TY - GEN A1 - Kempke, Nils-Christian A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - A Massively Parallel Interior-Point-Method for Arrowhead Linear Programs N2 - In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required, especially for large-scale linear programs. This article describes a new decomposition technique for systems of linear equations implemented in the parallel interior-point solver PIPS-IPM++. The algorithm exploits a matrix structure commonly found in optimization problems: a doubly-bordered block-diagonal or arrowhead structure. This structure is preserved in the linear KKT systems solved during each iteration of the interior-point method. We present a hierarchical Schur complement decomposition that distributes and solves the linear optimization problem; it is designed for high-performance architectures and scales well with the availability of additional computing resources. The decomposition approach uses the border constraints’ locality to decouple the factorization process. Our approach is motivated by large-scale unit-commitment problems. We demonstrate the performance of our method on a set of mid-to large-scale instances, some of which have more than 10^9 nonzeros in their constraint matrix. T3 - ZIB-Report - 24-13 KW - direct methods for linear systems KW - mathematical programming KW - parallel computation KW - linear programming KW - large-scale problems KW - interior-point methods Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-98829 SN - 1438-0064 ER - TY - GEN A1 - Cao, Karl-Kien A1 - Anderson, Lovis A1 - Böhme, Aileen A1 - Breuer, Thomas A1 - Buschmann, Jan A1 - Fiand, Frederick A1 - Frey, Ulrich A1 - Fuchs, Benjamin A1 - Kempe, Nils-Christian A1 - von Krbek, Kai A1 - Medjroubi, Wided A1 - Riehm, Judith A1 - Sasanpour, Shima A1 - Simon, Sonja A1 - Vanaret, Charlie A1 - Wetzel, Manuel A1 - Xiao, Mengzhu A1 - Zittel, Janina T1 - Evaluation of Uncertainties in Linear-Optimizing Energy System Models - Compendium T2 - DLR-Forschungsbericht N2 - Für die Energiesystemforschung sind Software-Modelle ein Kernelement zur Analyse von Szenarien. Das Forschungsprojekt UNSEEN hatte das Ziel eine bisher unerreichte Anzahl an modellbasierten Energieszenarien zu berechnen, um Unsicherheiten – vor allem unter Nutzung linear optimierender Energiesystem-Modelle - besser bewerten zu können. Hierfür wurden umfangreiche Parametervariationen auf Energieszenarien angewendet und das wesentliche methodische Hindernis in diesem Zusammenhang adressiert: die rechnerische Beherrschbarkeit der zu lösenden mathematischen Optimierungsprobleme. Im Vorläuferprojekt BEAM-ME wurde mit der Entwicklung und Anwendung des Open-Source-Lösers PIPS-IPM++ die Grundlage für den Einsatz von High-Performance-Computing (HPC) zur Lösung dieser Modelle gelegt. In UNSEEN war dieser Löser die zentrale Komponente eines Workflows, welcher zur Generierung, Lösung und multi-kriteriellen Bewertung von Energieszenarien auf dem Hochleistungscomputer JUWELS am Forschungszentrum Jülich implementiert wurde. Zur effizienten Generierung und Kommunikation von Modellinstanzen für Methoden der mathematischen Optimierung auf HPC wurde eine weitere Workflow-Komponente von der GAMS Software GmbH entwickelt: der Szenariogenerator. Bei der Weiterentwicklung von Lösungsalgorithmen für linear optimierende Energie-Systemmodelle standen gemischt-ganzzahlige Optimierungsprobleme im Fokus, welche für die Modellierung konkreter Infrastrukturen und Maßnahmen zur Umsetzung der Energiewende gelöst werden müssen. Die in diesem Zusammenhang stehenden Arbeiten zur Entwicklung von Algorithmen wurden von der Technischen Universität Berlin verantwortet. Bei Design und Implementierung dieser Methoden wurde sie vom Zuse Instituts Berlin unterstützt. Y1 - 2023 U6 - https://doi.org/10.57676/w2rq-bj85 IS - DLR-FB-2023-15 ER - TY - GEN A1 - Koch, Thorsten A1 - Berthold, Timo A1 - Pedersen, Jaap A1 - Vanaret, Charlie T1 - Progress in Mathematical Programming Solvers from 2001 to 2020 N2 - This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time. T3 - ZIB-Report - 21-20 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82779 SN - 1438-0064 ER - TY - JOUR A1 - Anderson, Lovis A1 - Turner, Mark A1 - Koch, Thorsten T1 - Generative deep learning for decision making in gas networks JF - Mathematical Methods of Operations Research N2 - A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%. Y1 - 2022 U6 - https://doi.org/10.1007/s00186-022-00777-x VL - 95 SP - 503 EP - 532 PB - Springer Nature ER - TY - CHAP A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-33271-5_4 VL - 13884 SP - 52 EP - 68 PB - Springer ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. T3 - ZIB-Report - 22-28 KW - cut selection KW - anlalytic center KW - mixed-integer programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89065 