Abstract
In this paper, we propose a heuristic based upon the large neighborhood search for the disjunctively constrained knapsack problem (DCKP). The proposed method combines a two-phase procedure and a large neighborhood search. First, the two-phase procedure is applied in order to provide a starting feasible solution for the large neighborhood search. The first phase serves to determine a feasible solution by successively solving two subproblems: the weighted independent set and the classical binary knapsack. The second phase tries to improve the quality of the solutions by using a descent method which applies both degrading and re-optimizing strategies. Second, a large neighborhood search is introduced in order to diversify the search space. Finally, the performance of the proposed method is computationally analyzed on a set of benchmark instances of the literature where its provided results are compared to those reached by Cplex solver and some recent algorithms. The provided results show that the method is very competitive since it is able to reach new solutions within small runtimes.
Keywords
- Heuristic
- Knapsack
- Neighborhood
- Re-optimisation
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References
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman and Company, San Francisco (1979)
Hifi, M.: An iterative rounding search-based algorithm for the disjunctively constrained knapsack problem. Eng. Optim. doi:10.1080/0305215X.2013.819096 (Published online: 19 Sep 2013)
Hifi, M., Michrafy, M.: Reduction strategies and exact algorithms for the disjunctively constrained knapsack problem. Comput. Oper. Res. 34, 2657–2673 (2007)
Hifi, M., Michrafy, M.: A reactive local search algorithm for the disjunctively constrained knapsack problem. J. Oper. Res. Soc. 57, 718–726 (2006)
Hifi, M., Otmani, N.: An algorithm for the disjunctively constrained knapsack problem. Int. J. Oper. Res. 13, 22–43 (2012)
Hifi, M., Otmani, N.: An algorithm for the disjunctively constrained knapsack problem. In: IEEE - International Conference on Communications, Computing and Control Applications, pp. 1–6 (2011)
Hifi, M., Negre, S., Ould Ahmed Mounir, M.: Local branching-based algorithm for the disjunctively constrained knapsack problem. In: IEEE Proceedings of the International Conference on Computers and Industrial Engineering, pp. 279–284 (2009)
Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0-1 knapsack problem. Manage. Sci. 45, 414–424 (1999)
Pferschy, U., Schauer, J.: The knapsack problem with conflict graphs. J. Graph Algorithms Appl. 13, 233–249 (2009)
Pisinger, D., Sigurd, M.: Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem. INFORMS J. Comput. 19, 36–51 (2007)
Pisinger, D., Ropke, S.: Large neighborhood search. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146, pp. 399–419. Springer, New York (2010)
Sadykov, R., Vanderbeck, F.: Bin packing with conflicts: a generic branch-and-price algorithm. INFORMS J. Comput. 25(2), 244–255 (2013)
Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)
Yamada, T., Kataoka, S., Watanabe, K.: Heuristic and exact algorithms for the disjunctively constrained knapsack problem. Inf. Process. Soc. Jap. J. 43, 2864–2870 (2002)
Yamada, T., Kataoka, S.: Heuristic and exact algorithms for the disjunctively constrained knapsack problem. In: EURO 2001, Rotterdam, The Netherlands, pp. 9–11 (2001)
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Hifi, M., Saleh, S., Wu, L. (2014). A Fast Large Neighborhood Search for Disjunctively Constrained Knapsack Problems. In: Fouilhoux, P., Gouveia, L., Mahjoub, A., Paschos, V. (eds) Combinatorial Optimization. ISCO 2014. Lecture Notes in Computer Science(), vol 8596. Springer, Cham. https://doi.org/10.1007/978-3-319-09174-7_34
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DOI: https://doi.org/10.1007/978-3-319-09174-7_34
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