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Volumn 12, Issue C, 2005, Pages 69-121

Computational Integer Programming and Cutting Planes

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EID: 53449093660     PISSN: 09270507     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0927-0507(05)12002-7     Document Type: Review
Times cited : (35)

References (114)
  • 5
    • 0003465839 scopus 로고
    • Finding cuts in the TSP
    • March, Technical Report 95-05, DIMACS
    • Applegate, D., R. E. Bixby, V. Chvátal, W. Cook (March, 1995). Finding cuts in the TSP. Technical Report 95-05, DIMACS
    • (1995)
    • Applegate, D.1    Bixby, R.E.2    Chvátal, V.3    Cook, W.4
  • 6
    • 3042514606 scopus 로고    scopus 로고
    • On the facets of the mixed-integer knapsack polyhedron
    • Atamtürk A. On the facets of the mixed-integer knapsack polyhedron. Mathematical Programming 98 (2003) 145-175
    • (2003) Mathematical Programming , vol.98 , pp. 145-175
    • Atamtürk, A.1
  • 7
    • 10844248146 scopus 로고    scopus 로고
    • Sequence independent lifting for mixed integer programming
    • Atamtürk A. Sequence independent lifting for mixed integer programming. Operations Research 52 (2004) 487-490
    • (2004) Operations Research , vol.52 , pp. 487-490
    • Atamtürk, A.1
  • 8
    • 0012649845 scopus 로고    scopus 로고
    • On capacitated network design cut-set polyhedral
    • Atamtürk A. On capacitated network design cut-set polyhedral. Mathematical Programming 92 (2002) 425-437
    • (2002) Mathematical Programming , vol.92 , pp. 425-437
    • Atamtürk, A.1
  • 10
    • 34250395123 scopus 로고
    • Facets of the knapsack polytope
    • Balas E. Facets of the knapsack polytope. Mathematical Programming 8 (1975) 146-164
    • (1975) Mathematical Programming , vol.8 , pp. 146-164
    • Balas, E.1
  • 11
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • Balas E., Ceria S., and Cornuéjols G. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58 (1993) 295-324
    • (1993) Mathematical Programming , vol.58 , pp. 295-324
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 12
    • 0037870067 scopus 로고    scopus 로고
    • Mixed 0-1 programming by lift-and-project in a branch-and-cut framework
    • Balas E., Ceria S., and Cornuéjols G. Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Management Science 42 (1996) 1229-1246
    • (1996) Management Science , vol.42 , pp. 1229-1246
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 15
    • 0002031108 scopus 로고
    • Pivot and complement: a heuristic for 0-1 programming
    • Balas E., and Martin R. Pivot and complement: a heuristic for 0-1 programming. Management Science 26 (1980) 86-96
    • (1980) Management Science , vol.26 , pp. 86-96
    • Balas, E.1    Martin, R.2
  • 16
    • 0000511675 scopus 로고
    • Facets of the knapsack polytope from minimal covers
    • Balas E., and Zemel E. Facets of the knapsack polytope from minimal covers. SIAM Journal on Applied Mathematics 34 (1978) 119-148
    • (1978) SIAM Journal on Applied Mathematics , vol.34 , pp. 119-148
    • Balas, E.1    Zemel, E.2
  • 17
    • 0012484821 scopus 로고    scopus 로고
    • Branch and cut based on the volume algorithm: Steiner trees in graphs and max-cut
    • Technical Report RC22221, IBM
    • Barahona, F., L. Ladanyi (2001). Branch and cut based on the volume algorithm: Steiner trees in graphs and max-cut. Technical Report RC22221, IBM
    • (2001)
    • Barahona, F.1    Ladanyi, L.2
  • 18
    • 0013152010 scopus 로고    scopus 로고
