Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms

Published Online:https://doi.org/10.1287/ijoc.1080.0284

References

  • Aardal K., Weismantel R., Wolsey L. A. Non-standard approaches to integer programming. Discrete Appl. Math. (2002) 123:5–74CrossrefGoogle Scholar
  • Agra A., Constantino M. F. Lifting two-integer knapsack inequalities. Math. Programming (2007) 109:115–154CrossrefGoogle Scholar
  • Arnold L. R., Bellmore M. A bounding minimization problem for primal integer programming. Oper. Res. (1974a) 22:383–392LinkGoogle Scholar
  • Arnold L. R., Bellmore M. A generated cut for primal integer programming. Oper. Res. (1974b) 22:137–143LinkGoogle Scholar
  • Arnold L. R., Bellmore M. Iteration skipping in primal integer programming. Oper. Res. (1974c) 22:129–136LinkGoogle Scholar
  • Atamtürk A. On the facets of the mixed-integer knapsack polyhedron. Math. Programming (2003) 98:145–175CrossrefGoogle Scholar
  • Atamtürk A. Sequence independent lifting for mixed-integer programming. Oper. Res. (2004) 52:487–490LinkGoogle Scholar
  • Atamtürk A., Nemhauser G. L., Savelsbergh M. W. P. Conflict graphs in solving integer programming problems. Eur. J. Oper. Res. (2000) 121:40–55CrossrefGoogle Scholar
  • Balas E. Facets of the knapsack polytope. Math. Programming (1975) 8:146–164CrossrefGoogle Scholar
  • Balas E., Zemel E. Facets of knapsack polytope from minimal covers. SIAM J. Appl. Math. (1984) 34:119–148CrossrefGoogle Scholar
  • Ben-Israel A., Charnes A. On some problems of diophantine programming. Cahiers du Centre d'Etudes de Recherche Operationelle (1962) 4:215–280Google Scholar
  • Bixby R. E., Boyd E. A., Indovina R. R. MIPLIB: A test set of mixed integer programming problems. SIAM News (1992) 25:16Google Scholar
  • Ceria S., Cordier C., Marchand H., Wolsey L. A. Cutting planes for integer programs with general integer variables. Math. Programming (1998) 81:201–214CrossrefGoogle Scholar
  • Chvátal V.Linear Programming (1983) (W. H. Freeman and Company, New York) Google Scholar
  • Dietrich B. L., Escudero L. F. Coefficient reduction for knapsack-like constraints in 0–1 program with variable upper bounds. Oper. Res. Lett. (1990) 2:9–14CrossrefGoogle Scholar
  • Garfinkel R. S., Nemhauser G. L.Integer Programming (1972) (Wiley-Interscience, New York) Google Scholar
  • Glover F. A new foundation for a simplified primal integer programming algorithm. Oper. Res. (1968) 16:724–740LinkGoogle Scholar
  • Gomory R. E. An algorithm for the mixed-integer problem. (1960) . Report P-1885, The Rand Corporation, Santa Monica, CAGoogle Scholar
  • Gu Z., Nemhauser G. L., Savelsbergh M. W. P. Lifted flow covers for mixed 0–1 integer programs. Math. Programming (1999) 85:439–467CrossrefGoogle Scholar
  • Gu Z., Nemhauser G. L., Savelsbergh M. W. P. Sequence independent lifting in mixed integer programming. J. Combin. Optim. (2000) 4:109–129CrossrefGoogle Scholar
  • Guignard M., Spielberg K. Logical reduction methods in 0–1 programming. Oper. Res. (1981) 29:49–74LinkGoogle Scholar
  • Hammer P. L., Johnson E. L., Peled U. N. Facets of regular 0–1 polytopes. Math. Programming (1975) 8:179–206CrossrefGoogle Scholar
  • Haus U., Köppe M., Weismantel R. A primal all-integer algorithm based on irreducible solutions. Math. Programming (2003) 96:205–246CrossrefGoogle Scholar
  • Henk M., Köppe M., Weismantel R. Integral decomposition of polyhedra and some applications in mixed integer programming. Math. Programming (2003) 94:193–206CrossrefGoogle Scholar
  • Hoffman K. L., Padberg M. Improving LP-representation of zero-one linear programs for branch-and-cut. ORSA J. Comput. (1991) 3:121–134LinkGoogle Scholar
