Lifted Cover Inequalities for 0-1 Integer Programs: Computation

Published Online:https://doi.org/10.1287/ijoc.10.4.427

References

  • Balas E. Facets of the Knapsack Polytope. Mathematical Programming (1975) 8 146 164 CrossrefGoogle Scholar
  • Balas E. , Zemel E. Facets of the Knapsack Polytope from Minimal Covers. SIAM Journal on Applied Mathematics (1978) 34 119 148 CrossrefGoogle Scholar
  • Bixby R. E. , Boyd E. A. , Dadmehr S. S. , Indovina R. R. The MIPLIB Mixed Integer Programming Library. (1992) . Technical report R92-36, Rice University Google Scholar
  • CPLEX Optimization, Inc. Using the CPLEX Callable Library and CPLEX Mixed Integer Library, Version 3.0 (1994) Google Scholar
  • Crowder H. , Johnson E. L. , Padberg M. W. Solving Large Scale Zero-One Linear Programming Problems. Operations Research (1983) 31 803 834 LinkGoogle Scholar
  • Gomory R. E. Some Polyhedra Related to Combinatorial Problems. Linear Algebra and Its Application (1969) 2 451 558 CrossrefGoogle Scholar
  • Grötschel M. , Jünger M. , Reinelt G. A Cutting Plane Algorithm for the Linear Ordering Problem. Operations Research (1984) 32 1195 1220 LinkGoogle Scholar
  • Gu Z. Lifted Cover Inequalities for 0–1 and Mixed 0–1 Integer Programs. (1995) . Ph.D. thesis, Georgia Institute of Technology Google Scholar
  • Gu Z. , Nemhauser G. L. , Savelsbergh M. W. P. Lifted Cover Inequalities for 0–1 Integer Programs: Complexity. INFORMS Journal on Computing (1994) . to appear Google Scholar
  • Gu Z. , Nemhauser G. L. , Savelsbergh M. W. P. Lifted Cover Inequalities for 0–1 Integer Programs: Algorithms. (1998) . In preparation Google Scholar
  • Hammer P. L. , Johnson E. L. , Peled U. N. Facets of Regular 0–1 Polytopes. Mathematical Programming (1975) 8 179 206 CrossrefGoogle Scholar
  • Hartvigsen D. , Zemel E. The Complexity of Lifted Inequalities for the Knapsack Problem. Discrete Applied Mathematics (1992) 39 113 123 CrossrefGoogle Scholar
  • Hoffman K. L. , Padberg M. W. LP-Based Combinatorial Problem Solving. Annals of Operations Research (1985) 4 145 194 CrossrefGoogle Scholar
  • Hoffman K. L. , Padberg M. W. Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut. ORSA Journal on Computing (1991) 3 121 134 LinkGoogle Scholar
  • IBM Corporation Optimization Subroutine Library, Guide and Reference (1990) Google Scholar
  • Johnson E. L. , Padberg M. W. A Note on the Knapsack Problem with Special Ordered Sets. Operations Research Letters (1981) 1 18 22 CrossrefGoogle Scholar
  • Martello S. , Toth P. Knapsack Problems: Algorithms and Computer Implementations (1990) (Wiley, New York) Google Scholar
  • Nemhauser G. L. , Savelsbergh M. W. P. , Sigismondi G. C. MINTO, a Mixed INTeger Optimizer. Operations Research Letters (1994) 15 47 58 CrossrefGoogle Scholar
  • Nemhauser G. L. , Vance P. H. Lifted Cover Facets of the 0–1 Knapsack Polytope with GUB Constraints. Operations Research Letters (1994) 16 255 263 CrossrefGoogle Scholar
  • Nemhauser G. L. , Wolsey L. A. Integer and Combinatorial Optimization (1988) (Wiley, New York) CrossrefGoogle Scholar
  • Padberg M. W. On the Facial Structure of set Packing Polyhedra. Mathematical Programming (1973) 5 199 215 CrossrefGoogle Scholar
  • Padberg M. , Rinaldi G. Optimization of a 532 City Symmetric Traveling Salesman Problem by Branch and Cut. Operations Research Letters (1987) 6 1 7 CrossrefGoogle Scholar
  • Van Roy T. J. , Wolsey L. A. Solving Mixed 0–1 Programs by Automatic Reformulation. Operations Research (1987) 35 45 57 LinkGoogle Scholar
  • Wolsey L. A. Faces for a Linear Inequality in 0–1 Variables. Mathematical Programming (1975) 8 165 178 CrossrefGoogle Scholar
  • Wolsey L. A. Facets and Strong Valid Inequalities for Integer Programs. Operations Research (1976) 24 367 372 LinkGoogle Scholar
  • Wolsey L. A. Valid Inequalities for 0–1 Knapsacks and MIPS with Generalized Upper Bound Constraints. Discrete Applied Mathematics (1990) 29 251 261 CrossrefGoogle Scholar
  • Zemel E. Lifting the Facets of Zero-One Polytopes. Mathematical Programming (1978) 15 268 277 CrossrefGoogle Scholar
  • Zemel E. Easily Computable Facets of the Knapsack Polytope. Mathematics of Operations Research (1989) 14 760 765 LinkGoogle Scholar
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