An exact algorithm for the knapsack sharing problem

Computers and Operations Research

Volumn 32, Issue 5, 2005, Pages 1311-1324

  Hifi, Mhand ^a,b,c   M'Halla, Hedi ^b   Sadfi, Slim ^a,b  

^a LaRIA   (France)

^b UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

^c PSL RESEARCH UNIVERSITY   (France)

Author keywords

Combinatorial optimization; Dynamic programming; Heuristics; Knapsack sharing; Optimization; Stabilization

Indexed keywords

COMPUTER SYSTEMS; DYNAMIC PROGRAMMING; HEURISTIC METHODS; MATHEMATICAL PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING;

COMBINATORIAL OPTIMIZATION; CRITICAL ELEMENTS; HEURISTIC APPROACH; KNAPSACK SHARING;

ALGORITHMS;

EID: 7544247596     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2003.11.005     Document Type: Article

References (25)

1. Gilmore P.C., Gomory R.E. The theory and computation of knapsack functions. Operations Research. 13:1966;879-919.
2. Hifi M., Zissimopoulos V. A recursive exact algorithm for weighted two-dimensional cutting. European Journal of Operational Research. 91:1996;553-564.
3. Martello S, Toth P, editors. Knapsack problems: algorithms and computer implementation. New York: Wiley; 1990.
4. Morabito R., Arenales M. Performance of two heuristics for solving large scale two-dimensional guillotine cutting problems. INFOR. 33:1995;145-155.
5. Hifi M., Roucairol C. Approximate and exact algorithms for constrained (un)weighted two-dimensional two-staged cutting stock problems. Journal of Combinatorial Optimization. 5:2001;465-494.
6. Valéro de Carvalho J.M., Ridrigues A.J. An LP-based approach to a two-stage cutting stock problem. European Journal of Operational Research. 84:1995;580-589.
7. Brown J.R. The knapsack sharing. Operations Research. 27:1979;341-355.
8. Tang C.S. A max-min allocation problem: its solutions and applications. Operations Research. 36:1988;359-367.
9. Martello S., Toth P. Upper bounds and algorithms for hard 0-1 knapsack problems. Operations Research. 45:1997;768-778.
10. Yamada T., Futakawa M. Heuristic and reduction algorithms for the knapsack sharing problem. Computers and Operations Research. 24:1997;961-967.
11. Hifi M., Sadfi S. The knapsack sharing problem. an exact algorithm Journal of Combinatorial Optimization. 6:2002;35-54.
12. Horowitz E., Sahni S. Computing partitions with applications to the knapsack problem. Journal of ACM. 21:1974;277-292.
13. Balas E., Zemel E. An algorithm for large zero-one knapsack problems. Operations Research. 28:1980;1130-1154.
14. Fayard D., Plateau G. An algorithm for the solution of the 0-1 knapsack problem. Computing. 28:1982;269-287.
15. Martello S., Pisinger D., Toth P. New trends in exact algorithms for the 0-1 knapsack problem. European Journal of Operational Research. 123:2000;325-332.
16. Pisinger D, Toth P. Knapsack problems, In: Du D-Z, Pardalos P, editors, Handbook of Combinatorial Optimization, Vol. 1, Dordrecht: Kluwer Academic Publishers; 1998. p. 299-428.
17. Martello S., Pisinger D., Toth P. Dynamic Programming and strong bounds for the 0-1 knapsack problem. Management Science. 45:1999;414-424.
18. Chu P., Beasley J.E. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics. 4:1998;63-86.
19. Freville A., Plateau G. The 0-1 bidimensional knapsack problem. toward an efficient high-level primitive tool Journal of Heuristics. 3:1996;147-167.
20. Brown J.R. Solving knapsack sharing with general tradeoff functions. Mathematical Programming. 5:1991;55-73.
21. Kuno T., Konno H., Zemel E. A linear-time algorithm for solving continuous maximum knapsack problems. Operations Research Letters. 10:1991;23-26.
22. Luss H. Minmax resource allocation problems. optimization and parametric analysis European Journal of Operational Research. 60:1992;76-86.
23. Pang J.S., Yu C.S. A min-max resource allocation problem with substitutions. European Journal of Operational Research. 41:1989;218-223.
24. Hifi M., Sadfi S., Sbihi A. An efficient algorithm for the knapsack sharing problem. Computational Optimization and Applications. 23:2002;27-45.
25. Yamada T., Futakawa M., Kataoka S. Some exact algorithms for the knapsack sharing problem. European Journal of Operational Research. 106:1998;177-183.