  • Johnson E. L., Kostreva M., Suhl U. H. Solving 0–1 integer programming problems arising from large-scale planning models. Oper. Res. (1981) 33:803–819LinkGoogle Scholar
  • Johnson E. L., Nemhauser G. L., Savelsbergh M. W. P. Progress in linear programming-based algorithms for integer programming: An exposition. INFORMS J. Comput. (2000) 12:2–23LinkGoogle Scholar
  • Kaparis K., Letchford A. N. Local and global lifted cover inequalities for the multidimensional knapsack problem. Eur. J. Oper. Res. (2008) 186:91–103CrossrefGoogle Scholar
  • Köppe M., Weismantel R. An algorithm for mixed integer optimization. Math. Programming (2003) 98:281–308CrossrefGoogle Scholar
  • Letchford A. N., Lodi A. Primal cutting plane algorithm revisited. Math. Methods Oper. Res. (2002) 56(1):67–81CrossrefGoogle Scholar
  • Letchford A. N., Lodi A. Primal separation algorithms. Quart. J. Belgian, French Italian Oper. Res. Soc. (2003) 1:209–224Google Scholar
  • Marchand H., Martin A., Weismantel R., Wolsey L. A. Cutting planes in integer and mixed integer programming. Discrete Appl. Math. (2002) 23:397–446CrossrefGoogle Scholar
  • Martin A., Weismantel R., Bixby R. E., Boyd E. A., Ríos-Mercado R. Z. The intersection of knapsack polyhedron and extensions. Proc. 6th IPCO Conf. (1998) (Springer-Verlag, Copenhagen) 243–256Google Scholar
  • Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (Wiley-Interscience, New York) CrossrefGoogle Scholar
  • Padberg M. W. On the facial structure of set packing polyhedra. Math. Programming (1973) 5:199–215CrossrefGoogle Scholar
  • Padberg M. W. A note on zero-one programming. Oper. Res. (1975) 23:833–837LinkGoogle Scholar
  • Padberg M. W., Hong S. On the symmetric travelling salesman problem: A computational study. Math. Programming (1980) 12:78–107CrossrefGoogle Scholar
  • Rajan D. Designing capacitated survivable networks: Polyhedral analysis and algorithms. (2004) . Ph.D. thesis, University of California, Berkeley, BerkeleyGoogle Scholar
  • Richard J.-P. P., de Farias I. R., Nemhauser G. L. Lifted inequalities for 0–1 mixed integer programming: Basic theory and algorithms. Math. Programming (2003a) 98:89–113CrossrefGoogle Scholar
  • Richard J.-P. P., de Farias I. R., Nemhauser G. L. Lifted inequalities for 0–1 mixed integer programming: Superlinear lifting. Math. Programming (2003b) 98:115–143CrossrefGoogle Scholar
  • Savelsbergh M. W. P. Preprocessing and probing techniques for mixed integer programming problems. ORSA J. Comput. (1994) 6:445–454LinkGoogle Scholar
  • Sharma S., Sharma B. New technique for solving primal all-integer linear programming. Opsearch (1997) 34:62–68CrossrefGoogle Scholar
  • Wolsey L. A. Facets and strong inequalities for integer programs. Oper. Res. (1976) 24:367–372LinkGoogle Scholar
  • Wolsey L. A. Valid inequalities and superadditivity for 0–1 integer programs. Math. Oper. Res. (1977) 2:66–77LinkGoogle Scholar
  • Young R. D. A primal (all-integer) integer programming algorithm. J. Res. National Bureau Standards (1965) 69B:213–250CrossrefGoogle Scholar
  • Young R. D. A simplified primal (all-integer) integer programming algorithm. Oper. Res. (1968) 16:750–782LinkGoogle Scholar
  • Young R. D. The eclectic primal algorithm: Cutting-plane method that accommodates hybrid subproblem solution techniques. Math. Programming (1975) 9:294–312CrossrefGoogle Scholar
  • Zeng B., Richard J.-P. P. Sequence independent lifting for 0–1 knapsack problems with disjoint cardinality constraints. Optimization Online (2006) September 20). http://www.optimization-online.org/DB_HTML/2006/09/1468.htmlGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.