Cover inequalities for robust knapsack sets-Application to the robust bandwidth packing problem

Networks

Volumn 59, Issue 1, 2012, Pages 59-72

  Klopfenstein, Olivier ^a   Nace, Dritan ^b  

^a ORANGE LABS   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

bandwidth packing problem; knapsack cover inequalities; knapsack set; polyhedral analysis; robust optimization; routing

Indexed keywords

KNAPSACK COVER INEQUALITIES; KNAPSACK SET; PACKING PROBLEMS; POLYHEDRAL ANALYSIS; ROBUST OPTIMIZATION; ROUTING;

BANDWIDTH; COMBINATORIAL OPTIMIZATION; OPTIMIZATION;

INTEGER PROGRAMMING;

EID: 83555166228     PISSN: 00283045     EISSN: 10970037     Source Type: Journal    
DOI: 10.1002/net.20488     Document Type: Article

References (24)

1. A. Atamtürk, Strong formulations of robust mixed 0-1 programming, Math Program 108 (2006), 235-250. (Pubitemid 43999759)
2. E. Balas, Facets of the knapsack polytope, Math Program 8 (1975), 146-164.
3. R. E. Bellman, Dynamic programming, Princeton University Press, Princeton, NJ, 1957 (Republished 2003).
4. P. Belotti, A. Capone, G. Carello, and, F. Malucelli, Multi-layer MPLS network design: The impact of statistical multiplexing, Comput Networks 52 (2008), 1291-1307.
5. A. Ben-Tal, and, A. Nemirovski, Robust solutions of linear programming problems contamined with uncertain data, Math Program A 88 (2000), 411-424.
6. D. Bertsimas, and, M. Sim, Robust discrete optimization and network flows, Math Program B 98 (2003), 49-71.
7. D. Bertsimas, and, M. Sim, The price of robustness, Oper Res 52-1 (2004), 35-53. (Pubitemid 40000812)
8. H. Crowder, E. Johnson, and, M. Padberg, Solving large-scale zero-one linear programming problems, Oper Res 31 (1983), 803-844.
9. C. E. Ferreira, A. Martin, and, R. Weismantel, Solving multiple knapsack problems by cutting planes, SIAM J Optim 6 (1996), 858-877.
10. V. Gabrel, and, M. Minoux, A scheme for exact separation of extended cover inequalities and application to multidimensional knapsack problems, Oper Res Lett 30 (2002), 252-264. (Pubitemid 35166193)
11. Z. Gu, G. L. Nemhauser, and, M. W. P. Savelsbergh, Lifted cover inequalities for 0-1 integer programs: computation, INFORMS J Comput 10 (1998), 427-437. (Pubitemid 128669148)
12. Z. Gu, G. L. Nemhauser, and, M. W. P. Savelsbergh, Lifted cover inequalities for 0-1 integer programs: complexity, INFORMS J Comput 11-1 (1999), 117-123.
13. H. Kellerer, U. Pferschy, and, D. Pisinger, Knapsack Problems, Springer, New York, 2004.
14. O. Klopfenstein, and, D. Nace, A robust approach to the chance-constrained knapsack problem, Oper Res Lett 36 (2008), 628-632.
15. O. Klopfenstein, Tractable algorithms for chance-constrained combinatorial problems, RAIRO-Oper Res 43 (2009), 157-187.
16. A. Koster, and, M. Kutschka, Multicommodity single path routing with submodular bandwidth consumption, Proc Int Network Optim Conf (INOC) (2009).
17. S. Martello, and, P. Toth, Knapsack problems: Algorithms and computer implementations, Wiley, New York, 1990.
18. G. L. Nemhauser, and, L. A. Wolsey, Integer and combinatorial optimization, Wiley, New York, 1999.
19. A. Ouorou, and, J.-P. Vial, A model for robust capacity planning for telecommunications networks under demand uncertainty, Proc Workshop on Des Reliable Commun Networks (DRCN) (2007).
20. K. Park, S. Kang, and, S. Park, An integer programming approach to the bandwidth packing problem, Manage Sci 42 (1996), 1277-1291. (Pubitemid 126557129)
21. M. C. Pinar, A note on robust 0-1 optimization with uncertain cost coefficients, 4OR, Quarterly J Belg Fr Ital Oper Res Soc 2 (2004), 309-316.
22. A. Prékopa, Probabilistic programming, Stochastic Programming, Vol. 10 of Handbooks in OR&MS, A. Ruszczynski, and, A. Shapiro, editors, Elsevier, Amsterdam, 2003, pp. 267-351.
23. L. A. Wolsey, Faces for linear inequality in 0-1 variables, Math Program 8 (1975), 165-178.
24. E. Zemel, Easily computable facets of the knapsack problem, Math Oper Res 14 (1989), 760-774.