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.
MOMIP: Multi-objective (mixed) integer programming
Austrian Science Fund (FWF)
October 1, 2018 - September 30, 2021, extended to September 30, 2022
Sophie N. Parragh
Duleabom An, Miriam Enzi, Markus Sinnl, Oryan Rampon.
Gutjahr, M., Parragh, S.N., Tricoire, F. (2023). Adaptive Large Neighborhood Search for a personnel task scheduling problem with task selection and parallel task assignments. (submitted) https://arxiv.org/abs/2302.04494, opens an external URL in a new window
Forget, N., Parragh, S.N. (2022). Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming. (submitted) https://arxiv.org/abs/2210.05385, opens an external URL in a new window
Bökler, F., Parragh, S.N., Sinnl, M., Tricoire, F. (2022). An outer approximation algorithm for
multi-objective mixed-integer linear and non-linear programming (submitted) https://arxiv.org/abs/2103.16647, opens an external URL in a new window
An, B., Parragh, S.N., Sinnl, M., Tricoire, F. (2022). A matheuristic for tri-objective binary integer programming (submitted) http://arxiv.org/abs/2205.03386, opens an external URL in a new window
Nazemi, N., Parragh, S.N., Gutjahr, W. (2022). Bi-objective risk-averse facility location using a subset-based representation of the conditional value-at-risk. In Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES, ISBN 978-989-758-548-7, pages 77-85. 10.5220/0010914900003117, opens an external URL in a new window [Best Student Paper Award]
Nazemi, N., Parragh, S. N., Gutjahr, W. J. (2022). Bi-objective facility location under uncertainty with an application in last-mile disaster relief. Annals of Operations Research, 319, 1689-1716. https://doi.org/10.1007/s10479-021-04422-4, opens an external URL in a new window
Parragh, S.N., Tricoire, F., Gutjahr, W.J. (2022). A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem. OR Spectrum, 44, 419-459. https://doi.org/10.1007/s00291-020-00616-7, opens an external URL in a new window Preprint: https://arxiv.org/abs/2004.11248, opens an external URL in a new window
Enzi, M., Parragh, S.N., Puchinger, J. (2022). The bi-objective multimodal car-sharing problem. OR Spectrum, 44, 307–348. https://doi.org/10.1007/s00291-021-00631-2, opens an external URL in a new window Preprint: http://arxiv.org/abs/2010.10344, opens an external URL in a new window
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, 293(1), 290-303. https://doi.org/10.1016/j.ejor.2020.11.046, opens an external URL in a new window, Preprint: https://arxiv.org/abs/2001.05490, opens an external URL in a new window
An D., Parragh S., Sinnl M. and Tricoire F. (2021). A LP Relaxation based Matheuristic for Multi-objective Integer Programming. In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems: ICORES, ISBN 978-989-758-485-5, pages 88-98. DOI: 10.5220/0010347000880098, opens an external URL in a new window, Preprint: https://arxiv.org/abs/2102.03582, opens an external URL in a new window
Gutjahr, M., Kellerer, H., Parragh, S.N. (2021). Heuristic approaches for scheduling jobs and vehicles in a cyclic flexible manufacturing system. Procedia Computer Science 180, 825-832. https://doi.org/10.1016/j.procs.2021.01.332, opens an external URL in a new window
Alvarez-Miranda, E., Goycoolea, M., Ljubic, I., Sinnl, M. (2021) The Generalized Reserve Set Covering Problem with Connectivity and Buffer Requirements. European Journal of Operational Research, 289(3), 1013-1029. https://doi.org/10.1016/j.ejor.2019.07.017, opens an external URL in a new window
Preprint: https://arxiv.org/abs/1909.04473, opens an external URL in a new window
Enzi, M., Parragh, S. N., & Pisinger, D. (2020). Modeling and solving a vehicle-sharing problem. arXiv preprint arXiv:2003.08207. https://arxiv.org/abs/2003.08207, opens an external URL in a new window (submitted for publication)