Mack, D.: A parallel tabu search algorithm for solving the container loading problem. Parallel Comput. 29(5), 641–662 (2003)
Davies, A.: Approaches to the container loading problem. PhD thesis, University of Wales, Swansea (2000)
Davies, A.P., Bischoff, E.E.: Weight distribution considerations in container loading. Eur. J. Oper. Res. 114(3), 509–527 (1999)
Eglese, R.: Simulated annealing: a tool for operations research. Eur. J. Oper. Res. 46, 271–281 (1990)
Eley, M.: Solving container loading problems by block arrangement. Eur. J. Oper. Res. 141(2), 393–409 (2002)
Eley, M.: A bottleneck assignment approach to the multiple container loading problem. OR Spektrum 25(1), 45–60 (2003)
Fanslau, T., Bortfeldt, A.: A tree search algorithm for solving the container loading problem. INFORMS J. Comput. 22(2), 222–235 (2010)
Fuellerer, G., Doerner, K.F., Hartl, R.F., Iori, M.: Metaheuristics for vehicle routing problems with three-dimensional loading constraints. Eur. J. Oper. Res. 201(3), 751–759 (2010)
Gehring, H., Bortfeldt, A.: A parallel genetic algorithm for solving the container loading problem. Int. Trans. Oper. Res. 9(4), 497–511 (2002)
Gendreau, M., Iori, M., Laporte, G., Martello, S.: A tabu search algorithm for a routing and container loading problem. Transp. Sci. 40(3), 342–350 (2006)
George, J.A., Robinson, D.F.: A heuristic for packing boxes into a container. Comput. Oper. Res. 7(3), 147–156 (1980)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Dordrecht (1997)
Hoos, H.H., Stützle, T.: Stochastic Local Search—Foundations and Applications. Morgan Kaufmann, San Francisco (2005)
Ivancic, N., Mathur, K., Mohanty, B.: An integer programming based heuristic approach to the three-dimensional packing problem. J. Manuf. Oper. Manag. 2(4), 268–298 (1989)
Kirkpatrick, S., Gelatt, C.D. Jr., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Mack, D., Bortfeldt, A., Gehring, H.: A parallel hybrid local search algorithm for the container loading problem. Int. Trans. Oper. Res. 11(5), 511–533 (2004)
Moura, A., Oliveira, J.F.: A grasp approach to the container-loading problem. IEEE Intell. Syst. 20, 50–57 (2005)
Moura, A., Oliveira, J.F.: An integrated approach to the vehicle routing and container loading problems. OR Spektrum 31(4), 775–800 (2009)
Parreño, F., Alvarez-Valdes, R., Oliveira, J., Tamarit, J.: A maximal-space algorithm for the container loading problem. INFORMS J. Comput. 20(3), 412–422 (2008)
Parreño, F., Alvarez-Valdes, R., Oliveira, J., Tamarit, J.: Neighborhood structures for the container loading problem: a VNS implementation. J. Heuristics 16(1), 1–22 (2010)
Pisinger, D.: A tree search heuristic for the container loading problem. Ric. Oper. 28, 31–48 (1998)
Pisinger, D.: Heuristics for the container loading problem. Eur. J. Oper. Res. 141, 382–392 (2002)
Raidl, G.R.: The multiple container packing problem: a genetic algorithm approach with weighted codings. ACM SIGAPP Appl. Comput. Rev. 7(2), 22–31 (1999)
Raidl, G.R., Kodydek, G.: Genetic algorithms for the multiple container packing problem. In: PPSN V: Proceedings of the 5th International Conference on Parallel Problem Solving from Nature, pp. 875–884. Springer, London (1998)
Ratcliff, M., Bischoff, E.: Allowing for weight considerations in container loading. OR Spektrum 20, 65–71 (1998)
Sang-Moon, S., Lee, S.-W., Yeo, G.-T., Jeon, M.-G.: An effective evolutionary algorithm for the multiple container packing problem. Prog. Nat. Sci. 18(3), 337–344 (2008)
Tarantilis, C., Zachariadis, E.E., Kiranoudis, C.T.: A hybrid metaheuristic algorithm for the integrated vehicle routing and three-dimensional container-loading problem. IEEE Trans. Intell. Trasp. Syst. 10(2), 1524–9050 (2009)
Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2002)
Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S, 4th edn. Statistics and Computing. Springer, Berlin (2002)
Wang, L., Guo, S., Chen, S., Zhu, W., Lim, A.: Two natural heuristics for 3D packing with practical loading constraints. In: PRICAI 2010: Trends in Artificial, pp. 256–267 (2010)
Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ceschia, S., Schaerf, A. Local search for a multi-drop multi-container loading problem. J Heuristics 19, 275–294 (2013). https://doi.org/10.1007/s10732-011-9162-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-011-9162-6