SN - 1438-0064 ER - TY - JOUR A1 - Koch, Thorsten A1 - Berthold, Timo A1 - Pedersen, Jaap A1 - Vanaret, Charlie T1 - Progress in mathematical programming solvers from 2001 to 2020 JF - EURO Journal on Computational Optimization N2 - This study investigates the progress made in lp and milp solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving lp/milp, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for lp and around 50 for milp, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time. Y1 - 2022 U6 - https://doi.org/10.1016/j.ejco.2022.100031 VL - 10 SP - 100031 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Kunt, Tim A1 - Katamish, Bassel A1 - Vanaret, Charlie A1 - Sasanpour, Shima A1 - Clarner, Jan-Patrick A1 - Koch, Thorsten T1 - Developing heuristic solution techniques for large-scale unit commitment models N2 - Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1% and up to 35%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that Gurobi could not solve within two days, our FP method provided feasible solutions in under one hour. T3 - ZIB-Report - 25-03 KW - Energy system optimization models KW - Unit commitment KW - Mixed-integer programming KW - Large-scale optimization KW - Primal heuristics Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99555 SN - 1438-0064 ER - TY - CHAP A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu T1 - A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming T2 - Operations Research Proceedings 2023. OR 2023. N2 - The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-58405-3_28 SP - 217 EP - 244 ER - TY - THES A1 - Turner, Mark T1 - Cutting Plane Selection for Mixed-Integer Linear Programming N2 - Mixed-Integer Linear Programming (MILP) is a ubiquitous and practical modelling paradigm that is essential for optimising a broad range of real-world systems. The backbone of all modern MILP solvers is the branch-and-cut algorithm, which is a hybrid of the branch-and-bound and cutting planes algorithms. Cutting planes (cuts) are linear inequalities that tighten the relaxation of a MILP. While a lot of research has gone into deriving valid cuts for MILPs, less emphasis has been put on determining which cuts to select. Cuts in general are generated in rounds, and a subset of the generated cuts must be added to the relaxation. The decision on which subset of cuts to add is called cut selection. This is a crucial task since adding too many cuts makes the relaxation large and slow to optimise over. Conversely, adding too few cuts results in an insufficiently tightened relaxation, and more relaxations need to be enumerated. To further emphasise the difficulty, the effectiveness of an applied cut is both dependent on the other applied cuts, and the state of the MILP solver. In this thesis, we present theoretical results on the importance and difficulty of cut selection, as well as practical results that use cut selection to improve general MILP solver performance. Improving general MILP solver performance is of great importance for practitioners and has many runoff effects. Reducing the solve time of currently solved systems can directly improve efficiency within the application area. In addition, improved performance enables larger systems to be modelled and optimised, and MILP to be used in areas where it was previously impractical due to time restrictions. Each chapter of this thesis corresponds to a publication on cut selection, where the contributions of this thesis can naturally be divided into four components. The first two components are motivated by instance-dependent performance. In practice, for each subroutine, including cut selection, MILP solvers have adjustable parameters with hard-coded default values. It is ultimately unrealistic to expect these default values to perform well for every instance. Rather, it would be ideal if the parameters were dependent on the given instance. To show this motivation is well founded, we first introduce a family of parametric MILP instances and cuts to showcase worst-case performance of cut selection for any fixed parameter value. We then introduce a graph neural network architecture and reinforcement learning framework for learning instance-dependent cut scoring parameters. In the following component, we formalise language for determining if a cut has theoretical usefulness from a polyhedral point of view in relation to other cuts. In addition, to overcome issues of infeasible projections and dual degeneracy, we introduce analytic center based distance measures. We then construct a lightweight multi-output regression model that predicts relative solver performance of an instance for a set of distance measures. The final two components are motivated by general MILP solver improvement via cut selection. Such improvement was shown to be