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 - 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 - 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 - 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 - JOUR A1 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP JF - INFORMS Journal on Computing N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1287/ijoc.2017.0762 VL - 30 IS - 1 SP - 11 EP - 30 ER - TY - JOUR A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - 制約整数計画ソルバ SCIP の並列化 JF - 統計数理 N2 - 制約整数計画(CIP: Constraint Integer Programs)は,制約プログラミング(CP: Constraint Programming),混合整数計画(MIP: Mixed Integer Programming),充足可能性問題(SAT: Satisfability Problem)の研究分野におけるモデリング技術と解法を統合している.その結果,制約整数計画は,広いクラスの最適化問題を扱うことができる.SCIP(Solving Constraint Integer Programs)は,CIP を解くソルバとして実装され,Zuse Institute Berlin(ZIB)の研究者を中心として継続的に拡張が続けられている.本論文では,著者らによって開発された SCIP に対する2 種類の並列化拡張を紹介する.一つは,複数計算ノード間で大規模に並列動作する ParaSCIPである.もう一つは,複数コアと共有メモリを持つ 1 台の計算機上で(スレッド)並列で動作する FiberSCIP である.ParaSCIP は,HLRN II スーパーコンピュータ上で,一つのインスタンスを解くために最大 7,168 コアを利用した動作実績がある.また,統計数理研究所の Fujitsu PRIMERGY RX200S5 上でも,最大 512 コアを利用した動作実績がある.統計数理研究所のFujitsu PRIMERGY RX200S5 上では,これまでに最適解が得られていなかった MIPLIB2010のインスタンスである dg012142 に最適解を与えた. N2 - The paradigm of constraint integer programming (CIP) combines modeling and solving techniques from the fields of constraint programming (CP), mixed-integer programming (MIP) and satisfability problem (SAT). This paradigm allows us to address a wide range of optimization problems. SCIP is an implementation of the idea of CIP and is now being continuously extended by a group of researchers centered at Zuse Institute Berlin (ZIB). This paper introduces two parallel extensions of SCIP. One is ParaSCIP, which is intended to run on a large scale distributed memory computing environment, and the other is FiberSCIP, intended to run on a shared memory computing environment. ParaSCIP has been run successfully on the HLRN II supercomputer utilizing up to 7,168 cores to solve a single difficult MIP. It has also been tested on an ISM supercomputer (Fujitsu PRIMERGY RX200S5 using up to 512 cores). The previously unsolved instance dg012142 from MIPLIB2010 was solved by using the ISM supercomputer. Y1 - 2013 UR - https://www.ism.ac.jp/editsec/toukei/pdf/61-1-047.pdf VL - 61 IS - 1 SP - 47 EP - 78 ER - TY - CHAP A1 - Heinz, Stefan A1 - Krumke, Sven A1 - Megow, Nicole A1 - Rambau, Jörg A1 - Tuchscherer, Andreas A1 - Vredeveld, Tjark ED - Erlebach, Thomas ED - Persiano, Giuseppe T1 - The Online Target Date Assignment Problem T2 - Proc. 3rd Workshop on Approximation and Online Algorithms Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/894/ VL - 3879 SP - 230 EP - 243 PB - Springer ER - TY - JOUR A1 - Heinz, Stefan A1 - Kaibel, Volker A1 - Peinhardt, Matthias A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - LP-Based Local Approximation for Markov Decision Problems Y1 - 2006 IS - 343 PB - Matheon ER - TY - JOUR A1 - Heinz, Stefan A1 - Schlechte, Thomas A1 - Stephan, Rüdiger A1 - Winkler, Michael T1 - Solving steel mill slab design problems JF - Constraints N2 - The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. (INFORMS J Comput 18:129–134, 2006). The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. (INFORMS J Comput 18:129–134, 2006) for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results (Schaus et al., Constraints 16:125–147, 2010). Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality. Y1 - 2012 U6 - https://doi.org/10.1007/s10601-011-9113-8 VL - 17 IS - 1 SP - 39 EP - 50 ER - TY - CHAP A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-Based Primal Heuristics for Mixed Integer Programming T2 - Optimization in the Real World N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time. Y1 - 2015 SN - 978-4-431-55419-6 U6 - https://doi.org/10.1007/978-4-431-55420-2_3 VL - 13 SP - 37 EP - 53 PB - Springer Japan ER -