Solution of large quadratic knapsack problems through aggressive reduction

INFORMS Journal on Computing

Volumn 19, Issue 2, 2007, Pages 280-290

  Pisinger, W David ^a   Rasmussen, Anders Bo ^a   Sandvik, Rune ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Algorithms; Analysis of algorithms: Computational complexity; programming; Branch and bound; Integer; Programming; Quadratic; programming; Relaxation

Indexed keywords

EID: 35548981671     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1050.0172     Document Type: Article

References (21)

1. Balas, E, E. Zemel. 1980. An algorithm for large zero-one knapsack problems. Oper. Res. 28 1130-1154.
2. Billionnet, A., F. Calmels. 1996. Linear programming for the 0-1 quadratic knapsack problem. Eur. J. Oper. Res. 92 310-325.
3. Billionnct, A., A. Faye, E. Soutif. 1999. A new upper-bound and an exact algorithm for the 0-1 quadratic knapsack problem. Eur. J. Oper. Res. 112 664-672.
4. Caprara, A., D. Pisinger, P. Toth. 1999. Exact solution of the quadratic knapsack problem. INFORMS J. Comput. 11 125-137. Chaillou, P. P. Hansen, Y. Mahieu. 1989. Best network flow bound for the quadratic knapsack problem. B. Simcone, ed. Combi-natorial Optimization, Lecture Notes in Mathematics, Vol, 1403, Springer Verlag, Heidelberg, Germany, 225-235.
5. Cook, W., P. Seymour. 2003. Tour mergining via branch-decomposition. INFORMS J. Comput. 15 233-248.
6. Erkut, E. 1990. The discrete p-dispersion problem. Eur. J. Oper. Res. 46 48-60.
7. Ferreira, C. E., A. Martin, C. C. de Souza, R. Weismantel, L. A. Wolsey. 1996. Formulations and valid inequalities for node capacitated graph partitioning. Math. Programming 74 247-266.
8. Gallo, G., P. L. Hammer, B. Simeone. 1980. Quadratic knapsack problems. Math. Programming Stud. 12 132-149.
9. Hammer, P. L., D. J. Rader. 1997. Efficient methods for solving quadratic 0-1 knapsack problems. INFOR 35 170-182.
10. Helmberg, C., F. Rendl, R. Weismantel. 1996. Quadratic knapsack relaxations using cutting planes and semidefinite programming. W. H. Cunningham, S. T. McCormick, M. Queyranne, eds. Proc. Fifth IPCO Conf., Vol. 1084. Springer Verlag, Heidelberg, Germany, 175-189.
11. Johnson, E. L., A. Mehrotra, G. L. Nemhauser. 1993. Min-cut clustering. Math. Programming 62 133-152.
12. Kellerer, H., U. Pferschy, D. Pisinger. 2004. Knapsack Problems. Springer Verlag, Heidelberg, Germany.
13. Kincaid, R. K. 1992. Good solutions to discrete noxious location problems via metaheuristics. Ann. Oper. Res. 40 265-281.
14. Michelon, P., L. Veilleux. 1996. Lagrangean methods for the 0-1 quadratic knapsack problem. Eur. J. Oper. Res. 92 326-341.
15. Park, K., K. Lee, S. Park. 1996. An extended formulation approach to the edge-weighted maximal clique problem. Eur. J. Oper. Res. 95 671-682.
16. Pisinger, D. 2006. Upper bounds and exact algorithms for p-dispersion problems. Comput. Oper. Res. 33 1380-1398.
17. Polzin, T., S. Vahdati. 2002. Extending reduction techniques for the Steiner tree problem: A combination of alternative-and bound-based approaches. R. H. Möhring, R. Raman, eds. Algorithms-ESA 2002, Lecture Notes in Computer Science, Vol. 2461. Springer Verlag, Heidelberg, Germany, 795-807.
18. Rasmussen, A. B., R. Sandvik. 2002. Kvaliteten af gransev ærdier for det kvadratiske knapsack problem. Working Paper Project 02-09-7, (D. Pisinger, supervisor), DIKU, University of Copenhagen, Copenhagen, Denmark.
19. Rhys, J. 1970. A selection problem of shared fixed costs and network flows. Management Sci 17 200-207.
20. Thomadsen, T., J. Larsen. 2007. A hub location problem with fully interconnected backbone and access networks. Comput. Oper. Res. 34 2520-2531.
21. Witzgall, C. 1975. Mathematical methods of site selection for electronic message systems (EMS). Technical Report, National Bureau of Standards, Gaithersburg, MD.