    • The volume algorithm: producing primal solutions with a subgradient method
    • Barahona F., and Ranga Anbil. The volume algorithm: producing primal solutions with a subgradient method. Mathematical Programming 87 3 (2000) 385-399
    • (2000) Mathematical Programming , vol.87 , Issue.3 , pp. 385-399
    • Barahona, F.1    Ranga Anbil2
  • 20
    • 9644308639 scopus 로고
    • Partitioning procedures for solving mixed variables programming
    • Benders J.F. Partitioning procedures for solving mixed variables programming. Numerische Mathematik 4 (1962) 238-252
    • (1962) Numerische Mathematik , vol.4 , pp. 238-252
    • Benders, J.F.1
  • 28
  • 29
    • 34249770791 scopus 로고
    • The Steiner tree problem I: formulations, compositions and extension of facets
    • Chopra S., and Rao M.R. The Steiner tree problem I: formulations, compositions and extension of facets. Mathematical Programming 64 2 (1994) 209-229
    • (1994) Mathematical Programming , vol.64 , Issue.2 , pp. 209-229
    • Chopra, S.1    Rao, M.R.2
  • 30
    • 0343649098 scopus 로고
    • Using path inequalities in a branch-and-cut code for the symmetric traveling salesman problem
    • L. A. Wolsey, G. Rinaldi eds
    • Clochard, J. M., D. Naddef (1993). Using path inequalities in a branch-and-cut code for the symmetric traveling salesman problem, in: L. A. Wolsey, G. Rinaldi (eds.), Proceedings on the Third IPCO Conference 291-311.
    • (1993) Proceedings on the Third IPCO Conference , pp. 291-311
    • Clochard, J.M.1    Naddef, D.2
  • 33
    • 0020815626 scopus 로고
    • Solving large-scale zero-one linear programming problems
    • Crowder H., Johnson E., and Padberg M.W. Solving large-scale zero-one linear programming problems. Operations Reserch 31 (1983) 803-834
    • (1983) Operations Reserch , vol.31 , pp. 803-834
    • Crowder, H.1    Johnson, E.2    Padberg, M.W.3
  • 34
    • 0001391104 scopus 로고
    • Decomposition principle for linear programs
    • Dantzig G.B., and Wolfe P. Decomposition principle for linear programs. Operations Research 8 (1960) 101-111
    • (1960) Operations Research , vol.8 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 37
    • 0040684856 scopus 로고
    • Parallel branch-and-bound algorithms for general mixed integer programming on the CM-5
    • Eckstein J. Parallel branch-and-bound algorithms for general mixed integer programming on the CM-5. SIAM Journal on Optimization 4 (1994) 794-814
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 794-814
    • Eckstein, J.1
  • 42
    • 0001052304 scopus 로고
    • Blocking and anti-blocking pairs of polyhedra
    • Fulkerson D.R. Blocking and anti-blocking pairs of polyhedra. Mathematical Programming 1 (1971) 168-194
    • (1971) Mathematical Programming , vol.1 , pp. 168-194
    • Fulkerson, D.R.1
  • 44
    • 77950535951 scopus 로고    scopus 로고
    • Goffin, J. L., J. P. Vial (1999). Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method. Technical Report 99.02, Logilab, Universite de Geneve. To appear in Optimization Methods and Software
    • Goffin, J. L., J. P. Vial (1999). Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method. Technical Report 99.02, Logilab, Universite de Geneve. To appear in Optimization Methods and Software
  • 45
    • 84958977914 scopus 로고
    • Outline of an algorithm for integer solutions to linear programs
    • Gomory R.E. Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Society 64 (1958) 275-278
    • (1958) Bulletin of the American Society , vol.64 , pp. 275-278
    • Gomory, R.E.1
  • 48
    • 0002882891 scopus 로고    scopus 로고
