Separation algorithms for 0-1 knapsack polytopes

Mathematical Programming

Volumn 124, Issue 1-2, 2010, Pages 69-91

  Kaparis, Konstantinos ^a   Letchford, Adam N ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Cutting planes; Integer programming; Knapsack problems

Indexed keywords

0-1 LINEAR PROGRAMMING; COMPUTATIONAL RESULTS; CUTTING PLANES; IMPROVE-A; KNAPSACK PROBLEMS; POLYTOPES; SEPARATION ALGORITHMS; VALID INEQUALITY;

DYNAMIC PROGRAMMING; HEURISTIC ALGORITHMS; LINEARIZATION; TOPOLOGY;

INTEGER PROGRAMMING;

EID: 77955174954     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-010-0359-5     Document Type: Article

References (32)

1. Achterberg, T., Koch, T., Martin, A.: MIPLIB 2003. Oper. Res. Lett. 34, 361-372
2. A. Atamtürk 2005 Cover and pack inequalities for (mixed) integer programming Ann. of Oper. Res. 139 21 38 1091.90053 10.1007/s10479-005-3442-1 (Pubitemid 41361093)
3. E. Balas 1975 Facets of the knapsack polytope Math. Program. 8 146 164 0316.90046 10.1007/BF01580440 437053
4. E. Balas E. Zemel 1978 Facets of the knapsack polytope from minimal covers SIAM J. Appl. Math. 34 119 148 0385.90083 10.1137/0134010 469227
5. J.E. Beasley 1990 OR-Library: distributing test problems by electronic mail J. Oper. Res. Soc. 41 1069 1072
6. T. Bektas O. Oguz 2007 On separating cover inequalities for the multidimensional knapsack problem Comp. Oper. Res. 34 1771 1776 1159.90460 10.1016/j.cor.2005.05.032 2259193 (Pubitemid 44556975)
7. Boccia M.: Using exact knapsack separation for the single-source capacitated facility location problem. Working paper, Department of Engineering, University of Sannio (2006)
8. E.A. Boyd 1992 A pseudo-polynomial network flow formulation for exact knapsack separation Networks 22 503 514 0766.90059 10.1002/net.3230220507 1170951
9. E.A. Boyd 1993 Generating Fenchel cutting planes for knapsack polyhedra SIAM J. Optimization 3 734 750 0797.90067 10.1137/0803038
10. E.A. Boyd 1994 Fenchel cutting planes for integer programs Oper. Res. 42 53 64 0809.90104 10.1287/opre.42.1.53 1261374
11. P.C. Chu J.E. Beasley 1998 A genetic algorithm for the multidimensional knapsack problem J. Heur. 4 63 86 0913.90218 10.1023/A:1009642405419
12. Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms. MIT Press, Cambridge, MA (2001)
13. H. Crowder E. Johnson M. Padberg 1983 Solving large-scale 0-1 linear programming programs Oper. Res. 31 803 834 0576.90065 10.1287/opre.31.5.803
14. C.E. Ferreira A. Martin R. Weismantel 1996 Solving multiple knapsack problems by cutting planes SIAM J. Opt. 6 858 877 0856.90082 10.1137/S1052623493254455 1402209
15. V. Gabrel M. Minoux 2002 A scheme for exact separation of extended cover inequalities and application to multidimensional knapsack problems Oper. Res. Lett. 30 252 264 1049.90074 1934743
16. Z. Gu G.L. Nemhauser M.W.P. Savelsbergh 1998 Lifted cover inequalities for 0-1 integer programs: computation INFORMS J. Computing 10 427 437 10.1287/ijoc.10.4.427 1656936
17. Z. Gu G.L. Nemhauser M.W.P. Savelsbergh 1999 Lifted cover inequalities for 0-1 integer programs: complexity INFORMS J. Computing 11 117 123 1092.90527 10.1287/ijoc.11.1.117 1688131
18. Z. Gu G.L. Nemhauser M.W.P. Savelsbergh 2000 Sequence independent lifting in mixed integer programming J. Comb. Opt. 4 109 129 0964.90030 10.1023/A:1009841107478 1747826
19. Helmberg, C., Weismantel, R.: Cutting plane algorithms for semidefinite relaxations. In: Pardalos, P.M., Wolkowicz, H. (eds.) Fields Institute Communications. vol. 18, pp. 197-213 (1998)
20. K.L. Hoffman M.W. Padberg 1991 Improving LP-representations of zero-one linear programs for branch-and-cut ORSA J. Comput. 3 121 134 0755.90062
21. K. Kaparis A.N. Letchford 2008 Local and global lifted cover inequalities for the multidimensional knapsack problem Eur. J. Opl Res. 186 91 103 1138.90016 10.1016/j.ejor.2007.01.032 2363858 (Pubitemid 47600531)
22. Karp R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds) Complexity of Computer Computations., Plenum, New York (1972)
23. D. Klabjan G.L. Nemhauser C. Tovey 1998 The complexity of cover inequality separation Oper. Res. Lett. 23 35 40 0957.90094 10.1016/S0167- 6377(98)00025-X 1664241
24. Nemhauser G.L., Wolsey L.A.: Integer and Combinatorial Optimization. Wiley, New York (1988)
25. M.W. Padberg 1980 (1, k)-configurations and facets for packing problems Math. Program. 18 94 99 0431.90050 10.1007/BF01588301 557118
26. D. Pisinger 1995 A minimal algorithm for the 0-1 knapsack problem Oper. Res. 46 758 767 1660413
27. T.J. Van Roy L.A. Wolsey 1987 Solving mixed integer programming problems using automatic reformulation Oper. Res. 35 45 57 0614.90082 10.1287/opre.35.1.45 908859
28. Y. Vimont S. Boussier M. Vasquez 2008 Reduced costs propagation in an efficient implicit enumeration for the 0-1 multidimensional knapsack problem J. Comb. Opt. 15 165 178 1138.90014 10.1007/s10878-007-9074-4 2367016
29. R. Weismantel 1997 On the 0-1 knapsack polytope Math. Program. 77 49 68 1436358
30. J.W.J. Williams 1964 Algorithm 232-Heapsort Commun. ACM 7 347 348
31. L.A. Wolsey 1975 Faces for a linear inequality in 0-1 variables Math. Program. 8 165 178 0314.90063 10.1007/BF01580441 373604
32. E. Zemel 1989 Easily computable facets of the knapsack polytope Math. Oper. Res. 14 760 765 0689.90057 10.1287/moor.14.4.760 1031212