TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Bushe, Julian T1 - Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation’s feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Borndörfer et al., 2016] on a test set of real world instances. Y1 - 2023 U6 - https://doi.org/https://doi.org/10.4230/OASIcs.ATMOS.2023.13 VL - 115 SP - 13:1 EP - 13:15 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Schade, Stanley T1 - A Robustness Analysis of Long Distance Train Crew Schedules in Germany T2 - Proceedings Of The Fifth Iinternational Conference On Railway Technology: Research, Development and Maintenance N2 - Nowadays railway networks are highly complex and often very fragile systems. A wide variety of individual operations that influence each other have to go hand in hand to end up with a smoothly and efficiently running system. Many of these operations suffer from uncertainty as trains could be delayed, the signaling system be disrupted or scheduled crews could be ill. Usually these opartions could be organized hierarchically from long term strategical decisions to real time decision management. Each stage in the hierarchy defines a different mathematical optimization problem, which is solved sequentially. At every stage the knowledge about preceding or succeeding planning stages may vary and also the interaction between two stages in this chain of problems may vary from almost no interaction to highly dependent situations. This paper deals with a topic that is an example for the latter case, namely the interaction between vehicle schedules, vehicle punctuality, and crew schedules. To reduce the number of potential rescheduling actions we developed a software tool in cooperation with our practical partner DB Fernverkehr AG (DBF) to predict a certain set of critical crew schedules. This tool evaluates, predicts, and determines "bottlenecks" in the crew schedule in the sense of potentially required rescheduling actions due to likely delays. The approach was tested on real life crew and train timetable data of DBF and can be regarded as the computation of key performance indicators, which is often desired. For our experiments we had access to the operated timetable and crew schedule of DBF for periods of two and six weeks in 2019. Y1 - 2023 U6 - https://doi.org/10.4203/ccc.1.23.17 SN - 2753-3239 VL - CCC 1 ER - TY - CHAP A1 - Bortoletto, Enrico A1 - Lindner, Niels A1 - Masing, Berenike T1 - Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [Borndörfer et al., 2020]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [Bortoletto et al., 2022]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.3 VL - 106 SP - 3:1 EP - 3:19 ER - TY - CHAP A1 - Bortoletto, Enrico A1 - Lindner, Niels A1 - Masing, Berenike T1 - Periodic Timetabling with Cyclic Order Constraints T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - Periodic timetabling for highly utilized railway networks is a demanding challenge. We formulate an infrastructure-aware extension of the Periodic Event Scheduling Problem (PESP) by requiring that not only events, but also activities using the same infrastructure must be separated by a minimum headway time. This extended problem can be modeled as a mixed-integer program by adding constraints on the sum of periodic tensions along certain cycles, so that it shares some structural properties with standard PESP. We further refine this problem by fixing cyclic orders at each infrastructure element. Although the computational complexity remains unchanged, the mixed-integer programming model then becomes much smaller. Furthermore, we also discuss how to find a minimal subset of infrastructure elements whose cyclic order already prescribes the order for the remaining parts of the network, and how cyclic order information can be modeled in a mixed-integer programming context. In practice, we evaluate the impact of cyclic orders on a real-world instance on the S-Bahn Berlin network, which turns out to be computationally fruitful. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.7 VL - 115 SP - 7:1 EP - 7:18 ER - TY - CHAP A1 - Masing, Berenike A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Integrating Line Planning for Construction Sites into Periodic Timetabling via Track Choice T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - We consider maintenance sites for urban rail systems, where unavailable tracks typically require changes to the regular timetable, and often even to the line plan. In this paper, we present an integrated mixed-integer linear optimization model to compute an optimal line plan that makes best use of the available tracks, together with a periodic timetable, including its detailed routing on the tracks within the stations. The key component is a flexible, turn-sensitive event-activity network that allows to integrate line planning and train routing using a track choice extension of the Periodic Event Scheduling Problem (PESP). Major goals are to maintain as much of the regular service as possible, and to keep the necessary changes rather local. Moreover, we present computational results on real construction site scenarios on the S-Bahn Berlin network. We demonstrate that this integrated problem is indeed solvable on practically relevant instances. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.5 VL - 115 SP - 5:1 EP - 5:15 ER - TY - CHAP A1 - Masing, Berenike ED - Trautmann, Norbert ED - Drägi, Mario T1 - Optimal Line Planning in the Parametric City T2 - Operations Research Proceedings 2021. OR 2021. N2 - We formulate the line planning problem in public transport as a mixed integer linear program (MILP), which selects both passenger and vehicle routes, such that travel demands are met with respect to minimized travel times for both operators and users. We apply MILP to the Parametric City, a generic city model developed by Fielbaum et al. [2]. While the infrastructure graph and demand are entirely rotation symmetric, asymmetric optimal line plans can occur. Using group theory, we analyze the properties of symmetric solutions and introduce a symmetry gap to measure their deviation of the optimum. We also develop a 1+1+2√g-approximation algorithm, depending only on the cost related parameter g. Supported by computational experiments, we conclude that in practice symmetric line plans provide good solutions for the line planning problem in the Parametric City. Y1 - 2022 SN - 978-3-031-08623-6 U6 - https://doi.org/10.1007/978-3-031-08623-6_7 SP - 39 EP - 44 PB - Springer, Cham ER - TY - CHAP A1 - Lindner, Niels A1 - van Lieshout, Rolf T1 - Benders Decomposition for the Periodic Event Scheduling Problem T2 - Operations Research Proceedings 2021 N2 - The Periodic Event Scheduling Problem (PESP) is the central mathematical model behind the optimization of periodic timetables in public transport. We apply Benders decomposition to