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Volumn 96, Issue 3, 2003, Pages 439-467

A polyhedral study of the cardinality constrained knapsack problem

Author keywords

Branch and cut; Cardinality constrained programming; Knapsack problem; Mixed integer programming

Indexed keywords

0-1 PROGRAMMING; ALTERNATIVE APPROACH; BRANCH-AND-CUT; CARDINALITIES; CARDINALITY CONSTRAINTS; COMPUTATIONAL RESULTS; CONTINUOUS VARIABLES; CONVEX HULL; FACET-DEFINING INEQUALITIES; FEASIBLE SET; KNAPSACK PROBLEMS; MIXED-INTEGER PROGRAMMING; NON-TRIVIAL; POLYHEDRAL STUDIES; VALID INEQUALITY;

EID: 14944345436     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0420-8     Document Type: Article
Times cited : (36)

References (49)
  • 1
    • 34250395123 scopus 로고
    • Facets of the knapsack polytope
    • Balas, E.: Facets of the knapsack polytope. Math. Program. 8, 146-164 (1975)
    • (1975) Math. Program , vol.8 , pp. 146-164
    • Balas, E.1
  • 2
    • 77957040455 scopus 로고
    • Disjunctive programming
    • Balas, E.: Disjunctive programming. Ann. Discrete Math. 5, 3-51 (1979)
    • (1979) Ann. Discrete Math , vol.5 , pp. 3-51
    • Balas, E.1
  • 3
    • 0022135711 scopus 로고
    • On the facial structure of scheduling polyhedra
    • Balas, E.: On the facial structure of scheduling polyhedra. Math. Program. Study 24, 179-218 (1985)
    • (1985) Math. Program. Study , vol.24 , pp. 179-218
    • Balas, E.1
  • 4
    • 0038706615 scopus 로고    scopus 로고
    • Disjunctive programming: Properties of the convex hull of feasible points
    • PII S0166218X9800136X
    • Balas, E.: Disjunctive programming: properties of the convex hull of feasible points. Discrete Appl. Math. 89, 3-44 (1998) (Pubitemid 128400151)
    • (1998) Discrete Applied Mathematics , vol.89 , Issue.1-3 , pp. 3-44
    • Balas, E.1
  • 7
    • 0014924953 scopus 로고
    • Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables
    • J. Lawrence (Ed.), Tavistock Publications
    • Beale, E.L.M.,Tomlin, J.A.: Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables. In: J. Lawrence (Ed.), Proceedings of the Fifth International Conference on Operations Research, Tavistock Publications, 1970, pp. 447-454
    • (1970) Proceedings of the Fifth International Conference on Operations Research , pp. 447-454
    • Beale, E.L.M.1    Tomlin, J.A.2
  • 9
    • 0008633562 scopus 로고    scopus 로고
    • Computational study of a family of mixed-integer quadratic programming problems
    • Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74, 121-140 (1996) (Pubitemid 126407431)
    • (1996) Mathematical Programming, Series B , vol.74 , Issue.2 PART A , pp. 121-140
    • Bienstock, D.1
  • 11
    • 0020815626 scopus 로고
    • Solving large scale zero-one problems
    • Crowder, H., Johnson, E.L., Padberg, M.W.: Solving large scale zero-one problems. Oper. Res. 31, 803-834 (1983)
    • (1983) Oper. Res , vol.31 , pp. 803-834
    • Crowder, H.1    Johnson, E.L.2    Padberg, M.W.3
  • 12
    • 0008644215 scopus 로고
    • On the significance of solving linear programming problems with some integer variables
    • Dantzig, G.B.: On the significance of solving linear programming problems with some integer variables. Econometrica 28, 30-44 (1960)
    • (1960) Econometrica , vol.28 , pp. 30-44
    • Dantzig, G.B.1
  • 14
    • 0035329662 scopus 로고    scopus 로고
    • A family of facets for the uncapacitated p-median polytope
