Cutting analysis for MKP

Proceedings of the Fifth Mexican International Conference in Computer Science, ENC 2004

Volumn , Issue , 2004, Pages 298-303

  Osorio, María A ^a   Hernández, Edgar Gómez ^a  

^a BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONSTRAINT THEORY; DATA ACQUISITION; GENETIC ALGORITHMS; HEURISTIC METHODS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY; TREES (MATHEMATICS);

BINARY PROBLEMS; CUTTING ANALYSIS; LANGRAGIAN RELAXATION THEORY; MULTIDIMENSIONAL KNAPSACK STRATEGY (MKP);

FORMAL LOGIC;

EID: 14244267930     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ENC.2004.1342620     Document Type: Conference Paper

References (26)

1. E. Balas, An Additive Algorithm for Solving Linear Programs with Zero-One Variables, Operations Research 13 (1965) 517-546.
2. P. Chu and J. Beasley, A Genetic Algorithm for the Multidimensional Knapsack Problem, Journal of Heuristics 4 (1998) 63-86.
3. Y. Crama and J. Mazzola,. On the Strength of Relaxations of Multidimensional Knapsack Problems, INFOR 32 (1994) 219-225.
4. G.B. Dantzig, Discrete Variables Problems, Operations Research 5 (1957) 266-277.
5. R. Dembo and P. Hammer, A Reduction Algorithm for Knapsack Problems, Methods of O.R. 36 (1980) 49-60.
6. A. Fréville and G. Plateau, Hard 0-1 Multiknapsack Test Problems for Size Reduction Methods, Investigación Operativa 1 (1990), 251-270.
7. A. Fréville and G. Plateau, An efficient preprocessing procedure for the multidimensional 0-1 knapsack problem, Discrete Applied Mathematics 49 (1994) 189-212.
8. B. Gavish and H. Pirkul, Efficient Algorithms for Solving Multiconstraint Zero-One Knapsack Problems to Optimality, Mathematical Programming 31 (1985) 78-105.
9. F. Glover, Surrogate Constraints, Operations Research 16 (1968) 741-749.
10. F. Glover, Flows in Arborescences, Management Science, 17 (1971) 568-586.
11. F. Glover, Surrogate Constraint Duality in Mathematical Programming, Operations Research 23 (1975) 434-451.
12. F. Glover and G.A. Kochenberger, Critical Event Tabu Search for Multidimensional Knapsack Problems, in Meta-Heuristics: Theory and Applications, eds. I.H. Osman and J.P. Kelly, Kluwer Academic Publishers, 1996, pp. 407-427.
13. F. Glover, H. Sherali and Y. Lee (1997). "Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming", Computational Optimization and Applications 8 (1997) 151-172.
14. F. Granot and P. L. Hammer, On the use of boolean functions in 0-1 linear programming, Methods of Operations Research (1971) 154-184.
15. P. Hammer, M. Padberg and U. Peled, Constraint Pairing in Integer Programming, INFOR 13 (1975) 68-81.
16. S. Hanafi and A. Fréville, An efficient tabu search approach for the 0-1 multidimensional knapsack problem, EJOR 106 (1998) 659-675.
17. J. N. Hooker, "Logic-based methods for optimization", in A. Borning, ed., Principles and Practice of Constraint Programming, Lecture Notes in Computer Science 874 (1994) 336-349.
18. J. N. Hooker and M.A. Osorio (1999). "Mixed Logical/Linear Programming". Discrete Applied Mathematics 96-97 (1999) 395-442.
19. A. Lǿkketangen and F. Glover, Probabilistic Move Selection in Tabu Search for Zero-One Mixed Integer Programming Problems, in: Meta-Heuristics: Theory and Applications, eds. I.H. Osman and J.P. Kelly, 1996, pp.467-487.
20. M.A. Osorio, F. Glover, and P. Hammer (2002). "Cutting and Surrogate Constraint Analysis for Improved Multidimensional Knapsack Solutions". Annals of Operations Research 117(2002), 71-93.
21. M.A. Osorio, and F. Glover, Exploiting Surrogate Constraint Analysis for Fixing Variables in both Bounds for Multidimensional Knapsack Problems, in Proc. Fourth Mexican Int. Conf. on Comp.Science, eds, E. Chávez et al., IEEE Computer Society (2003), 263-267.
22. M.A. Osorio, and M. Laguna, Logic Cuts for the Generalized Assignment Problem, European Journal of Operational Research 151(2003), 238-246.
23. M.A. Osorio, and R. Mújica, Logic Cuts Generation in a Branch and Cut Framework for Location Problems, Investigación Operativa, 8(1999), 155-166.
24. H. Pirkul, A Heuristic solution Procedure for the Multiconstraint Zero-One Knapsack, Problem, Naval Research Logistics 34 (1987) 161-172.
25. S. Senju, S. and Y. Toyoda, An Approach to Linear Programming with 0-1 Variables, Management Science 15 (1968) 196-207.
26. W. Shih, A Branch and Bound Method for the Multiconstraint Zero-one Knapsack Problem, J. Opl. Res. Soc. 30(1979), 369-378.