Solving Large-Scale Integer Optimization Problems

  • Kurt Spielberg
  • Uwe H. Suhl
Part of the Progress in Scientific Computing book series (PSC, volume 7)


We survey proven state-of-the-art solution techniques for solving large-scale integer optimization problems and describe an experimental software system for the solution of large 0–1 integer optimization problems. This system is built around a large commercial LP-system (MPSX/370) and uses sophisticated data structures for an efficient implementation. Numerical results for difficult and large real-life problems were significantly better than with traditional branch-and-bound algorithms such as implemented in commercial software systems.


Integer Solution Side Constraint Logical Test Optimal Integer Solution Integer Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Balas, An additive algorithm for solving linear programs with zero-one variables, Opns. Res. 13(1965), 517–546MathSciNetCrossRefGoogle Scholar
  2. 2.
    J.F. Benders, Partitioning procedures for solving mixed variables programming problems, Numerische Mathematik 4(1961), 238–252MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Brearley, G. Mitra, and H.P Williams, Analysis of mathematical programming problems prior to applying the simplex method, Math. Programming 8 (1975), 54–83MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    R. Breu and C.A. Burdet, Branch and Bound experiments in 0–1 programming, Mathematical Programming Study, 2(1974), 1–50MathSciNetCrossRefGoogle Scholar
  5. 5.
    H.P. Crowder, E.L Johnson and M.W. Padberg, Solving Large-Scale Zero-One Linear Programming Problems, Opns. Res. 31(5)(1983), 803–834zbMATHCrossRefGoogle Scholar
  6. 6.
    M. Guignard and K. Spielberg, Logical Reduction Methods in Zero-One Programming, Opns. Res. 29(1981), 49–74MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    R. S. Garfinkel and G. L. Nemhauser, Integer Programming, Wiley, N.Y., 1972zbMATHGoogle Scholar
  8. 8.
    M. Guignard, K. Spielberg and U. Suhl, Survey of enumerative methods for integer programming, in Proc. Share 51, (ACM 1978) 2161–2170Google Scholar
  9. 9.
    E.L. Johnson, M.M Kostreva and U.H. Suhl, Solving 0–1 Integer Programming Problems arising from Large Scale Planning Models, Opns. Res. 33(4), 803–819Google Scholar
  10. 10.
    E. Kalan, Aspects of large-scale in-core linear programming ACM Proc. of annual conference (1971), 304–313Google Scholar
  11. 11.
    E.L. Johnson and M.W. Padberg, Degree-Two Inequalities, Clique Facets and Biperfect Graphs, Ann. Discrete Math. 16(1982), 169–187MathSciNetzbMATHGoogle Scholar
  12. 12.
    E.L. Johnson and U.H. Suhl, Experiments in integer programming, Discrete Applied Mathematics 2(1980), 39–55MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    A.H. Land and S. Powell, Computer codes for problems of Integer Programming, Annals of Discrete Mathematics 5(1979), 221–269MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    C.E. Lemke and K. Spielberg, Direct search algorithms for zero-one and mixed-integer programming, Opns. Res. 15(1967), 892–914MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    T.G. Mairs, G.W. Wakefield, E.L. Johnson and K. Spielberg, On a production allocation and distribution problem, Man. Science 24(1978), 1622–1630Google Scholar
  16. 16.
    L.A. Oley and R.S. Sjoquist, Automatic Reformulation Of Mixed and Pure Integer Models To Reduce Solution Time In APEX IV, Paper presented at the ORSA/TIMS Meeting in San Diego, California, October 1982Google Scholar
  17. 17.
    C.J. Piper, Implicit enumeration: a computational study, Rep. 115, School of Bus. Adm., Univ. of West. Ont., 1974Google Scholar
  18. 18.
    H.P. Williams, Model Building in Mathematical Programming, John Wiley, 1978zbMATHGoogle Scholar

Copyright information

© Birkhäuser Boston 1987

Authors and Affiliations

  • Kurt Spielberg
  • Uwe H. Suhl

There are no affiliations available

Personalised recommendations