possible, albeit difficult to achieve, by the first half of this thesis. We relate branch-and-bound and cuts through their underlying disjunctions. Using a history of previously computed Gomory mixed-integer cuts, we reduce the solve time of SCIP over the 67% of affected MIPLIB 2017 instances by 4%. In the final component, we introduce new cut scoring measures and filtering methods based on information from other MILP solving processes. The new cut selection techniques reduce the solve time of SCIP over the 97% of affected MIPLIB 2017 instances by 5%. KW - Mixed-Integer Programming KW - Cutting Planes KW - Cut Selection KW - Machine Learning Y1 - 2024 ER - TY - JOUR A1 - Vanaret, Charlie T1 - Interval constraint programming for globally solving catalog-based categorical optimization JF - Journal of Global Optimization N2 - In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. A novel catalog-based contractor (or filtering operator) guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive and generic approach that is exact, rigorous (robust to roundoff errors) and can be easily implemented in an off-the-shelf interval-based continuous solver that interleaves branching and constraint propagation. We demonstrate the validity of the approach on a numerical problem in which a categorical variable is described by a two-dimensional property space. A Julia prototype is available as open-source software under the MIT license. Y1 - 2024 U6 - https://doi.org/10.1007/s10898-023-01362-0 VL - 89 SP - 457 EP - 476 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu T1 - A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming N2 - The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set. T3 - ZIB-Report - 23-21 KW - cutting plane selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91691 SN - 1438-0064 ER - TY - GEN A1 - Tjusila, Gennesaret A1 - Besancon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. T3 - ZIB-Report - 23-15 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90902 ER - TY - GEN A1 - Anderson, Lovis A1 - Turner, Mark A1 - Koch, Thorsten T1 - Generative deep learning for decision making in gas networks N2 - A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%. T3 - ZIB-Report - 20-38 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81103 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming N2 - Cut selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. T3 - ZIB-Report - 22-04 KW - cut selection KW - mixed-integer linear programming KW - reinforcement learning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86055 SN - 1438-0064 ER - TY - JOUR A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming JF - Open Journal of Mathematical Optimization N2 - Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. Y1 - 2023 U6 - https://doi.org/10.5802/ojmo.25 VL - 4 SP - 5 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Koch, Thorsten T1 - Low-precision first-order method-based fix-and-propagate heuristics for large-scale mixed-integer linear optimization N2 - We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). FOMs, using only matrix-vector products instead of matrix factorizations, are well suited for GPU acceleration and have recently gained more attention for their application to large-scale linear programming problems (LPs). We employ PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LP problems, to solve the LP-relaxation of our MIPs to low accuracy. This solution is used to motivate fixings within our fix-and-propagate framework. We implemented four different FP variants using primal and dual LP solution information. We evaluate the performance of our heuristics on MIPLIB 2017, showcasing that the low-accuracy LP solution produced by the FOM does not lead to a loss in quality of the FP heuristic solutions when compared to a high-accuracy interior-point method LP solution. Further, we use our FP framework to produce high-accuracy solutions for large-scale (up to 243 million non-zeros and 8 million decision variables) unit-commitment energy-system optimization models created with the modeling framework REMix. For the largest problems, we can generate solutions with under 2% primal-dual gap in less than 4 hours, whereas commercial solvers cannot generate feasible solutions within two days of runtime. This study represents the first successful application of FOMs in large-scale mixed-integer optimization, demonstrating their efficacy and establishing a foundation for future research in this domain. T3 - ZIB-Report - 25-04 KW - Integer programming KW - Large scale optimization KW - Linear Programming KW - Primal heuristics KW - OR in energy Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99612 SN - 1438-0064 ER - TY - JOUR A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017. Y1 - 2023 PB - Springer ER -