MOMIP: Multi-objective (mixed) integer programming

3-year research project funded by the Austrian Science Fund (FWF) within the Matching Funds Program.

We live in a world full of trade-offs and quite often we only know comparably little about them. In almost every problem situation we encounter it is difficult to define the one and only goal to aim for, especially whenever more than one decision maker or stakeholder is involved. Thus, many if not all practical problems involve several and often conflicting objectives. Prominent examples are environmental concerns versus cost or customer satisfaction versus profitability. 

Our research is mainly rooted in the fields of transportation, logistics, and supply chain management and many relevant problems arising in these fields can be modeled as mixed integer linear programs. This means that there exist only rather simple, linear relationships between input parameters and decision variables and some variables may assume only integer values, e.g., the decision whether a distribution center should be built or not can only be 1 (yes) or 0 (no) but not 0.2. 

Despite the fact that these problems are often comparably easy to formulate they are quite often very difficult to solve. In addition, whenever multiple conflicting objectives are of concern, it is usually not possible to identify one best solution with respect to all of the considered goals. Rather, a set of optimal compromise solutions exists which are “better” than the other possible solutions and incomparable among each other. Each such solution represents a possible trade-off.

The computation of this set of optimal trade-off solutions is a complex task. All currently available exact methods have limitations. Either they are only applicable to problems with at most two objectives or they cannot describe the complete set of trade-off solutions. The kernel of this project is the development of efficient generic algorithms, using the branch-and-bound idea in a way that allows to exploit the multi-objective nature of the considered problems, and thus to close this gap for mixed integer linear programs with up to three objectives.

In order to illustrate the applicability of our algorithms, we will use them to solve practical problems arising in sustainable supply chain management, disaster relief distribution planning and green vehicle routing. Decision makers will thus receive additional information on the trade-off relationship between the considered goals. They will be given the possibility to compare different solutions and to finally choose the most suitable solution out of the set ofall optimal compromise solutions.

Research Project

MOMIP: Multi-objective (mixed) integer programming

Funding Agency

Austrian Science Fund (FWF)


October 1, 2018 - September 30, 2021

Project leader

Sophie N. Parragh


Project collaborators

Duleabom An, Miriam Enzi, Markus Sinnl.


  • The next "Recent Advances in Multi-Objective Optimization" (RAMOO) workshop will take place in Linz on September 17, 2020 Registration is now possible. The workshop will be entirely online.
  • Participation in the yearly Workshop "Recent advances in multi-objective Optimization" ( taking place in Nantes, November 15, 2018.


  • An, D., Sinnl, M., Tricoire F., Parragh, S.N.  "A LP relaxation based matheuristic for multi-objective optimization", ICORES, Feb 2021, online.
  • Parragh, S.N., "Integrated logistics planning: a bi-objective optimization perspective", Invoted Talk, ISM, Nov 2020, online. 
  • Parragh, S.N., Tricoire, F., Gutjahr, W.J. "Branch-and-Benders-cut for bi-objective integer programming: application to a stochastic facility location problem". Invited Talk, RAMOO - Recent Advances in Multi-Objective Optimization, Sep 26, 2019, Aarhus, Denmark.
  • Parragh, S.N., Enzi, M., Puchinger, J. "Solving the bi-objective multimodal car-sharing problem including time-dependent user preferences". OR 2019, Sep 3-6, 2019, Dresden, Germany.
  • An, D., Sinnl, M., Tricoire F., Parragh, S.N.  "A comparison of lower bound set algorithms for multi-objective branch-and-bound", OR 2019, Sep 3-6, 2019, Dresden, Germany.


Parragh, S. N., Tricoire, F., & Gutjahr, W. (2021). A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem. OR Spectrum, accepted. arXiv preprint arXiv:2004.11248 

Enzi, M., Parragh, S. N., & Puchinger, J. (2021). The bi-objective multimodal car-sharing problem, OR Spectrum, accepted.

Nazemi, N., Parragh, S. N., & Gutjahr, W. (2020). Bi-objective facility location in the presence of uncertainty (submitted for publication)

Enzi, M., Parragh, S. N., & Pisinger, D. (2020). Modeling and solving a vehicle-sharing problem. arXiv preprint arXiv:2003.08207 (submitted for publication)

Enzi, M., Parragh, S. N., Pisinger, D., & Prandtstetter, M. (2021). Modeling and solving the multimodal car-and ride-sharing problem. European Journal of Operational Research, arXiv preprint arXiv:2001.05490. 

Alvarez-Miranda, E., Goycoolea, M., Ljubic, I., Sinnl, M. (2019) The Generalized Reserve Set Covering Problem with Connectivity and Buffer Requirements. European Journal of Operational Research,