the incidence-based MIP formulation of PESP. The resulting formulation exhibits particularly nice features: The subproblem is a minimum cost network flow problem, and feasibility cuts are equivalent to the well-known cycle inequalities by Odijk. We integrate the Benders approach into a branch-and-cut framework, and assess the performance of this method on instances derived from the benchmarking library PESPlib. Y1 - 2022 U6 - https://doi.org/10.1007/978-3-031-08623-6_43 SP - 289 EP - 294 PB - Springer International Publishing CY - Cham ER - TY - GEN ED - D'Emidio, Mattia ED - Lindner, Niels T1 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - OASIcs, Volume 106, ATMOS 2022, Complete Volume Y1 - 2022 SN - 978-3-95977-259-4 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022 VL - 106 PB - Schloss Dagstuhl -- Leibniz-Zentrum für Informatik ER - TY - GEN A1 - Maristany de las Casas, Pedro A1 - Borndörfer, Ralf A1 - Kraus, Luitgard A1 - Sedeño-Noda, Antonio T1 - An FPTAS for Dynamic Multiobjective Shortest Path Problems N2 - We propose in this paper the Dynamic Multiobjective Shortest Problem. It features multidimensional states that can depend on several variables and not only on time; this setting is motivated by flight planning and electric vehicle routing applications. We give an exact algorithm for the FIFO case and derive from it an FPTAS, which is computationally efficient. It also features the best known complexity in the static case. T3 - ZIB-Report - 20-31 KW - Multiobjective Shortest Paths KW - Time Dependent Shortest Paths KW - Multiobjective Approximation Algorithms KW - Flight Planning Problem Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-80954 ER - TY - CHAP A1 - Prause, Felix A1 - Borndörfer, Ralf T1 - A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance T2 - 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024) N2 - We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach. Y1 - 2024 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2024.13 VL - 123 SP - 13:1 EP - 13:19 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc E. A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 8.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. T3 - ZIB-Report - 21-41 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85309 SN - 1438-0064 ER - TY - GEN A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Dionísio, João A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Ghannam, Mohammed A1 - Gleixner, Ambros A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hedtke, Ivo A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Kamp, Dominik A1 - Koch, Thorsten A1 - Kofler, Kevin A1 - Lentz, Jurgen A1 - Manns, Julian A1 - Mexi, Gioni A1 - Mühmer, Erik A1 - E. Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Xu, Liding T1 - The SCIP Optimization Suite 9.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. T3 - ZIB-Report - 24-02-29 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95528 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs N2 - A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML. T3 - ZIB-Report - 23-28 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93095 SN - 1438-0064 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - Enabling research through the SCIP optimization suite 8.0 JF - ACM Transactions on Mathematical Software N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP. Y1 - 2023 U6 - https://doi.org/10.1145/3585516 VL - 49 IS - 2 SP - 1 EP - 21 ER - TY - CHAP A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2025 N2 - A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-95976-9_14 VL - 15763 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Müller, Benjamin A1 - Serrano, Felipe A1 - Vigerske, Stefan A1 - Wegscheider, Fabian T1 - Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0 JF - Journal of Global Optimization N2 - For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided. Y1 - 2023 U6 - https://doi.org/10.1007/s10898-023-01345-1 ER - TY - JOUR A1 - Chmiela, Antonia A1 - Muñoz, Gonzalo A1 - Serrano, Felipe T1 - Monoidal strengthening and unique lifting in MIQCPs JF - Mathematical Programming B Y1 - 2025 U6 - https://doi.org/10.1007/s10107-024-02112-0 VL - 210 SP - 189 EP - 222 ER - TY - JOUR A1 - Chmiela, Antonia A1 - Muñoz, Gonzalo A1 - Serrano, Felipe T1 - On the implementation and strengthening of intersection cuts for QCQPs JF - Mathematical Programming B Y1 - 2023 U6 - https://doi.org/10.1007/s10107-022-01808-5 VL - 197 SP - 549 EP - 586 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Khalil, Elias B. A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Pokutta, Sebastian T1 - Learning to Schedule Heuristics in Branch and Bound T2 - Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021 N2 - Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances. Y1 - 2021 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Muñoz, Gonzalo A1 - Serrano, Felipe T1 - Monoidal strengthening and unique lifting in MIQCPs T2 - Integer Programming and Combinatorial Optimization. IPCO 2023. N2 - Using the recently proposed maximal quadratic-free sets and the well-known monoidal strengthening procedure, we show how to improve inter- section cuts for quadratically-constrained optimization problems by exploiting integrality requirements. We provide an explicit construction that allows an efficient implementation of the strengthened cuts along with computational results showing their improvements over the standard intersection cuts. We also show that, in our setting, there is unique lifting which implies that our strengthening procedure is generating the best possible cut coefficients for the integer variables. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-32726-1_7 VL - 13904 SP - 87 EP - 99 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Muñoz, Gonzalo A1 - Serrano, Felipe T1 - On the implementation and strengthening of intersection cuts for QCQPs T2 - Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021 N2 - The generation of strong linear inequalities for QCQPs has been recently tackled by a number of authors using the intersection cut paradigm - a highly studied tool in integer programming whose flexibility has triggered these renewed efforts in non-linear settings. In this work, we consider intersection cuts using the recently proposed construction of maximal quadratic-free sets. Using these sets, we derive closed-form formulas to compute intersection cuts which allow for quick cut-computations by simply plugging-in parameters associated to an arbitrary quadratic inequality being violated by a vertex of an LP relaxation. Additionally, we implement a cut-strengthening procedure that dates back to Glover and evaluate these techniques with extensive computational experiments. Y1 - 2021 U6 - https://doi.org/10.1007/978-3-030-73879-2_10 VL - 22 SP - 134 EP - 147 ER -