An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem

European Journal of Operational Research

Volumn 199, Issue 2, 2009, Pages 339-348

  Wilbaut, Christophe ^a   Salhi, Saïd ^b   Hanafi, Saïd ^a  

^a UNIVERSITÉ DE VALENCIENNES   (France)

^b UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Exact methods; Fixation techniques; Heuristics; Knapsack

Indexed keywords

0-1 MULTIDIMENSIONAL KNAPSACK PROBLEMS; EXACT METHODS; FEASIBLE SOLUTIONS; FIXATION TECHNIQUES; HEURISTICS; ITERATIVE SCHEMES; KNAPSACK; SEARCH SPACES;

INTEGER PROGRAMMING;

HEURISTIC METHODS;

EID: 67349260706     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2008.11.036     Document Type: Article

References (30)

1. Babayev D.A., and Mardanov S.S. Reducing the number of variables in integer and linear programming problems. Computational Optimization and Applications 3 (1994) 99-109
2. Beasley J.E. OR-Library: distributing test problems by electronic mail. Journal of the Operational Research Society 41 (1990) 1069-1072
3. Chu P., and Beasley J.E. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4 (1998) 63-86
4. Danna E., Rothberg E., and Le Pape C. Exploring relaxations induced neighborhoods to improve MIP solutions. Mathematical Programming 102 (2005) 71-90
5. Fischetti M., and Lodi A. Local branching. Mathematical Programming 98 (2003) 23-47
6. Fleszar K., and Hindi K.S. Fast, effective heuristics for the 0-1 multi-dimensional knapsack problem. Computers and Operations Research (2008) 10.1016/j.cor.2008.03.003
7. Fréville A., and Hanafi S. The multidimensional 0-1 knapsack problem - bounds and computational aspects. Annals of Operations Research 139 (2005) 195-227
8. Gilmore P.C., and Gomory R.E. The theory and computation of knapsack functions. Operations Research 14 (1966) 1045-1075
9. Glover F. Adaptive memory projection methods for integer programming. In: Rego C., and Alidaee B. (Eds). Metaheuristic Optimization Via Memory and Evolution (2005), Kluwer Academic Publishers 425-440
10. Glover F., and Kochenberger G. Critical event tabu search for multidimensional knapsack problems. In: Osman I., and Kelly J. (Eds). Meta Heuristics: Theory and Applications (1996), Kluwer Academic Publishers 407-427
11. Hanafi S., and Fréville A. An efficient tabu search approach for the 0-1 multidimensional knapsack problem. European Journal of Operational Research 106 (1998) 659-675
12. Hanafi S., and Glover F. Exploiting nested inequalities and surrogate constraints. European Journal of Operational Research 179 (2007) 50-63
13. Kellerer H., Pferschy U., and Pisinger D. Knapsack Problems (2004), Springer
14. Lorie J.H., and Savage L.J. Three problems in capital rationing. The Journal of Business 28 (1955) 229-239
15. Meier H., Christofides N., and Salkin G. Capital budgeting under uncertaintyan integrated approach using contingent claims analysis and integer programming. Operations Research 49 (2001) 196-206
16. Nemhauser G.L., and Wolsey L.A. Integer and Combinatorial Optimization (1999), Wiley-Interscience, New York
17. Osorio M.A., Glover F., and Hammer P. Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions. Annals of Operations Research 117 (2002) 71-93
18. Salhi S., and Drezner Z. Location analysis: theory and applications. IMA - Journal of Management Mathematics 17 (2007) 305-425
19. Savelsberg M.W.P. Preprocessing and probing techniques for mixed integer programming problems. ORSA Journal of Computing 6 (1994) 445-454
20. Shih W. A branch and bound method for the multiconstraint zero-one knapsack problem. Journal of the Operational Research Society 30 (1979) 369-378
21. Vasquez M., and Hao J.K. A logic-constrained knapsack formulation and a tabu algorithm for the daily photograph scheduling of an earth observation satellite. Computational Optimization and Applications 20 (2001) 137-157
22. Vasquez M., and Hao J.K. Une approche hybride pour le sac à dos multidimensionnel en variables 0-1. RAIRO Operations Research 35 (2001) 415-438
23. Vasquez M., and Vimont Y. Improved results on the 0-1 multidimensional knapsack problem. European Journal of Operational Research 165 (2005) 70-81
24. Volgenant A., and Zwiers I.Y. Partial enumeration in heuristics for some combinatorial optimization problems. Journal of the Operational Research Society 58 (2007) 73-79
25. Weingartner H.M. Capital budgeting of interrelated projects: survey and synthesis. Management Science 12 (1966) 485-516
26. Wilbaut, C., 2006. Heuristiques hybrides pour la résolution de problèmes en nombres entiers mixtes. Ph.D. Thesis, Université de Valenciennes et du Hainaut Cambrésis.
27. Wilbaut C., and Hanafi S. New convergent heuristics for 0-1 mixed integer programming. European Journal of Operational Research 195 (2009) 62-74
28. Wilbaut C., Hanafi S., Fréville A., and Balev S. Tabu search: global intensification using dynamic programming. Control and Cybernetic 35 3 (2006) 579-598
29. Wilbaut C., Hanafi S., and Salhi S. A survey of effective heuristics and their application to a variety of knapsack problems. IMA - Journal of Management Mathematics (2008) 10.1093/imaman/dpn004
30. Zhu N., and Broughan K. A note on reducing the number of variables in integer programming problems. Computational Optimization and Applications 8 (1997) 263-272