Abstract
In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of non-dominated extreme points. Finding it is a computationally hard problem in general. While solvers for similar problems exist, there are none known for multi-objective mixed integer linear programs (MOMILPs) or multi-objective mixed integer quadratically constrained quadratic programs (MOMIQCQPs). We present PaMILO, the first solver for finding non-dominated extreme points of MOMILPs and MOMIQCQPs. It can be found on github under https://github.com/FritzBo/PaMILO. PaMILO provides an easy-to-use interface and is implemented in C++17. It solves occurring subproblems employing either CPLEX or Gurobi. PaMILO adapts the Dual-Benson algorithm for multi-objective linear programming (MOLP). As it was previously only defined for MOLPs, we describe how it can be adapted for MOMILPs, MOMIQCQPs and even more problem classes in the future.
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References
Antunes, C. H., Martins, A. G., & Brito, I. S. (2004). A multiple objective mixed integer linear programming model for power generation expansion planning. Energy, 29(4), 613–627.
Benson, H. P. (1995). Concave minimization: Theory, applications and algorithms. In Handbook of global optimization, pp. 43–148. Springer.
Bökler, F. (2018). Output-sensitive complexity of multiobjective combinatorial optimization with an application to the multiobjective shortest path problem. Ph.D. thesis
Bökler, F., Parragh, S.N., Sinnl, M., & Tricoire, F. (2021). An outer approximation algorithm for multi-objective mixed-integer linear and non-linear programming. Preprint. https://doi.org/10.48550/ARXIV.2103.16647
Bökler, F., & Mutzel, P. (2015). Output-sensitive algorithms for enumerating the extreme nondominated points of multiobjective combinatorial optimization problems. In Algorithms—ESA 2015, LNCS, Vol. 9294, pp. 288–299
Borndörfer, R., Schenker, S., Skutella, M., & Strunk, T. (2016). Polyscip. In Mathematical Software—ICMS 2016. LNCS, Vol. 9725, pp. 259–264
Csirmaz, L. (2021). Inner approximation algorithm for solving linear multiobjective optimization problems. Optimization, 70(7), 1487–1511.
Ehrgott, M., Löhne, A., & Shao, L. (2012). A dual variant of Benson’s “outer approximation algorithm for multiple objective linear programming. Journal of Global Optimization, 52(4), 757–778.
Ehrgott, M., Waters, C., Kasimbeyli, R., & Ustun, O. (2009). Multiobjective programming and multiattribute utility functions in portfolio optimization. INFOR: Information Systems and Operational Research, 47(1), 31–42.
Hamel, A. H., Löhne, A., & Rudloff, B. (2014). Benson type algorithms for linear vector optimization and applications. Journal of Global Optimization, 59(4), 811–836.
Heyde, F., & Löhne, A. (2008). Geometric duality in multiple objective linear programming. SIAM Journal on Optimization, 19(2), 836–845.
Kirlik, G., & Sayın, S. (2015). Computing the nadir point for multiobjective discrete optimization problems. Journal of Global Optimization, 62(1), 79–99.
Löhne, A., & Weißing, B. (2017). The vector linear program solver Bensolve—notes on theoretical background. European Journal of Operational Research, 260(3), 807–813.
Löhne, A., Rudloff, B., & Ulus, F. (2014). Primal and dual approximation algorithms for convex vector optimization problems. Journal of Global Optimization, 60(4), 713–736.
Mavrotas, G., & Diakoulaki, D. (1998). A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research, 107(3), 530–541.
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Bökler, F., Nemesch, L., Wagner, M.H. (2023). PaMILO: A Solver for Multi-objective Mixed Integer Linear Optimization and Beyond. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_20
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