TY - GEN A1 - Arnold, Thomas A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Henrion, René A1 - Grötschel, Martin A1 - Koch, Thorsten A1 - Tischendorf, Caren A1 - Römisch, Werner ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs T2 - MATHEON - Mathematics for Key Technologies N2 - 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 Y1 - 2014 U6 - https://doi.org/10.4171/137 VL - 1 SP - 135 EP - 146 PB - European Mathematical Society ER - TY - JOUR A1 - Bernal, David E. A1 - Vigerske, Stefan A1 - Trespalacios, Francisco A1 - Grossmann, Ignacio E. T1 - Improving the performance of DICOPT in convex MINLP problems using a feasibility pump JF - Optimization Methods and Software N2 - 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. Y1 - 2017 ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Analyzing the computational impact of MIQCP solver components JF - Numerical Algebra, Control and Optimization N2 - 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. Y1 - 2012 U6 - https://doi.org/10.3934/naco.2012.2.739 VL - 2 IS - 4 SP - 739 EP - 748 ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vigerske, Stefan T1 - Large Neighborhood Search beyond MIP T2 - Proceedings of the 9th Metaheuristics International Conference (MIC 2011) N2 - 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. Y1 - 2011 SN - 978-88-900984-3-7 SP - 51 EP - 60 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Vigerske, Stefan ED - Lee, Jon ED - Leyffer, Sven T1 - Extending a CIP framework to solve MIQCPs T2 - Mixed Integer Nonlinear Programming N2 - 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. Y1 - 2012 SN - 978-1-4614-1927-3 VL - 154 SP - 427 EP - 444 PB - Springer ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - Enabling research through the SCIP optimization suite 8.0 JF - ACM Transactions on Mathematical Software N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP. Y1 - 2023 U6 - https://doi.org/10.1145/3585516 VL - 49 IS - 2 SP - 1 EP - 21 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Müller, Benjamin A1 - Serrano, Felipe A1 - Vigerske, Stefan A1 - Wegscheider, Fabian T1 - Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0 JF - Journal of Global Optimization N2 - For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided. Y1 - 2023 U6 - https://doi.org/10.1007/s10898-023-01345-1 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Vigerske, Stefan T1 - A Computational Study of Perspective Cuts JF - Mathematical Programming Computation N2 - The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time. Y1 - 2023 U6 - https://doi.org/10.1007/s12532-023-00246-4 VL - 15 SP - 703 EP - 731 ER - TY - CHAP A1 - Bley, Andreas A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Vigerske, Stefan T1 - Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling T2 - Modeling, Simulation and Optimization of Complex Processes. Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-25707-0_3 SP - 25 EP - 39 ER - TY - JOUR A1 - Furini, Fabio A1 - Traversi, Emiliano A1 - Belotti, Pietro A1 - Frangioni, Antonio A1 - Gleixner, Ambros A1 - Gould, Nick A1 - Liberti, Leo A1 - Lodi, Andrea A1 - Misener, Ruth A1 - Mittelmann, Hans A1 - Sahinidis, Nikolaos V. A1 - Vigerske, Stefan A1 - Wiegele, Angelika T1 - QPLIB: A Library of Quadratic Programming Instances JF - Mathematical Programming Computation N2 - This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-018-0147-4 VL - 11 IS - 2 SP - 237 EP - 265 ER -