Aggregation and Mixed Integer Rounding to Solve MIPs

References

• Balas E., Mangasarian O. L., et al. Disjunctive programs: cutting planes from logical conditions. Nonlinear programing Vol. 2 (1975) (Academic Press, New York) 279–312Google Scholar
• Balas E., Ceria S., Cornuéjols G. Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Management Sci. (1996) 42:1229–1246Link, Google Scholar
• Balas E., Ceria S., Cornuéjols G., Natraj G. Gomory cuts revisited. Oper. Res. Lett. (1996) 19:1–9Crossref, Google Scholar
• Barany I., Van Roy T. J., Wolsey L. A. Strong formulations for multi-item capacitated lot-sizing. Management Sci. (1984) 30:1255–1261Link, Google Scholar
• Bienstock D., Günlük O. Capacitated network design—polyhedral structure and computation. ORSA J. Comput. (1996) 8:243–259Link, Google Scholar
• Bixby R. E., Ceria S., McZeal C. M., Savelsbergh M. W. P.An updated mixed integer programming library: MIPLIB 3.0 (1998) . Text and problems available at http://www.caam.rice.edu/~bixby/miplib/miplib.htmlGoogle Scholar
• Brockmüller B., Günlük O., Wolsey L. A.Designing private line networks (1998) (Université Catholique de Louvain, Louvain-la-Neuve, Belgium) . Revised version of CORE DP9647Google Scholar
• Caprara A., Fischetti M. {0, 1/2}-Chvátal-Gomory cuts. Mathematical Programming (1996) 74:221–236Crossref, Google Scholar
• Ceria S., Cornuéjols G., Dawande M., Balas E., Clausen J. Combining and strengthening Gomory cuts. (1995) Proc. 4th IPCO Conference(Copenhagen, Denmark) 438–451Springer-VerlagCrossref, Google Scholar
• Ceria S., Cordier C., Marchand H., Wolsey L. A. Cutting planes for integer programs with general integer variables. Mathematical Programming (1998) 81:201–214Crossref, Google Scholar
• Ceria S., Pataki G. Solving integer and disjunctive programs with lift-and-project. Proc. 6th IPCO Conference (1998) Houston, TX:271–284Crossref, Google Scholar
• Cook W. J., Kannan R., Schrijver A. Chvátal closures for mixed integer programming problems. Mathematical Programming (1990) 47:155–174Crossref, Google Scholar
• Cordier C., Marchand H., Laundy R., Wolsey L. A. bc-opt:a branch-and-cut code for mixed intger programs. Mathematical Programming (1999) 86:335–353Crossref, Google Scholar
• Gomory R. E., Bellman R. E., Hall M. Solving linear programming problems in integers. Combinatorial Analysis (1960a) (American Mathematical Society)211–216Crossref, Google Scholar
• Gomory R. E.An algorithm for the mixed integer problem. RM-2597 (1960b) (The Rand Corporation)Google Scholar
• Gu Z., Nemhauser G. L., Savelsbergh M. W. P. Lifted flow covers for mixed 0-1 integer programs. Mathematical Programming (1999) 85:439–468Crossref, Google Scholar
• Günlük O., Pochet Y.Mixing mixed-integer inequalities (1998) (Université Catholique de Louvain, Louvain-la-Neuve, Belgium) . CORE Discussion Paper DP9811Google Scholar
• Lovász L., Schrijver A. Cones of matrices and set functions and 0-1 optimization. SIAM J. Optimiz. (1991) 1:166–190Crossref, Google Scholar
• Magnanti T. L., Mirchandani P., Vachani R. The convex hull of two core capacitated network design problems. Mathematical Programming (1993) 60:233–250Crossref, Google Scholar
• Marchand H., Wolsey L. A. The 0-1 knapsack problem with a single continuous variable. Mathematical Programming (1997) 85:15–33Crossref, Google Scholar
• Marchand H. A study of the mixed knapsack set and its use to solve mixed integer programs. Ph.D. Dissertation, Faculté des Sciences Appliquées. (1998) (Université catholique de Louvain, Louvain-la-Neuve, Belgium) Google Scholar
• Martin A., Weismantel R.Contributions to general mixed integer knapsack problems (1997) (Konrad-Zuse-Zentrum für Informationstechnik, Berlin) . Preprint, SC 97-35Google Scholar
• Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (Wiley, New York) Crossref, Google Scholar
• Nemhauser G. L., Wolsey L. A. A recursive procedure for generating all cuts for 0-1 mixed integer programs. Mathematical Programming (1990) 46:379–390Crossref, Google Scholar
• Padberg M. W., Van Roy T. J., Wolsey L. A. Valid linear inequalities for fixed charge problems. Oper. Res. (1985) 33:842–861Link, Google Scholar
• Pamips. Esprit Project 8755. (1995) . Public Report Reference DR4.3.5/IGoogle Scholar
• Pochet Y., Wolsey L. A. Integer knapsacks and flow covers with divisible coeffcients: polyhedra, optimization and separation. Discrete Appl. Math. (1995) 59:57–74Crossref, Google Scholar
• Savelsbergh M. W. P., Nemhauser G. L. Functional description of MINTO, a Mixed INTeger Optimizer. (1993) . Report COC-91-03A, Georgia Institute of Technology, Atlanta, GAGoogle Scholar
• Van Roy T. J., Wolsey L. A. Solving mixed 0-1 problems by automatic reformulation. Oper. Res. (1987) 35:45–57Link, Google Scholar
• Wolsey L. A.Integer Programming (1998) (Wiley, New York) Google Scholar