The multidimensional knapsack problem: Structure and algorithms

INFORMS Journal on Computing

Volumn 22, Issue 2, 2010, Pages 250-265

  Puchinger, Jakob ^a   Raidl, Günther R ^b   Pferschy, Ulrich ^c  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^c UNIVERSITY OF GRAZ   (Austria)

Author keywords

Heuristics; Integer linear programming; Multidimensional knapsack problem

Indexed keywords

EID: 77952042144     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1090.0344     Document Type: Article

References (34)

1. Balas, E., E. Zemel. 1980. An algorithm for large zero-one knapsack problems. Oper. Res. 28(5) 1130-1154.
2. Balev, S., N. Yanev, A. Fréville, R. Andonov. 2008. A dynamic programming based reduction procedure for the multidimensional knapsack problem. Eur. J. Oper. Res. 186(1) 63-76.
3. Bertsimas, D., J. N. Tsitsiklis. 1997. Introduction to Linear Optimization. Athena Scientific, Nashua, NH.
4. Chu, P. C., J. E. Beasley. 1998. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 4(1) 63-86.
5. Danna, E., E. Rothberg, C. Le Pape. 2003. Integrating mixed integer programming and local search: A case study on job-shop scheduling problems. Fifth Internat. Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optim. Problems (CP-AI-OR 2003), Montreal, 65-79. http://www.crt.umontreal.ca/cpaior.
6. Dobson, G. 1982. Worst-case analysis of greedy heuristics for integer programming with nonnegative data. Math. Oper. Res. 7(4) 515-531.
7. Dyer, M. E., A. M. Frieze. 1989. Probabilistic analysis of the multidimensional knapsack problem. Math. Oper. Res. 14(1) 162-176.
8. Fischetti, M., A. Lodi. 2003. Local branching. Math. Programming Ser. B 98(1-3) 23-47.
9. Fréville, A. 2004. The multidimensional 0-1 knapsack problem: An overview. Eur. J. Oper. Res. 155(1) 1-21.
10. Fréville, A., S. Hanafi. 2005. The multidimensional 0-1 knapsack problem-Bounds and computational aspects. Ann. Oper. Res. 139(1) 195-227.
11. Fréville, A., G. Plateau. 1994. An efficient preprocessing procedure for the multidimensional 0-1 knapsack problem. Discrete Appl. Math. 49(1-3) 189-212.
12. Gavish, B., H. Pirkul. 1985. Efficient algorithms for solving the multiconstraint zero-one knapsack problem to optimality. Math. Programming 31(1) 78-105.
13. Gilmore, P. C., R. E. Gomory. 1966. The theory and computation of knapsack functions. Oper. Res. 14(6) 1045-1075.
14. Glover, F., G. A. Kochenberger. 1996. Critical event tabu search for multidimensional knapsack problems. I. H. Osman, J. P. Kelly, eds. Metaheuristics: Theory and Applications. Kluwer Academic Publishers, Boston, 407-427.
15. Goldberg, A. V., A. Marchetti-Spaccamela. 1984. On finding the exact solution of a zero-one knapsack problem. STOC '84: Proc. 16th Annual ACM Sympos. Theory Comput., ACM Press, New York, 359-368.
16. Gomes da Silva, C., J. Clímaco, J. R. Figueira. 2008. Core problems in bi-criteria {0, 1}-knapsack. Comput. Oper. Res. 35(7) 2292-2306.
17. Gottlieb, J. 1999. On the effectivity of evolutionary algorithms for multidimensional knapsack problems. C. Fonlupt, J.-K. Hao, E. Lutton, E. Ronald, M. Schoenaver, eds. Artificial Evolution: Proc. Fourth Eur. Conf., Lecture Notes in Computer Science, Vol.1829. Springer, Berlin, 23-37.
18. Kellerer, H., U. Pferschy, D. Pisinger. 2004. Knapsack Problems. Springer, Berlin.
19. Martello, S., P. Toth. 1988. A new algorithm for the 0-1 knapsack problem. Management Sci. 34(5) 633-644.
20. Pisinger, D. 1995. An expanding-core algorithm for the exact 0-1 knapsack problem. Eur. J. Oper. Res. 87(1) 175-187.
21. Pisinger, D. 1997. A minimal algorithm for the 0-1 knapsack problem. Oper. Res. 45(5) 758-767.
22. Pisinger, D. 1999. Core problems in knapsack algorithms. Oper. Res. 47(4) 570-575.
23. Puchinger, J. 2006. Combining metaheuristics and integer programming for solving cutting and packing problems. Ph.D. thesis, Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna.
24. Puchinger, J., G. R. Raidl. 2005. Combining metaheuristics and exact algorithms in combinatorial optimization: A survey and classification. J. Mira, J. R. Álvarez, eds. Artifical Intelligence Knowledge Engineering Applications: A Bioinspired Approach. Proc. First Internat. Work-Conference on the Interplay Between Natural and Artificial Comput., Lecture Notes in Computer Science, Vol.3562. Springer, Berlin, 41-53.
25. Puchinger, J., G. R. Raidl, M. Gruber. 2005. Cooperating memetic and branch-and-cut algorithms for solving the multidimensional knapsack problem. Proc. Sixth Metaheuristics Internat. Conf. (MIC 2005), Vienna, 775-780.
26. Puchinger, J., G. R. Raidl, U. Pferschy. 2006. The core concept for the multidimensional knapsack problem. J. Gottlieb, G. R. Raidl, eds. Evolutionary Comput. Combinatorial Optim.-EvoCOP 2006, Lecture Notes in Computer Science, Vol.3906. Springer, Berlin, 195-208.
27. Raidl, G. R. 1998. An improved genetic algorithm for the multiconstrained 0-1 knapsack problem. D. Fogel et al., eds. Proc. Fifth IEEE Internat. Conf. Evolutionary Comput., IEEE Press, Piscataway, NJ, 207-211.
28. Raidl, G. R., J. Gottlieb. 2005. Empirical analysis of locality, heritability and heuristic bias in evolutionary algorithms: A case study for the multidimensional knapsack problem. Evolutionary Comput. J. 13(4) 441-475.
29. Rinnooy Kan, A. H. G., L. Stougie, C. Vercellis. 1993. A class of generalized greedy algorithms for the multi-knapsack problem. Discrete Appl. Math. 42(2-3) 279-290.
30. Senju, S., Y. Toyoda. 1968. An approach to linear programming with 0-1 variables. Management Sci. 15(4) B-196-B-207.
31. Shih, W. 1979. A branch and bound method for the multiconstraint zero-one knapsack problem. J. Oper. Res. Soc. 30(4) 369-378.
32. Vasquez, M., J.-K. Hao. 2001. A hybrid approach for the 0-1 multidimensional knapsack problem. Proc. Internat. Joint Conf. Artificial Intelligence 2001 (IJCAI-01), Seattle, 328-333.
33. Vasquez, M., Y. Vimont. 2005. Improved results on the 0-1 multidimensional knapsack problem. Eur. J. Oper. Res. 165(1) 70-81.
34. Weingartner, H. M., D. N. Ness. 1967. Methods for the solution of the multidimensional 0/1 knapsack problem. Oper. Res. 15(1) 83-103.