@article{HumpolaSerrano, author = {Humpola, Jesco and Serrano, Felipe}, title = {Sufficient pruning conditions for MINLP in gas network design}, series = {EURO Journal on Computational Optimization}, volume = {5}, journal = {EURO Journal on Computational Optimization}, number = {1-2}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/s13675-016-0077-8}, pages = {239 -- 261}, abstract = {One-quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology optimization problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. We offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex continuous nonlinear program (NLP) can be certified by solving an MILP. This result provides an efficient pruning procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speedup for the necessary computations.}, language = {en} } @misc{Serrano, author = {Serrano, Felipe}, title = {Visible points, the separation problem, and applications to MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74016}, abstract = {In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require that every valid cut separating the infeasible point from the restricted feasible region is still valid for the original feasible region. We translate this requirement in terms of the separation problem and the reverse polar. In particular, if the reverse polar of the restricted feasible region is the same as the reverse polar of the feasible region, then any cut valid for the restricted feasible region that \emph{separates} the infeasible point, is valid for the feasible region. We show that the reverse polar of the \emph{visible points} of the feasible region from the infeasible point coincides with the reverse polar of the feasible region. In the special where the feasible region is described by a single non-convex constraint intersected with a convex set we provide a characterization of the visible points. Furthermore, when the non-convex constraint is quadratic the characterization is particularly simple. We also provide an extended formulation for a relaxation of the visible points when the non-convex constraint is a general polynomial. Finally, we give some conditions under which for a given set there is an inclusion-wise smallest set, in some predefined family of sets, whose reverse polars coincide.}, language = {en} } @article{SerranoSchwarzGleixner, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the relation between the extended supporting hyperplane algorithm and Kelley's cutting plane algorithm}, series = {Journal of Global Optimization}, volume = {78}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-020-00906-y}, pages = {161 -- 179}, abstract = {Recently, Kronqvist et al. (J Global Optim 64(2):249-272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147-152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm (J Soc Ind Appl Math 8(4):703-712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.}, language = {en} } @inproceedings{MuellerMuñozGasseetal., author = {M{\"u}ller, Benjamin and Muñoz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming}, series = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, booktitle = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, doi = {10.1007/978-3-030-45771-6_25}, pages = {322 -- 337}, abstract = {The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm's ability to generate strong dual bounds through extensive computational experiments.}, language = {en} } @misc{LenzSerrano, author = {Lenz, Ralf and Serrano, Felipe}, title = {Tight Convex Relaxations for the Expansion Planning Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81459}, abstract = {Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58\%.}, language = {en} } @inproceedings{SerranoMuñoz, author = {Serrano, Felipe and Muñoz, Gonzalo}, title = {Maximal Quadratic-Free Sets}, series = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, booktitle = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, doi = {10.1007/978-3-030-45771-6_24}, pages = {307 -- 321}, abstract = {The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined as a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed. To the best of our knowledge, this work is the first to provide maximal quadratic-free sets.}, language = {en} } @inproceedings{Serrano, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, series = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, volume = {11480}, booktitle = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, doi = {10.1007/978-3-030-17953-3_29}, pages = {385 -- 398}, abstract = {Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.}, language = {en} } @misc{SerranoSchwarzGleixner, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73253}, abstract = {Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (1967) and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by general, not necessarily convex, differentiable functions that satisfy a mild condition.}, language = {en} } @misc{Serrano, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71105}, abstract = {Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.}, language = {en} } @article{MuellerSerranoGleixner, author = {M{\"u}ller, Benjamin and Serrano, Felipe and Gleixner, Ambros}, title = {Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms}, series = {SIAM Journal on Optimization}, volume = {30}, journal = {SIAM Journal on Optimization}, number = {2}, doi = {10.1137/19M1249825}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72767}, pages = {1339 -- 1365}, abstract = {One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.}, language = {en} } @misc{SerranoMunoz, author = {Serrano, Felipe and Mu{\~n}oz, Gonzalo}, title = {Maximal Quadratic-Free Sets}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-76922}, abstract = {The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined as a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed. To the best of our knowledge, this work is the first to provide maximal quadratic-free sets.