Fast, effective heuristics for the 0-1 multi-dimensional knapsack problem

Computers and Operations Research

Volumn 36, Issue 5, 2009, Pages 1602-1607

  Fleszar, Krzysztof ^a   Hindi, Khalil S ^a  

^a AMERICAN UNIVERSITY OF BEIRUT   (Lebanon)

Author keywords

Heuristics; LP relaxation; Multi dimensional knapsack problem

Indexed keywords

CARBON FIBER REINFORCED PLASTICS; INTEGER PROGRAMMING; SOLUTIONS;

BENCHMARK PROBLEMS; HEURISTICS; KNAPSACK CONSTRAINTS; KNAPSACK PROBLEMS; LINEAR RELAXATIONS; LP RELAXATION; LP RELAXATIONS; MAXIMUM VALUES; MULTI-DIMENSIONAL; MULTI-DIMENSIONAL KNAPSACK PROBLEM; SOLUTION METHODS;

HEURISTIC METHODS;

EID: 55749107142     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2008.03.003     Document Type: Article

References (24)

1. Freville A., and Plateau G. An efficient preprocessing procedure for the multidimensional 0-1 knapsack problem. Discrete Applied Mathematics 49 (1994) 189-212
2. Bertsimas D., and Demir R. An approximate dynamic programming approach to multidimensional knapsack problems. Management Science 48 4 (2002) 550-565
3. Rothkopf MH, Pekec A, Harstad RM. Computationally manageable combinatorial auctions. Technical Report 95-09, Rutgers University, Piscataway, NJ; 1995.
4. DeVries S, Vohra R. Combinatorial auctions: a survey. Technical Report, Northwestern University, Evanston, IL; 2000.
5. Ferreira C., Grotschel M., Kiefl S., Krispenz C., Martin A., and Weismantel R. Some integer programs arising in the design of mainframe computers. ZOR-Methods Models Operation Research 38 1 (1993) 77-110
6. Peterson C.C. Computational experience with variants of the balas algorithm applied to the selection of research and development projects. Management Science 13 (1967) 736-750
7. Gilmore P.C., and Gomory R.E. The theory and computation of knapsack functions. Operations Research 14 (1966) 1045-1075
8. Freville A. The multidimensional 0-1 knapsack problem: an overview. European Journal of Operational Research 155 (2004) 1-21
9. Freville A., and Hanafi S. The multidimensional 0-1 knapsack problem-bounds and computational aspects. Annals of Operations Research 139 1 (2005) 195-227
10. Hanafi S., and Glover F. Exploiting nested inequalities and surrogate constraints. European Journal of Operational Research 179 1 (2007) 50-63
11. Osorio M.A., Glover F., and Hammer P. Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions. Annals of Operations Research 117 1-4 (2002) 71-93
12. Akcay Y., Li H., and Xu S.H. Greedy algorithm for the general multidimensional knapsack problem. Annals of Operations Research 150 1 (2007) 17-29
13. Toyoda Y. A simplified algorithm for obtaining approximate solutions to zero-one programming problems. Management Science 21 (1975) 1417-1427
14. Senju S., and Toyoda Y. An approach to linear programming with 0-1 linear variables. Management Science 15 (1968) 196-207
15. Loulou R., and Michaelides E. New greedy-like heuristics for the multidimensional 0-1 knapsack problem. Operations Research 27 6 (1979) 1101-1114
16. Kochenberger G.A., McCarl B.A., and Wyman F.P. A heuristic for general integer programming. Decision Sciences 5 1 (1974) 36-44
17. Magazine M.J., and Oguz O. Heuristic algorithm for the multidimensional zero-one knapsack problem. European Journal of Operational Research 16 3 (1984) 319-326
18. Volgenant A., and Zoon J.A. An improved heuristic for multidimensional 0-1 knapsack problem. Journal of Operational Research Society 41 10 (1990) 963-970
19. Volgenant A., and Zwiers I.Y. Partial enumeration in heuristics for some combinatorial optimization problems. Journal of the Operational Research Society 58 1 (2007) 73-79
20. Chu P.C., and Beasley J.E. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4 1 (1998) 63-86
21. Vasquez M, Hao J-K. A hybrid approach for the 0-1 multidimensional knapsack problem. In: IJCAI-01 Proceedings of the 7th international joint conference on artificial intelligence, Seatle, Washington, 2001. p. 328-33.
22. Vasquez M., and Vimont Y. Improved results on the 0-1 multidimensional knapsack problem. European Journal of Operational Research 165 1 (2005) 70-81
23. Pirkul H. Heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Research Logistics 34 2 (1987) 161-172
24. Gavish B., and Pirkul H. Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality. Mathematical Programming 31 1 (1985) 78-105