@misc{ChmielaMunozSerrano, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, doi = {10.1007/978-3-030-73879-2_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79994}, abstract = {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.}, language = {en} } @inproceedings{ChmielaMunozSerrano, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, series = {Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021}, volume = {22}, booktitle = {Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021}, doi = {10.1007/978-3-030-73879-2_10}, pages = {134 -- 147}, abstract = {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.}, language = {en} } @misc{BestuzhevaChmielaMuelleretal., author = {Bestuzheva, Ksenia and Chmiela, Antonia and M{\"u}ller, Benjamin and Serrano, Felipe and Vigerske, Stefan and Wegscheider, Fabian}, title = {Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89348}, abstract = {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.}, language = {en} } @inproceedings{ChmielaGleixnerLichockietal., author = {Chmiela, Antonia and Gleixner, Ambros and Lichocki, Pawel and Pokutta, Sebastian}, title = {Online Learning for Scheduling MIP Heuristics}, series = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, volume = {13884}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-33271-5_8}, pages = {114 -- 123}, abstract = {Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on hard-coded rules derived from empirical testing on a large heterogeneous corpora of benchmark instances might lead to sub-optimal performance. In this work, we propose an online learning approach that adapts the application of heuristics towards the single instance at hand. We replace the commonly used static heuristic handling with an adaptive framework exploiting past observations about the heuristic's behavior to make future decisions. In particular, we model the problem of controlling Large Neighborhood Search and Diving - two broad and complex classes of heuristics - as a multi-armed bandit problem. Going beyond existing work in the literature, we control two different classes of heuristics simultaneously by a single learning agent. We verify our approach numerically and show consistent node reductions over the MIPLIB 2017 Benchmark set. For harder instances that take at least 1000 seconds to solve, we observe a speedup of 4\%.}, language = {en} } @inproceedings{ChmielaKhalilGleixneretal.2021, author = {Chmiela, Antonia and Khalil, Elias B. and Gleixner, Ambros and Lodi, Andrea and Pokutta, Sebastian}, title = {Learning to Schedule Heuristics in Branch and Bound}, series = {Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021}, booktitle = {Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021}, year = {2021}, abstract = {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.}, language = {en} } @inproceedings{ChmielaMunozSerrano, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {Monoidal strengthening and unique lifting in MIQCPs}, series = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, volume = {13904}, booktitle = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, doi = {10.1007/978-3-031-32726-1_7}, pages = {87 -- 99}, abstract = {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.}, language = {en} } @misc{TurnerChmielaKochetal., author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93095}, abstract = {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.}, language = {en} } @inproceedings{TurnerChmielaKochetal., author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, abstract = {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.}, language = {en} } @misc{BestuzhevaBesanconChenetal., author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc E. and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85309}, abstract = {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.}, language = {en} } @article{BestuzhevaChmielaMuelleretal., author = {Bestuzheva, Ksenia and Chmiela, Antonia and M{\"u}ller, Benjamin and Serrano, Felipe and Vigerske, Stefan and Wegscheider, Fabian}, title = {Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0}, series = {Journal of Global Optimization}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-023-01345-1}, abstract = {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.}, language = {en} } @inproceedings{MexiBesanconBolusanietal., author = {Mexi, Gioni and Besan{\c{c}}on, Mathieu and Bolusani, Suresh and Chmiela, Antonia and Hoen, Alexander and Gleixner, Ambros}, title = {Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization}, series = {Proceedings of Conference of the Society for Operations Research in Germany}, booktitle = {Proceedings of Conference of the Society for Operations Research in Germany}, language = {en} } @article{BestuzhevaBesanconChenetal., author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {Enabling research through the SCIP optimization suite 8.0}, series = {ACM Transactions on Mathematical Software}, volume = {49}, journal = {ACM Transactions on Mathematical Software}, number = {2}, doi = {10.1145/3585516}, pages = {1 -- 21}, abstract = {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.}, language = {en} } @inproceedings{GasseBowlyCappartetal., author = {Gasse, Maxime and Bowly, Simon and Cappart, Quentin and Charfreitag, Jonas and Charlin, Laurent and Ch{\´e}telat, Didier and Chmiela, Antonia and Dumouchelle, Justin and Gleixner, Ambros and Kazachkov, Aleksandr M. and Khalil, Elias and Lichocki, Pawel and Lodi, Andrea and Lubin, Miles and Maddison, Chris J. and Christopher, Morris and Papageorgiou, Dimitri J. and Parjadis, Augustin and Pokutta, Sebastian and Prouvost, Antoine and Scavuzzo, Lara and Zarpellon, Giulia and Yang, Linxin and Lai, Sha and Wang, Akang and Luo, Xiaodong and Zhou, Xiang and Huang, Haohan and Shao, Shengcheng and Zhu, Yuanming and Zhang, Dong and Quan, Tao and Cao, Zixuan and Xu, Yang and Huang, Zhewei and Zhou, Shuchang and Binbin, Chen and Minggui, He and Hao, Hao and Zhiyu, Zhang and Zhiwu, An and Kun, Mao}, title = {The Machine Learning for Combinatorial Optimization Competition (ML4CO): results and insights}, series = {Proceedings of Conference on Neural Information Processing Systems}, booktitle = {Proceedings of Conference on Neural Information Processing Systems}, language = {en} } @misc{BolusaniBesanconBestuzhevaetal., author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Bestuzheva, Ksenia and Chmiela, Antonia and Dion{\´i}sio, Jo{\~a}o and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Ghannam, Mohammed and Gleixner, Ambros and Graczyk, Christoph and Halbig, Katrin and Hedtke, Ivo and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Kamp, Dominik and Koch, Thorsten and Kofler, Kevin and Lentz, Jurgen and Manns, Julian and Mexi, Gioni and M{\"u}hmer, Erik and E. Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Turner, Mark and Vigerske, Stefan and Weninger, Dieter and Xu, Liding}, title = {The SCIP Optimization Suite 9.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-95528}, abstract = {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.}, language = {en} } @article{ChmielaMunozSerrano, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, series = {Mathematical Programming B}, volume = {197}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-022-01808-5}, pages = {549 -- 586}, language = {en} }