Higher-order cover cuts from zero–one knapsack constraints augmented by two-sided bounding inequalities
Tài liệu tham khảo
Ahuja, 1993
Balas, 1975, Facets of the knapsack polytope, Mathematical Programming, 8, 146, 10.1007/BF01580440
Balas, 1977, Critical cutsets of graphs and canonical facets of set-packing polytopes, Mathematics of Operations Research, 2, 15, 10.1287/moor.2.1.15
Balas, 1978, Facets of the knapsack polytope from minimal covers, SIAM Journal on Applied Mathematics, 34, 119, 10.1137/0134010
Bazaraa, 2005
Bazaraa, 2006
Cornuéjols, 1989, On the 0–1 facets of the set covering polytope, Mathematical Programming, 43, 45, 10.1007/BF01582277
Crowder, 1983, Solving large-scale zero–one linear programming problems, Operations Research, 31, 803, 10.1287/opre.31.5.803
Geoffrion, 1969, An improved implicit enumeration approach for integer programming, Operations Research, 17, 437, 10.1287/opre.17.3.437
Glover, 1965, A multiphase-dual algorithm for the zero–one integer programming problem, Operations Research, 13, 879, 10.1287/opre.13.6.879
Glover, 1971, Flows in arborescences, Management Science, 17, 568, 10.1287/mnsc.17.9.568
F. Glover, H.D. Sherali, Second order cover cuts, Mathematical Programming (ISSN: 0025-5610 1436-4646) (2007), doi:10.1007/s10107-007-0098-4. (Online)
Glover, 2005, Some classes of valid inequalities and convex hull characterizations for dynamic fixed-charge problems under nested constraints, Annals of Operations Research, State-of-the-Art in Integer Programming, 140, 215, 10.1007/s10479-005-3972-6
Glover, 1997, Generating cuts from surrogate constraint analysis for zero–one and multiple choice programming, Computational Optimization and Applications, 8, 152, 10.1023/A:1008621204567
Gu, 1998, Cover inequalities for 0–1 linear programs: Computation, INFORMS Journal on Computing, 10, 427, 10.1287/ijoc.10.4.427
Gu, 2000, Sequence independent lifting in mixed integer programming, Journal of Combinatorial Optimization, 4, 109, 10.1023/A:1009841107478
Hammer, 1975, Facets of regular 0–1 polytopes, Mathematical Programming, 8, 179, 10.1007/BF01580442
S. Hanafi, Contribution à la résolution de problèmes duaux de grande taille en optimisation combinatoire, Ph.D. Thesis, University of Valenciennes, France, 1993
S. Hanafi, F. Glover, Exploiting nested inequalities and surrogate constraints, Research Report, University of Valenciennes, France, and University of Colorado, Boulder, CO, 2005
Johnson, 1981, A note on the knapsack problem with special ordered sets, Operations Research Letters, 1, 18, 10.1016/0167-6377(81)90019-5
Laurent, 1989, A generalization of antiwebs to independence systems and their canonical facets, Mathematical Programming, 45, 97, 10.1007/BF01589098
Moura, 2003, Rank inequalities and separation algorithms for packing designs and sparse triple systems, Theoretical Computer Science, 297, 367, 10.1016/S0304-3975(02)00648-5
Nemhauser, 1994, Lifted cover facets of the 0–1 knapsack polytope with GUB constraints, Operations Research Letters, 16, 255, 10.1016/0167-6377(94)90038-8
Nemhauser, 1999
Nemhauser, 1994, MINTO, a mixed INTeger optimizer, Operations Research Letters, 15, 47, 10.1016/0167-6377(94)90013-2
Osorio, 2002, Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions, Annals of Operations Research, 117, 71, 10.1023/A:1021513321301
Savelsbergh, 1994, Preprocessing and probing for mixed integer programming problems, ORSA Journal on Computing, 6, 445, 10.1287/ijoc.6.4.445
Sherali, 1995, Sequential and simultaneous liftings of minimal cover inequalities for generalized upper bound constrained knapsack polytopes, SIAM Journal on Discrete Mathematics, 8, 133, 10.1137/S0895480192230607
Sherali, 1992, A global optimization algorithm for polynomial programming problems using a reformulation–linearization technique, Journal of Global Optimization, 2, 101, 10.1007/BF00121304
K. Spielberg, M. Guignard, A sequential (quasi) hot start method for BB (0, 1) mixed integer programming, in: Mathematical Programming Symposium, Atlanta, GA, 2000
Vasquez, 2005, Improved results on the 0–1 multidimensional knapsack problem, European Journal of Operational Research, 165, 70, 10.1016/j.ejor.2004.01.024
Wolsey, 1975, Faces for a linear inequality in 0-1 variables, Mathematical Programming, 8, 165, 10.1007/BF01580441
Zemel, 1989, Easily computable facets of the knapsack polytope, Mathematics of Operations Research, 14, 760, 10.1287/moor.14.4.760
B. Zeng, J.-P.P. Richard, Sequence independent lifting for 0–1 knapsack problems with disjoint cardinality constraints, School of Industrial Engineering, Purdue University, West Lafayette, IN, 2006, Manuscript