    • Presolve analysis of linear programs prior to apply an interior point method
    • Gondzio J. Presolve analysis of linear programs prior to apply an interior point method. INFORMS Journal on Computing 9 (1997) 73-91
    • (1997) INFORMS Journal on Computing , vol.9 , pp. 73-91
    • Gondzio, J.1
  • 50
    • 0001621683 scopus 로고
    • Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints
    • Grötschel M., Monma C.L., and Stoer M. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research 40 (1992) 309-330
    • (1992) Operations Research , vol.40 , pp. 309-330
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 53
  • 56
    • 34250461535 scopus 로고
    • The traveling-salesman problem and minimum spanning trees: part II
    • Held M., and Karp R. The traveling-salesman problem and minimum spanning trees: part II. Mathematical Programming 1 (1971) 6-25
    • (1971) Mathematical Programming , vol.1 , pp. 6-25
    • Held, M.1    Karp, R.2
  • 57
    • 0003529551 scopus 로고
    • Convex analysis and minimization algorithms, part 2: advanced theory and bundle methods
    • Springer-Verlag
    • Hiriart-Urruty J.B., and Lemarechal C. Convex analysis and minimization algorithms, part 2: advanced theory and bundle methods. Grundlehren der Mathematischen Wissenschaften Vol. 306 (1993), Springer-Verlag
    • (1993) Grundlehren der Mathematischen Wissenschaften , vol.306
    • Hiriart-Urruty, J.B.1    Lemarechal, C.2
  • 58
    • 0026125207 scopus 로고
    • Improved LP-representations of zero-one linear programs for branch-and-cut
    • Hoffman K.L., and Padberg M.W. Improved LP-representations of zero-one linear programs for branch-and-cut. ORSA Journal on Computing 3 (1991) 121-134
    • (1991) ORSA Journal on Computing , vol.3 , pp. 121-134
    • Hoffman, K.L.1    Padberg, M.W.2
  • 61
    • 0002431626 scopus 로고
    • A note on the knapsack problem with special ordered sets
    • Johnson E., and Padberg M.W. A note on the knapsack problem with special ordered sets. Operations Research Letters 1 (1981) 18-22
    • (1981) Operations Research Letters , vol.1 , pp. 18-22
    • Johnson, E.1    Padberg, M.W.2
  • 64
    • 77950527022 scopus 로고    scopus 로고
    • ZIMPL user guide
    • 01-20, Konrad-Zuse-Zentrum Für Informationstechnik Berlin
    • Koch, T. (2001). ZIMPL user guide. Technical Report Preprint 01-20, Konrad-Zuse-Zentrum Für Informationstechnik Berlin
    • (2001) Technical Report Preprint
    • Koch, T.1
  • 65
    • 4544305931 scopus 로고    scopus 로고
    • SteinLib: an updated library on Steiner tree problems in graphs
    • Du D.-Z., and Cheng X. (Eds), Kluwer
    • Koch T., Martin A., and Voß S. SteinLib: an updated library on Steiner tree problems in graphs. In: Du D.-Z., and Cheng X. (Eds). Steiner Tress in Industries (2001), Kluwer 285-325
    • (2001) Steiner Tress in Industries , pp. 285-325
    • Koch, T.1    Martin, A.2    Voß, S.3
  • 66
    • 77957093543 scopus 로고
    • Computer codes for problems of integer programming
    • Land A., and Powell S. Computer codes for problems of integer programming. Annals of Discrete Mathematics 5 (1979) 221-269
    • (1979) Annals of Discrete Mathematics , vol.5 , pp. 221-269
    • Land, A.1    Powell, S.2
  • 67
    • 39649093787 scopus 로고    scopus 로고
    • An explicit exact SDP relaxation for nonlinear 0-1 programs
    • K. Aardal, A. M. H. Gerards eds
    • Lasserre, J. B. (2001). An explicit exact SDP relaxation for nonlinear 0-1 programs, in: K. Aardal, A. M. H. Gerards (eds.), Lecture Notes in Computer Science, 293-303.
