Skip to main content
SpringerLink
Log in

Optimising a nonlinear utility function in multi-objective integer programming

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.

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. Abbas M., Chaabane D.: Optimizing a linear function over an integer efficient set. Eur. J. Oper. Res. 174(2), 1140–1161 (2006)

    Article  Google Scholar 

  2. Benson H.P., Sun E.: Outcome space partition of the weight set in multiobjective linear programming. J. Optim. Theory Appl. 105(1), 17–36 (2000)

    Article  Google Scholar 

  3. Benson H.P., Sun E.: A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program. Eur. J. Oper. Res. 139(1), 26–41 (2002)

    Article  Google Scholar 

  4. Dhaenens C., Lemesre J., Talbi E.G.: K-PPM: a new exact method to solve multi-objective combinatorial optimization problems. Eur. J. Oper. Res. 200(1), 45–53 (2010)

    Article  Google Scholar 

  5. Ehrgott M.: A discussion of scalarization techniques for multiple objective integer programming. Ann. Oper. Res. 147, 343–360 (2006)

    Article  Google Scholar 

  6. Ehrgott M., Gandibleux X.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22(4), 425–460 (2000)

    Article  Google Scholar 

  7. Ehrgott M., Gandibleux X.: (ed.): Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys, International Series in Operations Research Management Science. Vol. 52, Kluwer, Boston (2002)

    Google Scholar 

  8. Ehrgott M., Gandibleux X.: Approximative solution methods for multiobjective combinatorial optimization. Top 12(1), 1–89 (2004)

    Article  Google Scholar 

  9. Galand L., Perny P., Spanjaard O.: Choquet-based optimisation in multiobjective shortest path and spanning tree problems. Eur. J. Oper. Res. 204(2), 303–315 (2010)

    Article  Google Scholar 

  10. Galand L., Perny P., Spanjaard O.: A branch and bound algorithm for choquet optimization in multicriteria problems. In: Ehrgott, M., Naujoks, B., Stewart, T.J., Wallenius, J. (eds.) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems volume 634 of Lecture Notes in Economics and Mathematical Systems, pp. 355–365. Springer, Berlin (2010)

    Chapter  Google Scholar 

  11. Jorge J.M.: An algorithm for optimizing a linear function over an integer efficient set. Eur. J. Oper. Res. 195(1), 98–103 (2009)

    Article  Google Scholar 

  12. Klamroth K., Tind J., Zust S.: Integer programming duality in multiple objective programming. J. Glob. Optim. 29(1), 1–18 (2004)

    Article  Google Scholar 

  13. Klein D., Hannan E.: An algorithm for the multiple objective integer linear programming problem. Eur. J. Oper. Res. 9(4), 378–385 (1982)

    Article  Google Scholar 

  14. Le Huédé F., Grabisch M., Labreuche C., Savéant P.: Integration and propagation of a multi-criteria decision making model in constraint programming. J. Heurist. 12, 329–346 (2006)

    Article  Google Scholar 

  15. Özlen M., Azizoğlu M.: Multi-objective integer programming: a general approach for generating all non-dominated solutions. Eur. J. Oper. Res. 199(1), 25–35 (2009)

    Article  Google Scholar 

  16. Özpeynirci Ö., Köksalan M.: An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Manag. Sci. 56(12), 2302–2315 (2010)

    Article  Google Scholar 

  17. Perny P., Spanjaard O.: A preference-based approach to spanning trees and shortest paths problems. Eur. J. Oper. Res. 162(3), 584–601 (2005)

    Article  Google Scholar 

  18. Przybylski A., Gandibleux X., Ehrgott M.: A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discret. Optim. 7(3), 149–165 (2010)

    Article  Google Scholar 

  19. Przybylski A., Gandibleux X., Ehrgott M.: A recursive algorithm for finding all nondominated extreme points in the outcome set of a multiobjective integer programme. INFORMS J. Comput. 22(3), 371–386 (2010)

    Article  Google Scholar 

  20. Sylva J., Crema A.: A method for finding the set of non-dominated vectors for multiple objective integer linear programs. Eur. J. Oper. Res. 158(1), 46–55 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V, Melbourne, VIC, 3001, Australia

    Melih Ozlen

  2. Department of Industrial Engineering, Middle East Technical University, 06531, Ankara, Turkey

    Meral Azizoğlu

  3. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia

    Benjamin A. Burton

Authors
  1. Melih Ozlen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meral Azizoğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Benjamin A. Burton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Melih Ozlen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ozlen, M., Azizoğlu, M. & Burton, B.A. Optimising a nonlinear utility function in multi-objective integer programming. J Glob Optim 56, 93–102 (2013). https://doi.org/10.1007/s10898-012-9921-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-012-9921-4

Keywords

Search

Navigation