Skip to main content
Springer Nature Link
Log in

A branch-and-cut technique to solve multiobjective integer quadratic programming problems

  • Multiple Objective Optimization
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient solutions. The features of the method are as follows. First, the branch and bound technique allows solving the relaxed problem according to any linear function and progressively generates integer solutions. Then, the efficient cut proposed reduces the search area by truncating domains containing non efficient solutions without having to enumerate them. Finally, at each node of the tree search, three fathoming rules are used to enhance the speed of the procedure. Computational experiments are presented in order to analyze the performance of the algorithm.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  • Chergui, M. E.-A., Moulaï, M., & Ouaïl, F. Z. (2008). Solving the multiple objective integer linear programming problem. Modeling, Computation and Optimization in Information Systems and Management Sciences, 14, 69–76.

    Article  Google Scholar 

  • Dantzig, G. B. (1959). Note on solving linear programs in integers. Naval Research Logistics, 6, 75–76.

    Article  Google Scholar 

  • Day, R. O., Kleeman, M. P., & Lamont, G. B. (2003). Solving the multiobjective quadratic assignment problem using a fast messy genetic algorithm. In Proceedings of the 2003 congress on evolutionary computation (Vol. 3, pp. 2277–2283).

  • Jain, E., Dahiya, K., & Verma, V. (2017). Integer quadratic fractional programming problems with bounded variables. Annals of Operations Research. https://doi.org/10.1007/s10479-017-2484-5.

  • Malakooti, B., & D’souza, G. I. (1987). Multiple objective programming for the quadratic assignment problem. International Journal of Production Research, 25(2), 285–300.

    Article  Google Scholar 

  • Markowitz, H. M. (1959). Portfolio selection: Efficient diversification of investments (pp. 77–91). New York: Wiley.

    Google Scholar 

  • Pisinger, D. (2007). The quadratic knapsack problem—-A survey. Discrete Applied Mathematics, 155(5), 623–648.

    Article  Google Scholar 

  • Steuer, R. E., Qi, Y., & Hirschberger, M. (2007). Suitable-portfolio investors, nondominated frontier sensitivity, and the effect on standard portfolio selection. Annals of Operations Research, 152, 297–317.

    Article  Google Scholar 

  • Steuer, R. E., Wimmer, M., & Hirschberger, M. (2013). Overviewing the transition of Markowitz bi-criterion portfolio selection to tri-criterion portfolio selection. Journal of Business Economics, 83(1), 61–85.

    Article  Google Scholar 

  • Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491–498.

    Article  Google Scholar 

  • Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for creating more-sustainable mutual funds. European Journal of Operational Research, 26(1), 331–338.

    Article  Google Scholar 

  • Zhang, H., Cesar, B. R., & Liang, M. (2013). Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers. Annals of Operations Research, 207(1), 261–278.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Operational Research, Faculty of Mathematics, USTHB, BP 32, Bab Ezzouar, 16111, Algiers, Algeria

    Fatma Zohra Ouaïl

  2. RECITS Laboratory, Faculty of Mathematics, USTHB, BP 32, Bab Ezzouar, 16111, Algiers, Algeria

    Mohamed El-Amine Chergui

Authors
  1. Fatma Zohra Ouaïl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed El-Amine Chergui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatma Zohra Ouaïl.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ouaïl, F.Z., Chergui, M.EA. A branch-and-cut technique to solve multiobjective integer quadratic programming problems. Ann Oper Res 267, 431–446 (2018). https://doi.org/10.1007/s10479-017-2698-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-017-2698-6

Keywords

Mathematics Subject Classification

Search

Navigation