@misc{BertholdGleixnerHeinzetal.2013, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {Analyzing the computational impact of MIQCP solver components}, issn = {1438-0064}, doi = {10.3934/naco.2012.2.739}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17754}, year = {2013}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @misc{BertholdGleixnerHeinzetal.2011, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {On the computational impact of MIQCP solver components}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11998}, number = {11-01}, year = {2011}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on linear outer approximation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @article{BertholdGleixnerHeinzetal.2012, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {Analyzing the computational impact of MIQCP solver components}, volume = {2}, journal = {Numerical Algebra, Control and Optimization}, number = {4}, doi = {10.3934/naco.2012.2.739}, pages = {739 -- 748}, year = {2012}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @misc{BertholdHeinzVigerske2012, author = {Berthold, Timo and Heinz, Stefan and Vigerske, Stefan}, title = {Extending a CIP framework to solve MIQCPs}, volume = {154}, journal = {Mixed Integer Nonlinear Programming}, editor = {Lee, Jon and Leyffer, Sven}, publisher = {Springer}, isbn = {978-1-4614-1927-3}, pages = {427 -- 444}, year = {2012}, abstract = {This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.}, language = {en} } @inproceedings{BertholdHeinzPfetschetal.2011, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc and Vigerske, Stefan}, title = {Large Neighborhood Search beyond MIP}, booktitle = {Proceedings of the 9th Metaheuristics International Conference (MIC 2011)}, isbn = {978-88-900984-3-7}, pages = {51 -- 60}, year = {2011}, abstract = {Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.}, language = {en} } @misc{ShinanoHeinzVigerskeetal.2013, author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, issn = {1438-0064}, doi = {10.1287/ijoc.2017.0762}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42595}, year = {2013}, abstract = {Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated.}, language = {en} } @article{ShinanoHeinzVigerskeetal.2018, author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, volume = {30}, journal = {INFORMS Journal on Computing}, number = {1}, doi = {10.1287/ijoc.2017.0762}, pages = {11 -- 30}, year = {2018}, abstract = {Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel.}, language = {en} } @misc{BertholdHeinzPfetschetal.2011, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc and Vigerske, Stefan}, title = {Large Neighborhood Search beyond MIP}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12989}, number = {11-21}, year = {2011}, abstract = {Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.}, language = {en} } @misc{BertholdHeinzVigerske2009, author = {Berthold, Timo and Heinz, Stefan and Vigerske, Stefan}, title = {Extending a CIP framework to solve MIQCPs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11371}, number = {09-23}, year = {2009}, abstract = {This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, issn = {1438-0064}, doi = {10.4171/137}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49947}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {135 -- 146}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{NeunSturmVigerske2010, author = {Neun, Winfried and Sturm, Thomas and Vigerske, Stefan}, title = {Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11644}, number = {10-01}, year = {2010}, abstract = {Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system REDUCE. Our long term goal is to integrate REDUCE as a workhorse'' for symbolic computations into a numerical solver.}, language = {en} } @article{NeunSturmVigerske2010, author = {Neun, Winfried and Sturm, Thomas and Vigerske, Stefan}, title = {Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests}, volume = {LNCS 6244}, journal = {Computer Algebra in Scientific Computing}, isbn = {978-3-642-15273-3}, pages = {205 -- 219}, year = {2010}, language = {en} } @misc{GamrathAndersonBestuzhevaetal.2020, 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}, year = {2020}, 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} } @article{BernalVigerskeTrespalaciosetal.2017, author = {Bernal, David E. and Vigerske, Stefan and Trespalacios, Francisco and Grossmann, Ignacio E.}, title = {Improving the performance of DICOPT in convex MINLP problems using a feasibility pump}, journal = {Optimization Methods and Software}, year = {2017}, abstract = {The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are diffcult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive that the nonlinear subproblems produced by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm for DICOPT. Computational comparisons with previous versions of DICOPT and other MINLP solvers on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solving time.}, language = {en} } @misc{VigerskeGleixner2016, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1335312}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59377}, year = {2016}, abstract = {This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.}, language = {en} } @misc{GleixnerEiflerGallyetal.2017, 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}, year = {2017}, 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} } @inproceedings{BleyGleixnerKochetal.2012, author = {Bley, Andreas and Gleixner, Ambros and Koch, Thorsten and Vigerske, Stefan}, title = {Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling}, booktitle = {Modeling, Simulation and Optimization of Complex Processes. Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam}, doi = {10.1007/978-3-642-25707-0_3}, pages = {25 -- 39}, year = {2012}, abstract = {In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.}, language = {en} } @misc{MuellerKuhlmannVigerske2017, author = {M{\"u}ller, Benjamin and Kuhlmann, Renke and Vigerske, Stefan}, title = {On the performance of NLP solvers within global MINLP solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_84}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64504}, year = {2017}, abstract = {Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.}, language = {en} } @inproceedings{MuellerKuhlmannVigerske2018, author = {M{\"u}ller, Benjamin and Kuhlmann, Renke and Vigerske, Stefan}, title = {On the performance of NLP solvers within global MINLP solvers}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_84}, pages = {633 -- 639}, year = {2018}, abstract = {Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.}, language = {en} }