    • (2001) Lecture Notes in Computer Science , vol.293-303
    • Lasserre, J.B.1
  • 68
    • 0344794572 scopus 로고    scopus 로고
    • A geometric study of duality gaps, with applications
    • Lemaréchal C., and Renaud A. A geometric study of duality gaps, with applications. Mathematical Programming 90 (2001) 399-427
    • (2001) Mathematical Programming , vol.90 , pp. 399-427
    • Lemaréchal, C.1    Renaud, A.2
  • 69
    • 0001332760 scopus 로고    scopus 로고
    • A computational study of search strategies for mixed integer programming
    • Linderoth J.T., and Savelsbergh M.W.P. A computational study of search strategies for mixed integer programming. INFORMS Journal on Computing 11 (1999) 173-187
    • (1999) INFORMS Journal on Computing , vol.11 , pp. 173-187
    • Linderoth, J.T.1    Savelsbergh, M.W.P.2
  • 72
    • 0032298664 scopus 로고    scopus 로고
    • Vehicle scheduling in public transit and lagrangean pricing
    • Löbel A. Vehicle scheduling in public transit and lagrangean pricing. Management Science 12 44 (1998) 1637-1649
    • (1998) Management Science , vol.12 , Issue.44 , pp. 1637-1649
    • Löbel, A.1
  • 73
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • Lovász L., and Schrijver A. Cones of matrices and set-functions and 0-1 optimization. SIAM Journal on Optimization 1 (1991) 166-190
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 77
    • 0002496107 scopus 로고    scopus 로고
    • The 0-1 knapsack problem with a single continuous variable
    • Marchand H., and Wolsey L.A. The 0-1 knapsack problem with a single continuous variable. Mathematical Programming 85 (1999) 15-33
    • (1999) Mathematical Programming , vol.85 , pp. 15-33
    • Marchand, H.1    Wolsey, L.A.2
  • 78
    • 0035328755 scopus 로고    scopus 로고
    • Aggregation and mixed integer rounding to solve MIPs
    • Marchand H., and Wolsey L.A. Aggregation and mixed integer rounding to solve MIPs. Operations Research 49 (2001) 363-371
    • (2001) Operations Research , vol.49 , pp. 363-371
    • Marchand, H.1    Wolsey, L.A.2
  • 79
    • 0040905027 scopus 로고    scopus 로고
    • Habilitations-Schrift, Technische Universität Berlin
    • Martin A. Integer programs with block structure (1998), Habilitations-Schrift, Technische Universität Berlin. Available as ZIB-Preprint SC-99-03, see www.zib.de
    • (1998) Integer programs with block structure
    • Martin, A.1
  • 80
    • 84958760311 scopus 로고    scopus 로고
    • Martin, A., R. Weismantel (1998). The intersection of knapsack polyhedra and extensions, in: R. E., Bixby, E. A. Boyd, R. Z. Fíos-Mercado (eds.), Integer Programming and Combinatorial Optimization, Proceedings of the 6th IPCO Conference, 243-256
    • Martin, A., R. Weismantel (1998). The intersection of knapsack polyhedra and extensions, in: R. E., Bixby, E. A. Boyd, R. Z. Fíos-Mercado (eds.), Integer Programming and Combinatorial Optimization, Proceedings of the 6th IPCO Conference, 243-256
  • 81
    • 0042124545 scopus 로고
    • Investigations of some branch and bound strategies for the solution of mixed integer linear programs
    • Mitra G. Investigations of some branch and bound strategies for the solution of mixed integer linear programs. Mathematical Programming 4 (1973) 155-170
    • (1973) Mathematical Programming , vol.4 , pp. 155-170
    • Mitra, G.1
  • 82
    • 4344639338 scopus 로고    scopus 로고
    • Polyhedral theory and branch-and-cut algorithms for the symmetric tsp
    • Gutin G., and Punnen A. (Eds), Kluwer
