Skip to main content
SpringerLink
Log in

Solving integer programs with a few important binary gub constraints

  • Section VIII Scientific And Engineering Applications Of MP
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

During a branch and bound search of an integer program, decisions have to be taken about which subproblem to solve next and which variable or special ordered set to branch on. Both these decisions are usually based on some sort of estimated change in the objective caused by different branching. When the next subproblem is chosen, the estimated change in the objective is often found by summing the change caused by changing all integer variables with non-integer values, as if they were independent. For special ordered sets the estimation is done for each set as a whole. The purpose of this paper is to report some results from trying to do a simultaneous estimation for all the variables in a binary gub constraint. By this, the analysed problems contain one or a few constraints saying that the sum ofn binary variables should be equal tom (<n).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E.M.L. Beale, Branch and bound methods for mathematical programming systems, Ann. Discr. Math. 5(1979)201–219.

    Google Scholar 

  2. A.L. Brearley, G. Mitra and H.P. Williams, Analysis of mathematical programming problems prior to applying the simplex method, Math. Progr. 8(1975)54–83.

    Google Scholar 

  3. D. Kennedy, Some branch and bound techniques for nonlinear optimization, Math. Progr. 42(1988)147–157.

    Google Scholar 

  4. A. Land and S. Powell, Computer codes for problems of integer programming, Ann. Discr. Math. 5(1979)221–269.

    Google Scholar 

  5. B. Nygreen, A possible way to reduce degeneracy in integer programming computations, Oper. Res. Lett. 6(1987)47–51.

    Google Scholar 

  6. B. Nygreen, European assembly constituencies for Wales — comparing of methods for solving a political districting problem, Math. Progr. 42(1988)159–169.

    Google Scholar 

  7. B. Nygreen, Branch and bound with estimation based on pseudo shadow prices, Math. Progr. 59(1991)59–69.

    Google Scholar 

  8. Scicon, SCICONIC/VM User Guide, Scicon Ltd., Milton Keynes.

Download references

Author information

Authors and Affiliations

  1. Division of Economics, The Norwegian Institute of Technology, Trondheim, Norway

    Bjørn Nygreen

Authors
  1. Bjørn Nygreen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I am grateful to Scicon Ltd. for giving me access to the SCICONIC source code.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nygreen, B. Solving integer programs with a few important binary gub constraints. Ann Oper Res 43, 455–465 (1993). https://doi.org/10.1007/BF02024842

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02024842

Keywords

Search

Navigation