    • DOI 10.1016/S0167-6377(01)00062-1, PII S0167637701000621
    • de Farias, Jr., I.R.: A family of facets for the uncapacitated p-median polytope. Oper. Res. Lett. 28, 161-167 (2001) (Pubitemid 32610337)
    • (2001) Operations Research Letters , vol.28 , Issue.4 , pp. 161-167
    • De Farias Jr., I.R.1
  • 15
    • 0000891832 scopus 로고    scopus 로고
    • A generalized assignment problem with special ordered sets: A polyhedral approach
    • de Farias, Jr., I.R., Johnson, E.L., Nemhauser, G.L.: A generalized assignment problem with special ordered sets: a polyhedral approach. Math. Program. 89, 187-203 (2000)
    • (2000) Math. Program , vol.89 , pp. 187-203
    • De Farias Jr., I.R.1    Johnson, E.L.2    Nemhauser, G.L.3
  • 16
    • 0008644216 scopus 로고    scopus 로고
    • Branch-and-cut for combinatorial optimisation problems without auxiliary binary variables
    • DOI 10.1017/S0269888901000030
    • de Farias, Jr., I.R., Johnson, E.L., Nemhauser, G.L.: Branch-and-cut for combinatorial optimization problems without auxiliary binary variables. Knowledge Eng. Rev. 16, 25-39 (2001) (Pubitemid 33691668)
    • (2000) Knowledge Engineering Review , vol.16 , Issue.1 , pp. 25-39
    • De Farias Jr., I.R.1    Johnson, E.L.2    Nemhauser, G.L.3
  • 18
    • 0035451608 scopus 로고    scopus 로고
    • A family of inequalities for the generalized assignment polytope
    • de Farias, Jr. I.R., Nemhauser, G.L.: A family of inequalities for the generalized assignment polytope. Oper. Res. Lett. 29, 49-51 (2001)
    • (2001) Oper. Res. Lett , vol.29 , pp. 49-51
    • De Farias Jr., I.R.1    Nemhauser, G.L.2
  • 21
    • 0003539701 scopus 로고    scopus 로고
    • Logic based approaches for mixed integer programming models and their application in process synthesis
    • M.F. Malone et al. (Eds.)
    • Grossmann, I.E., Hooker, J.N.: Logic Based Approaches for Mixed Integer Programming Models and their Application in Process Synthesis. in M.F. Malone et al. (Eds.), Proceedings of the Fifth FOCAPD Conference. AICHE Symposium Series 96, No. 232, 2000, pp. 70-83
    • (2000) Proceedings of the Fifth FOCAPD Conference. AICHE Symposium Series , vol.96 , Issue.232 , pp. 70-83
    • Grossmann, I.E.1    Hooker, J.N.2
  • 22
  • 23
    • 0000788402 scopus 로고    scopus 로고
    • Lifted flow cover inequalities for mixed 0-1 integer programs
    • Gu, Z., Nemhauser, G.L., Savelsbergh, M.W.P.: Lifted flow cover inequalities for mixed 0-1 integer programs. Math. Program. 85, 439-467 (1999)
    • (1999) Math. Program , vol.85 , pp. 439-467
    • Gu, Z.1    Nemhauser, G.L.2    Savelsbergh, M.W.P.3
  • 25
    • 0038207666 scopus 로고
    • LP-Based combinatorial problem solving
    • Hoffman, K., Padberg, M.W.: LP-Based combinatorial problem solving. Ann. Oper. Res. 4, 145-194 (1985)
    • (1985) Ann. Oper. Res , vol.4 , pp. 145-194
    • Hoffman, K.1    Padberg, M.W.2
  • 29
    • 18544400246 scopus 로고    scopus 로고
    • Mixed logical/linear programming
    • Hooker, J.N., Osorio, M.A.: Mixed Logical/Linear Programming. Discrete Appl. Math. 96/97, 395-442 (1999)
    • (1999) Discrete Appl. Math , vol.96-97 , pp. 395-442
    • Hooker, J.N.1    Osorio, M.A.2
  • 31
  • 32
    • 0010986664 scopus 로고    scopus 로고
    • Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
    • Jain, V., Grossmann, I.E.: Algorithms for hybrid milp/cp models for a class of optimization problems. INFORMS J. Comput. 4, 258-276 (2001) (Pubitemid 33645944)