    • Naddef D. Polyhedral theory and branch-and-cut algorithms for the symmetric tsp. In: Gutin G., and Punnen A. (Eds). The Traveling Salesman Problem and its Variations (2002), Kluwer
    • (2002) The Traveling Salesman Problem and its Variations
    • Naddef, D.1
  • 84
    • 0028742392 scopus 로고
    • Lifted cover facets of the 0-1 knapsack Polytope with GUB constraints
    • Nemhauser G.L., and Vance P.H. Lifted cover facets of the 0-1 knapsack Polytope with GUB constraints. Operations Research Letters 16 (1994) 255-263
    • (1994) Operations Research Letters , vol.16 , pp. 255-263
    • Nemhauser, G.L.1    Vance, P.H.2
  • 86
    • 0000689851 scopus 로고
    • A recursive procedure to generate all cuts for 0-1 mixed integer programs
    • Nemhauser G.L., and Wolsey L.A. A recursive procedure to generate all cuts for 0-1 mixed integer programs. Mathematical Programming 46 (1990) 379-390
    • (1990) Mathematical Programming , vol.46 , pp. 379-390
    • Nemhauser, G.L.1    Wolsey, L.A.2
  • 87
    • 34250429350 scopus 로고
    • On the facial structure of set packing polyhedra
    • Padberg M.W. On the facial structure of set packing polyhedra. Mathematical Programming 5 (1973) 199-215
    • (1973) Mathematical Programming , vol.5 , pp. 199-215
    • Padberg, M.W.1
  • 88
    • 0000214393 scopus 로고
    • A note on zero-one programming
    • Padberg M.W. A note on zero-one programming. OR 23 4 (1975) 833-837
    • (1975) OR , vol.23 , Issue.4 , pp. 833-837
    • Padberg, M.W.1
  • 89
    • 0002793189 scopus 로고
    • (1,k)-Configurations and facets for packing problems
    • Padberg M.W. (1,k)-Configurations and facets for packing problems. Mathematical Programming 18 (1980) 94-99
    • (1980) Mathematical Programming , vol.18 , pp. 94-99
    • Padberg, M.W.1
  • 91
    • 0034958493 scopus 로고    scopus 로고
    • Classical cuts for mixed-integer programming and branch-and-cut
    • Padberg M.W. Classical cuts for mixed-integer programming and branch-and-cut. Mathematical Methods of OR 53 (2001) 173-203
    • (2001) Mathematical Methods of OR , vol.53 , pp. 173-203
    • Padberg, M.W.1
  • 93
    • 0024029950 scopus 로고
    • Valid inequalities and separation for capacitated economic lot-sizing
    • Pochet Y. Valid inequalities and separation for capacitated economic lot-sizing. Operations Research Letters 7 (1988) 109-116
    • (1988) Operations Research Letters , vol.7 , pp. 109-116
    • Pochet, Y.1
  • 97
    • 0023250226 scopus 로고
    • Solving mixed integer programming problems using automatic reformulation
    • Van Roy T.J., and Wolsey L.A. Solving mixed integer programming problems using automatic reformulation. Operations Research 35 (1987) 45-57
    • (1987) Operations Research , vol.35 , pp. 45-57
    • Van Roy, T.J.1    Wolsey, L.A.2
  • 99
    • 0000278641 scopus 로고
    • Preprocessing and probing for mixed integer programming problems
    • Savelsbergh M.W.P. Preprocessing and probing for mixed integer programming problems. ORSA J. on Computing 6 (1994) 445-454
    • (1994) ORSA J. on Computing , vol.6 , pp. 445-454
    • Savelsbergh, M.W.P.1
  • 100
    • 77950532317 scopus 로고    scopus 로고
    • Branch-and-price: integer programming with column generation
    • Pardalos P., and Flouda C. (Eds), Kluwer
    • Savelsbergh M.W.P. Branch-and-price: integer programming with column generation. In: Pardalos P., and Flouda C. (Eds). Encylopedia of Optimization (2001), Kluwer
    • (2001) Encylopedia of Optimization
    • Savelsbergh, M.W.P.1
  • 102
    • 0039331672 scopus 로고
    • Linear programming solver software for personal computers: 1995 report
