@inproceedings{GhannamMexiLametal.2024, author = {Ghannam, Mohammed and Mexi, Gioni and Lam, Edward and Gleixner, Ambros}, title = {Branch and price for the length-constrained cycle partition problem}, booktitle = {Proceedings of INFORMS Optimization Society Conference}, year = {2024}, language = {en} } @inproceedings{HendrychBesanconPokutta2024, author = {Hendrych, Deborah and Besan{\c{c}}on, Mathieu and Pokutta, Sebastian}, title = {Solving the optimal experiment design problem with mixed-integer convex methods}, volume = {301}, booktitle = {22nd International Symposium on Experimental Algorithms (SEA 2024)}, doi = {10.4230/LIPIcs.SEA.2024.16}, pages = {16:1 -- 16:22}, year = {2024}, abstract = {We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances.}, language = {en} } @article{WilkenBesanconKratochviletal.2022, author = {Wilken, St. Elmo and Besan{\c{c}}on, Mathieu and Kratochv{\´i}l, Miroslav and Kuate, Chilperic Armel Foko and Trefois, Christophe and Gu, Wei and Ebenh{\"o}h, Oliver}, title = {Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models}, journal = {Metabolic Engineering}, year = {2022}, language = {en} } @inproceedings{BestuzhevaGleixnerAchterberg2023, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Achterberg, Tobias}, title = {Efficient Separation of RLT Cuts for Implicit and Explicit Bilinear Products}, volume = {13904}, booktitle = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-32726-1_2}, pages = {14 -- 28}, year = {2023}, abstract = {The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and improve the performance of RLT for bilinear product relations. First, a method for detecting bilinear product relations implicitly contained in mixed-integer linear programs is developed based on analyzing linear constraints with binary variables, thus enabling the application of bilinear RLT to a new class of problems. Our second contribution addresses the high computational cost of RLT cut separation, which presents one of the major difficulties in applying RLT efficiently in practice. We propose a new RLT cutting plane separation algorithm which identifies combinations of linear constraints and bound factors that are expected to yield an inequality that is violated by the current relaxation solution. A detailed computational study based on implementations in two solvers evaluates the performance impact of the proposed methods.}, language = {en} } @inproceedings{MexiBertholdGleixneretal.2023, author = {Mexi, Gioni and Berthold, Timo and Gleixner, Ambros and Nordstr{\"o}m, Jakob}, title = {Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning}, volume = {280}, booktitle = {29th International Conference on Principles and Practice of Constraint Programming (CP 2023)}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.CP.2023.27}, pages = {27:1 -- 27:19}, year = {2023}, abstract = {Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in so-called pseudo-Boolean solving, where solvers can reason directly with 0-1 integer linear inequalities rather than with clausal constraints extracted from such inequalities. In this work, we investigate how pseudo-Boolean conflict analysis can be integrated in MIP solving, focusing on 0-1 integer linear programs (0-1 ILPs). Phrased in MIP terminology, conflict analysis can be understood as a sequence of linear combinations and cuts. We leverage this perspective to design a new conflict analysis algorithm based on mixed integer rounding (MIR) cuts, which theoretically dominates the state-of-the-art division-based method in pseudo-Boolean solving. We also report results from a first proof-of-concept implementation of different pseudo-Boolean conflict analysis methods in the open-source MIP solver SCIP. When evaluated on a large and diverse set of 0-1 ILP instances from MIPLIB2017, our new MIR-based conflict analysis outperforms both previous pseudo-Boolean methods and the clause-based method used in MIP. Our conclusion is that pseudo-Boolean conflict analysis in MIP is a promising research direction that merits further study, and that it might also make sense to investigate the use of such conflict analysis to generate stronger no-goods in constraint programming.}, language = {en} } @article{BestuzhevaGleixnerVigerske2023, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Vigerske, Stefan}, title = {A Computational Study of Perspective Cuts}, volume = {15}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-023-00246-4}, pages = {703 -- 731}, year = {2023}, abstract = {The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time.}, language = {en} } @inproceedings{XuMexiBestuzheva2025, author = {Xu, Liding and Mexi, Gioni and Bestuzheva, Ksenia}, title = {Sparsity-driven Aggregation of Mixed Integer Programs}, volume = {338}, booktitle = {23rd International Symposium on Experimental Algorithms (SEA 2025)}, address = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.SEA.2025.27}, pages = {27:1 -- 27:15}, year = {2025}, language = {en} } @article{GemanderChenWeningeretal.2020, author = {Gemander, Patrick and Chen, Wei-Kun and Weninger, Dieter and Gottwald, Leona and Gleixner, Ambros}, title = {Two-row and two-column mixed-integer presolve using hashing-based pairing methods}, volume = {8}, journal = {EURO Journal on Computational Optimization}, number = {3-4}, doi = {10.1007/s13675-020-00129-6}, pages = {205 -- 240}, year = {2020}, abstract = {In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.}, language = {en} } @article{RouxPokuttaWirthetal.2021, author = {Roux, Christophe and Pokutta, Sebastian and Wirth, Elias and Kerdreux, Thomas}, title = {Efficient Online-Bandit Strategies for Minimax Learning Problems}, year = {2021}, abstract = {Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning [Namkoong and Duchi, 2016, Curi et al., 2020] or learning with non-standard aggregated losses [Shalev- Shwartz and Wexler, 2016, Fan et al., 2017]. More specifically, these problems are convex-linear problems where the minimization is carried out over the model parameters w ∈ W and the maximization over the empirical distribution p ∈ K of the training set indexes, where K is the simplex or a subset of it. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm. We argue that the efficiency of such approaches critically depends on the structure of K and propose two properties of K that facilitate designing efficient algorithms. We focus on a specific family of sets Sn,k encompassing various learning applications and provide high-probability convergence guarantees to the minimax values.}, language = {en} } @article{EiflerGleixner2023, author = {Eifler, Leon and Gleixner, Ambros}, title = {Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework}, volume = {34}, journal = {SIAM Journal on Optimization}, number = {1}, doi = {10.1137/23M156046X}, year = {2023}, abstract = {This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5\% more instances and reduce solving times by 26.8\% on the MIPLIB 2017 benchmark test set.}, language = {en} } @misc{EiflerGleixner2023, author = {Eifler, Leon and Gleixner, Ambros}, title = {Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-90159}, year = {2023}, abstract = {This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5\% more instances and reduce solving times by 26.8\% on the MIPLIB 2017 benchmark test set.}, language = {en} }