Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T06:45:23.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Une approche hybride pour le sac à dos multidimensionnel en variables 0–1

Published online by Cambridge University Press:  15 August 2002

Michel Vasquez  and
Jin-Kao Hao
Michel Vasquez
Affiliation:
LGI2P, Parc Scientifique Georges Besse, 30035 Nimes Cedex 1, France ; [email protected].
Jin-Kao Hao
Affiliation:
LERIA, Université d'Angers, 2 bd Lavoisier, 49045 Angers Cedex 1, France ; [email protected].
Get access

Abstract

We present, in this article, a hybrid approach forsolvingthe 0–1 multidimensional knapsack problem (MKP). This approach combineslinearprogramming and Tabu search.The resulting algorithm improves on the best result on many well-knownhard benchmarks.

Keywords

Sac-à-dos multidimensionnelprogrammation linéairerecherche tabou.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 4 , October 2001 , pp. 415 - 438
Copyright
© EDP Sciences, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aboudi, R. et Jörnsten, K., Tabu Search for General Zero-One Integer Programs using the Pivot and Complement Heuristic. ORSA J. Comput. 6 (1994) 82-93. CrossRef
Balas, E. et Martin, C.H., Pivot and Complement a Heuristic for 0-1 Programming. Management Sci. 26 (1980) 86-96. CrossRef
Battiti, R. et Tecchiolli, G., The reactive tabu search. ORSA J. Comput. 6 (1994) 128-140. CrossRef
R. Bellman et D. Stuart, Applied Dynamic Programming. Princeton University Press (1962).
P. Boucher et G. Plateau, Étude des méthodes de bruitage appliquées au problème du sac à dos à plusieurs contraintes en variables 0-1, dans JNPCC'99 5es journées nationales sur la résolution pratique de problèmes NP-complets (1999) 151-162.
Charon, I. et Hudry, O., The noising method: A new method for combinatorial optimization. Oper. Res. Lett. 14 (1993) 133-137. CrossRef
Chu, P.C. et Beasley, J.E., A genetic algorithm for the multidimensional knapsack problem. J. Heuristic 4 (1998) 63-86. CrossRef
Dammeyer, F. et Voß, S., Dynamic tabu list management using the reverse elimination method. Ann. Oper. Res. 41 (1993) 31-46. CrossRef
Dantzig, G.B., Discrete-variable extremum problems. Oper. Res. 5 (1957) 266-277. CrossRef
Drexl, A., A simulated annealing approach to the multiconstraint zero-one knapsack problem. Computing 40 (1988) 1-8. CrossRef
Fréville, A. et Plateau, G., Heuristic and reduction methods for multiple constraints 0-1 linear programming problems. Eur. J. Oper. Res. 24 (1986) 206-215. CrossRef
Fréville, A. et Plateau, G., Sac à dos multidimensionnel en variable 0-1 : encadrement de la somme des variables à l'optimum. RAIRO: Oper. Res. 27 (1993) 169-187. CrossRef
Fréville, A. et Plateau, G., The 0-1 bidimensional knapsack problem: Toward an efficient high-level primitive tool. J. Heuristics 2 (1997) 147-167.
X. Gandibleux et A. Fréville, The multiobjective tabu search method customized on the 0/1 multiobjective knapsack problem: The two objectives case. J. Heuristics (à paraître).
M. Garey et D. Johnson, Computers & Intractability A Guide to the Theory of NP-Completeness. W.H. Freeman and Company (1979).
Gavish, B. et Pirkul, H., Allocation of data bases and processors in a distributed computting system. Management of Distributed Data Processing 31 (1982) 215-231.
Gavish, B. et Pirkul, H., Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality. Math. Programming 31 (1985) 78-105. CrossRef
Gilmore, P.C. et Gomory, R.E., The theory and computation of knapsack functions. Oper. Res. 14 (1966) 1045-1074. CrossRef
Glover, F., Tabu search. ORSA J. Computing 2 (1990) 4-32. CrossRef
F. Glover et G.A. Kochenberger, Critical event tabu search for multidimensional knapsack problems, edité par I.H. Osman et J.P. Kelly, Metaheuristics: The Theory and Applications. Kluwer Academic Publishers (1996) 407-427.
M. Gondran et M. Minoux, Graphes & algorithmes. Eyrolles (1985).
S. Hanafi, A. El Abdellaoui et A. Fréville, Extension de la Méthode d'Élimination Inverse pour une gestion dynamique de la liste tabou. RAIRO (à paraître).
Hanafi, S. et Fréville, A., An efficient tabu search approach for the 0-1 multidimensional knapsack problem. Eur. J. Oper. Res. 106 (1998) 659-675. CrossRef
Lee, J.S. et Guignard, M., An approximate algorithm for multidimensional zero-one knapsack problems a parametric approach. Management Sci. 34 (1998) 402-410. CrossRef
Lorie, J. et Savage, L.J., Three problems in capital rationing. J. Business 28 (1955) 229-239. CrossRef
A. Lo/kketangen et F. Glover, Solving zéro-one mixed integer programming problems using tabu search. Eur. J. Oper. Res. 106 (1998). Special Issue on Tabu Search.
A. Lo/kketangen et F. Glover, Candidate list and exploration strategies for solving 0/1 mip problems using a pivot neighborhood, dans Metaheuristics. Kluwer Academic Publishers (1999).
S. Martello et P. Toth, Knapsack Problems: Algorithms and Computer Implementations. John Wiley (1990).
M.A. Osorio, F. Glover et P. Hammer, Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions, Technical report. Hearin Center for Enterprise Science. Report HCES-08-00 (2000).
W.H. Press, S.A. Teukolsky, W.T. Vetterling et B.P. Flannery, Numerical Recipes in C. Cambridge University Press (1992).
Shih, W., A branch & bound method for the multiconstraint zero-one knapsack problem. J. Oper. Res. Soc. 30 (1979) 369-378. CrossRef
Toyoda, Y., A simplified algorithm for obtaining approximate solutions to zero-one programming problem. Management Sci. 21 (1975) 1417-1427. CrossRef