    • Sharda R. Linear programming solver software for personal computers: 1995 report. OR{plus 45 degree rule}MS Today 22 5 (1995) 49-57
    • (1995) OR{plus 45 degree rule}MS Today , vol.22 , Issue.5 , pp. 49-57
    • Sharda, R.1
  • 103
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • Sherali H., and Adams W. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM Journal of Discrete Mathematics 3 (1990) 411-430
    • (1990) SIAM Journal of Discrete Mathematics , vol.3 , pp. 411-430
    • Sherali, H.1    Adams, W.2
  • 104
    • 31244436444 scopus 로고    scopus 로고
    • A modification of Benders' decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse
    • Sherali H.D., and Fraticelli B.M.P. A modification of Benders' decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse. Journal of Global Optimization 22 (2002) 319-342
    • (2002) Journal of Global Optimization , vol.22 , pp. 319-342
    • Sherali, H.D.1    Fraticelli, B.M.P.2
  • 107
    • 0000906834 scopus 로고    scopus 로고
    • Computational study of a column generation algorithm for bin packing and cutting stock problems
    • Vanderbeck F. Computational study of a column generation algorithm for bin packing and cutting stock problems. Mathematical Programming 46 (1999) 565-594
    • (1999) Mathematical Programming , vol.46 , pp. 565-594
    • Vanderbeck, F.1
  • 108
    • 0033725783 scopus 로고    scopus 로고
    • On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm
    • Vanderbeck F. On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Operations Research 48 1 (2000) 111-128
    • (2000) Operations Research , vol.48 , Issue.1 , pp. 111-128
    • Vanderbeck, F.1
  • 109
    • 77951506672 scopus 로고    scopus 로고
    • On the 0/1 knapsack polytope
    • Weismantel R. On the 0/1 knapsack polytope. Mathematical Programming 77 1 (1997) 49-68
    • (1997) Mathematical Programming , vol.77 , Issue.1 , pp. 49-68
    • Weismantel, R.1
  • 110
    • 0343970543 scopus 로고
    • A brief introduction to the ibm optimization subroutine library
    • Wilson D.G. A brief introduction to the ibm optimization subroutine library. SIAG/OPT Views and News 1 (1992) 9-10
    • (1992) SIAG/OPT Views and News , vol.1 , pp. 9-10
    • Wilson, D.G.1
  • 111
    • 34250395041 scopus 로고
    • Faces of linear inequalities in 0-1 variables
    • Wolsey L.A. Faces of linear inequalities in 0-1 variables. Mathematical Programming 8 (1975) 165-178
    • (1975) Mathematical Programming , vol.8 , pp. 165-178
    • Wolsey, L.A.1
  • 112
    • 0001615533 scopus 로고
    • Valid inequalities for 0-1 knapsacks and MIPs with generalized upper bound constraints
    • Wolsey L.A. Valid inequalities for 0-1 knapsacks and MIPs with generalized upper bound constraints. Discrete Applied Mathematics 29 (1990) 251-261
    • (1990) Discrete Applied Mathematics , vol.29 , pp. 251-261
    • Wolsey, L.A.1
  • 113
    • 0000271159 scopus 로고
    • Easily computable facets of the knapsack polytope
    • Zemel E. Easily computable facets of the knapsack polytope. Mathematics of Operations Research 14 (1989) 760-764
    • (1989) Mathematics of Operations Research , vol.14 , pp. 760-764
    • Zemel, E.1
  • 114
    • 0036250973 scopus 로고    scopus 로고
    • New bundle methods for solving Lagrangian relaxation dual problems
    • Zhao X., and Luh P.B. New bundle methods for solving Lagrangian relaxation dual problems. Journal of Optimization Theory and Applications 113 2 (2002) 373-397
    • (2002) Journal of Optimization Theory and Applications , vol.113 , Issue.2 , pp. 373-397
    • Zhao, X.1    Luh, P.B.2


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