    • (2001) INFORMS Journal on Computing , vol.13 , Issue.4 , pp. 258-276
    • Jain, V.1    Grossmann, I.E.2
  • 35
    • 0007797750 scopus 로고
    • On the solution of discrete programming problems
    • Markowitz, H.M., Manne, A.S.: On the solution of discrete programming problems. Econometrica 25, 84-110 (1957)
    • (1957) Econometrica , vol.25 , pp. 84-110
    • Markowitz, H.M.1    Manne, A.S.2
  • 39
    • 0000214393 scopus 로고
    • A note on zero-one programming
    • Padberg, M.W.: A Note on Zero-One Programming. Oper. Res. 23, 883-837 (1975)
    • (1975) Oper. Res , vol.23 , pp. 883-837
    • Padberg, M.W.1
  • 40
    • 0023313723 scopus 로고
    • Optimization of a 532-city symmetric traveling salesman problem by branch and cut
    • DOI 10.1016/0167-6377(87)90002-2
    • Padberg, M.W., Rinaldi, G.: Optimization of a 532-City symmetric traveling salesman problem by branch-and-Cut. Oper. Res. Lett. 6, 1-7 (1987) (Pubitemid 17601864)
    • (1987) Operations Research Letters , vol.6 , Issue.1 , pp. 1-7
    • Padberg, M.1    Rinaldi, G.2
  • 41
    • 0001412587 scopus 로고
    • Large-scale portfolio optimization
    • Perold, A.F.: Large-Scale portfolio optimization. Mgmt. Sci. 30, 1143-1160 (1984)
    • (1984) Mgmt. Sci , vol.30 , pp. 1143-1160
    • Perold, A.F.1
  • 42
    • 0001267667 scopus 로고
    • Structure of a Simple Scheduling Polyhedron
    • Queyranne, M.: Structure of a Simple Scheduling Polyhedron. Math. Program. 58, 263-285 (1993)
    • (1993) Math. Program , vol.58 , pp. 263-285
    • Queyranne, M.1
  • 43
    • 34250085380 scopus 로고
    • Symbolic integration of logic in MILP branch-and-bound methods for the synthesis of process networks
    • Raman R., Grossmann, I.E.: Symbolic Integration of Logic in MILP Branch-and-Bound Methods for the Synthesis of Process Networks. Ann. Oper. Res. 42, 169-191 (1993)
    • (1993) Ann. Oper. Res , vol.42 , pp. 169-191
    • Raman, R.1    Grossmann, I.E.2
  • 44
    • 84879208352 scopus 로고    scopus 로고
    • Branch-and-Check: A Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming
    • Principles and Practice of Constraint Programming - CP 2001
    • Thorsteinsson, E.S.: Branch-and-Check:A Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming. In: T.Walsh (Ed.), Proceedings of the Seventh International Conference on Principles and Practice of Constraint Programming, Lecture Notes of Computer Science 2239, Springer, 2001, pp. 16-30 (Pubitemid 33371064)
    • (2001) Lecture Notes in Computer Science , Issue.2239 , pp. 16-30
    • Thorsteinsson, E.S.1
  • 46
    • 0023250226 scopus 로고
    • Solving mixed-integer programming problems using automatic reformulation
    • van Roy, T.J.,Wolsey, L.A.: Solving mixed-integer programming problems using automatic reformulation. Oper. Res. 35, 45-57 (1987)
    • (1987) Oper. Res , vol.35 , pp. 45-57
    • Van Roy, T.J.1    Wolsey, L.A.2
  • 47
    • 34250395041 scopus 로고
    • Faces for a Linear Inequality in 0-1 Variables
    • Wolsey, L.A.: Faces for a Linear Inequality in 0-1 Variables. Math. Program. 8, 165-178 (1975)
    • (1975) Math. Program , vol.8 , pp. 165-178
    • Wolsey, L.A.1
  • 48
    • 0000413764 scopus 로고
    • Facets and strong valid inequalities for integer programs
    • Wolsey, L.A.: Facets and strong valid inequalities for integer programs. Oper. Res. 24, 367-372 (1976)
    • (1976) Oper. Res , vol.24 , pp. 367-372
    • Wolsey, L.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.