}, language = {en} } @misc{TurnerKochSerranoetal., author = {Turner, Mark and Koch, Thorsten and Serrano, Felipe and Winkler, Michael}, title = {Adaptive Cut Selection in Mixed-Integer Linear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86055}, abstract = {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.}, language = {en} } @misc{MuellerMuñozGasseetal., author = {M{\"u}ller, Benjamin and Muñoz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75179}, abstract = {The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm's ability to generate strong dual bounds through extensive computational experiments.}, language = {en} } @misc{MuellerSerranoGleixner, author = {M{\"u}ller, Benjamin and Serrano, Felipe and Gleixner, Ambros}, title = {Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72759}, abstract = {One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.}, language = {en} } @article{LenzSerrano, author = {Lenz, Ralf and Serrano, Felipe}, title = {Tight Convex Relaxations for the Expansion Planning Problem}, series = {Journal of Optimization Theory and Applications}, volume = {194}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-022-02029-8}, pages = {325 -- 352}, abstract = {Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improves the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58\%.}, language = {en} } @misc{MaherMiltenbergerPedrosoetal., author = {Maher, Stephen J. and Miltenberger, Matthias and Pedroso, Jo{\~a}o Pedro and Rehfeldt, Daniel and Schwarz, Robert and Serrano, Felipe}, title = {PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite}, issn = {1438-0064}, doi = {10.1007/978-3-319-42432-3_37}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61348}, abstract = {SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.}, language = {en} } @inproceedings{MaherMiltenbergerPedrosoetal., author = {Maher, Stephen J. and Miltenberger, Matthias and Pedroso, Jo{\~a}o Pedro and Rehfeldt, Daniel and Schwarz, Robert and Serrano, Felipe}, title = {PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite}, series = {Mathematical Software - ICMS 2016}, volume = {9725}, booktitle = {Mathematical Software - ICMS 2016}, publisher = {Springer}, doi = {10.1007/978-3-319-42432-3_37}, pages = {301 -- 307}, abstract = {SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.}, language = {en} } @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} } @article{TurnerKochSerranoetal., author = {Turner, Mark and Koch, Thorsten and Serrano, Felipe and Winkler, Michael}, title = {Adaptive Cut Selection in Mixed-Integer Linear Programming}, series = {Open Journal of Mathematical Optimization}, volume = {4}, journal = {Open Journal of Mathematical Optimization}, doi = {10.5802/ojmo.25}, pages = {5}, abstract = {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.}, 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} } @article{MuellerMunozGasseetal., author = {M{\"u}ller, Benjamin and Mu{\~n}oz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On generalized surrogate duality in mixed-integer nonlinear programming}, series = {Mathematical Programming}, volume = {192}, journal = {Mathematical Programming}, number = {1}, doi = {10.1007/s10107-021-01691-6}, pages = {89 -- 118}, abstract = {The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global ϵ-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm's ability to generate strong dual bounds through extensive computational experiments.}, language = {en} } @misc{MaherFischerGallyetal., author = {Maher, Stephen J. and Fischer, Tobias and Gally, Tristan and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Robert Lion and Hendel, Gregor and Koch, Thorsten and L{\"u}bbecke, Marco and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 4.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62170}, abstract = {The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.}, language = {en} } @misc{GamrathFischerGallyetal., author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, 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} } @misc{GamrathAndersonBestuzhevaetal., author = {Gamrath, Gerald and Anderson, Daniel and Bestuzheva, Ksenia and Chen, Wei-Kun and Eifler, Leon and Gasse, Maxime and Gemander, Patrick and Gleixner, Ambros and Gottwald, Leona and Halbig, Katrin and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Le Bodic, Pierre and Maher, Stephen J. and Matter, Frederic and Miltenberger, Matthias and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Tawfik, Christine and Vigerske, Stefan and Wegscheider, Fabian and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 7.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78023}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders' decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders' decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP.}, language = {en} } @misc{GleixnerEiflerGallyetal., author = {Gleixner, Ambros and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gemander, Patrick and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Vigerske, Stefan and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 5.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66297}, abstract = {This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 \% faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 \% faster overall and 23 \% faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG.}, language = {en} } @misc{GleixnerBastubbeEifleretal., author = {Gleixner, Ambros and Bastubbe, Michael and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Schubert, Christoph and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Walter, Matthias and Wegscheider, Fabian and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 6.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69361}, 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 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.}, 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} } @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} } @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} }