A reactive local search-based algorithm for the disjunctively knapsack problem

International audienceIn this paper, we propose a reactive local search-based algorithm for the disjunctively constrained knapsack problem (DCKP). DCKP is a variant of the standard knapsack problem, an NP-hard combinatorial optimization problem, with special disjunctive constraints. A disjunctive constraint is a couple of items for which only one item is packed. The proposed algorithm is based upon a reactive local search, where an explicit check for the repetition of configurations is added to the search process. Initially, two complementary greedy procedures are applied in order to construct a starting solution. Second, a degrading procedure is introduced in order (i) to escape to local optima and (ii) to introduce a diversification in the search space. Finally, a memory list is added in order to forbid the repetition of configurations. The performance of two versions of the algorithm has been evaluated on several problem instances and compared to the results obtained by running the Cplex solver. Encouraging results have been obtained

Benckmark inctances of the disjunctively constrained knapsack problem (DCKP)

This dataset includes the 6340 benchmark instances of the disjunctively constrained knapsack problem (DCKP). The first set I of 100 instances was introduced in [1] and [2]. The second set II of 6240 instances was introduced in [3] and expanded in [4]. We would like to thank these authors and co-authors for sharing the instances of the DCKP. The 6240 results obtained by our TSBMA algorithm in [5] are also presented here.[1] M. Hifi, M. Michrafy, A reactive local search-based algorithm for the disjunctively constrained knapsack problem, Journal of the Operational Research Society 57 (6) (2006) 718-726.[2] Z. Quan, L. Wu, Cooperative parallel adaptive neighbourhood search for the disjunctively constrained knapsack problem, Engineering Optimization 49 (9) 636 (2017) 1541-1557.[3] A. Bettinelli, V. Cacchiani, E. Malaguti, A branch-and-bound algorithm for the knapsack problem with conflict graph, INFORMS Journal on Computing 29 (3) (2017) 457-473.[4] S. Coniglio, F. Furini, P. San Segundo, A new combinatorial branch-and-bound algorithm for the knapsack problem with conflicts, European Journal of Operational Research 289 (2) (2021) 435-455.[5] Zequn WEI, Jin-Kao HAO. A threshold search based memetic algorithm for the disjunctively constrained knapsack problem. Computers & Operations Research. 136(2021) 105447.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Approaches For The 2d 0-1 Knapsack Problem With Conflict Graphs

This work deals with the 0-1 knapsack problem in its two-dimensional variant, when there is a conflict graph related to pairs of conflicting items. Conflicting items must not be packed together in a same bin. This problem also arises as a subproblem in the bin packing problem and in supply chain scenarious. We propose a heuristic that generates iteratively a solution using a so called greedy randomized procedure. In order to avoid local optima solutions, a penalization memory list is used, and several packing strategies under a two-dimensional grid of points are considered. The heuristic solutions are compared with those ones computed by means of an integer programming model, also proposed in this work and solved with CPLEX solver. The heuristic got optimal solutions for 75% of the instances in a lower CPU time compared with that to solve the integer model. © 2013 IEEE.Epstein, L., Levin, A., Stee, R.V., Two-dimensional packing with conflicts (2008) Acta Informatica, 45 (3), pp. 155-175Birgin, E.G., Lobato, R.D., Morabito, R., An effective recursive partitioning approach for the packing of identical rectangles in a rectangle (2010) Journal of the Operational Research Society, 61 (2), pp. 306-320Queiroz, T.A., Miyazawa, F., Wakabayashi, Y., Xavier, E., Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing (2012) Computers & Operations Research, 39, pp. 200-212Garey, M.R., Johnson, D.S., (1979) Computers and Intractability: A Guide to the Theory of NP-completeness, , San Francisco: FreemanYamada, T., Kataoka, S., Heuristic and exact algorithms for the disjunctively constrained knapsack problem (2001) Presented at EURO 2001: Rotterdam, , The NetherlandsYamada, T., Kataoka, S., Watanabe, K., Heuristic and exact algorithms for the disjunctively constrained knapsack problem (2002) Information Processing Society of Japan Journal, 43, pp. 2864-2870Hifi, M., Michrafy, M., A reactive local search-based algorithm for the disjunctively constrained knapsack problem (2006) Journal of the Operational Research Society, 57, pp. 718-726Hifi, M., Michrafy, M., Reduction strategies and exact algorithms for the disjunctively constrained knapsack problem (2007) Computers & Operations Research, 34, pp. 2657-2673Pferschy, U., Schauer, J., The knapsack problem with conflict graphs (2009) Journal of Graph Algorithms and Applications, 13 (2), pp. 233-249Akeb, H., Hifi, M., Mounir, M.E.O.A., Local branchingbased algorithms for the disjunctively constrained knapsack problem (2011) Computers & Industrial Engineering, 60, pp. 811-820Hifi, M., Otmani, N., An algorithm for the disjunctively constrained knapsack problem (2012) International Journal of Operational Research, 13, pp. 22-43Queiroz, T.A., Miyazawa, F.K., Problema da mochila 0-1 bidimensional com restricoes de disjuncao (2012) Anais Do XLIV Simpósio Brasileiro de Pesquisa Operacional, pp. 1-12. , Rio de Janeiro-RJJansen, K., Hring, S.O., Approximation algorithms for time constrained scheduling (1997) Information and Computation, 132 (2), pp. 85-108Khanafer, A., Clautiaux, F., Talbi, E.-G., New lower bounds for bin packing problems with conflicts (2010) European Journal of Operational Research, 206 (2), pp. 281-288Muritiba, A.E.F., Iori, M., Malaguti, E., Toth, P., Algorithms for the bin packing problem with conflicts (2010) INFORMS Journal on Computing, 22 (3), pp. 401-415Khanafer, A., Clautiaux, F., Talbi, E.-G., Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts (2012) Computers & Operations Research, 39, pp. 54-63Herz, J.C., A recursive computational procedure for two-dimensional stock-cutting (1972) IBM Journal of Research Development, pp. 462-469Scheithauer, G., Terno, J., The G4-heuristic for the pallet loading problem (1996) Journal of the Operational Research Society, 47, pp. 511-522Cintra, G.F., Miyazawa, F.K., Wakabayashi, Y., Xavier, E.C., Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation (2008) European Journal of Operational Research, 191, pp. 59-83Feo, T.A., Resende, M.G.C., A probabilistic heuristic for a computationally difficult set covering problem (1989) Operations Research Letters, 8, pp. 67-71Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., Optimization by simulated annealing (1983) Science, 220 (4598), pp. 671-680Martello, S., Vigo, D., Exact solution of the two-dimensional finite bin packing problem (1998) Management Science, 44 (3), pp. 388-39