@misc{BertholdHeinzVigerske, 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}, 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{BertholdHeinzPfetschetal., 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}, 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{BertholdGleixnerHeinzetal., 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}, 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{ArnoldBertholdHeinzetal., 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}, series = {MATHEON - Mathematics for Key Technologies}, 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}, 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} } @article{BertholdGleixnerHeinzetal.2012, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {Analyzing the computational impact of MIQCP solver components}, series = {Numerical Algebra, Control and Optimization}, 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{BertholdHeinzVigerske, author = {Berthold, Timo and Heinz, Stefan and Vigerske, Stefan}, title = {Extending a CIP framework to solve MIQCPs}, series = {Mixed Integer Nonlinear Programming}, volume = {154}, journal = {Mixed Integer Nonlinear Programming}, editor = {Lee, Jon and Leyffer, Sven}, publisher = {Springer}, isbn = {978-1-4614-1927-3}, pages = {427 -- 444}, 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., author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc and Vigerske, Stefan}, title = {Large Neighborhood Search beyond MIP}, series = {Proceedings of the 9th Metaheuristics International Conference (MIC 2011)}, booktitle = {Proceedings of the 9th Metaheuristics International Conference (MIC 2011)}, isbn = {978-88-900984-3-7}, pages = {51 -- 60}, 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{ArnoldBertholdHeinzetal., 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}, 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} } @article{ShinanoHeinzVigerskeetal., author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, series = {INFORMS Journal on Computing}, volume = {30}, journal = {INFORMS Journal on Computing}, number = {1}, doi = {10.1287/ijoc.2017.0762}, pages = {11 -- 30}, 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{ShinanoHeinzVigerskeetal., 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}, 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} } @misc{BertholdGleixnerHeinzetal., 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}, 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} } @misc{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Vigerske, Stefan and Winkler, Michael}, title = {制約整数計画ソルバ SCIP の並列化}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18130}, abstract = {制約整数計画(CIP: Constraint Integer Programming)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: Satisfiability Problems)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.}, language = {ja} } @article{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Vigerske, Stefan and Winkler, Michael}, title = {制約整数計画ソルバ SCIP の並列化}, series = {統計数理}, volume = {61}, journal = {統計数理}, number = {1}, pages = {47 -- 78}, abstract = {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.}, language = {ja} } @misc{BertholdHeinzLuebbeckeetal., author = {Berthold, Timo and Heinz, Stefan and L{\"u}bbecke, Marco and M{\"o}hring, Rolf and Schulz, Jens}, title = {A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11180}, number = {10-03}, abstract = {We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.}, language = {en} } @misc{BertholdHeinzPfetsch, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Nonlinear pseudo-Boolean optimization: relaxation or propagation?}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11232}, number = {09-11}, abstract = {Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.}, language = {en} } @misc{HeinzStephanSchlechte, author = {Heinz, Stefan and Stephan, R{\"u}diger and Schlechte, Thomas}, title = {Solving Steel Mill Slab Problems with Branch and Price}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11260}, number = {09-14}, abstract = {The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.}, language = {en} } @misc{AchterbergBertholdHeinzetal., author = {Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: Techniques and Applications}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10950}, number = {08-43}, abstract = {This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.}, language = {en} } @misc{HeinzSachenbacher, author = {Heinz, Stefan and Sachenbacher, Martin}, title = {Using Model Counting to Find Optimal Distinguishing Tests}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10832}, number = {08-32}, abstract = {Testing is the process of stimulating a system with inputs in order to reveal hidden parts of the system state. In the case of non-deterministic systems, the difficulty arises that an input pattern can generate several possible outcomes. Some of these outcomes allow to distinguish between different hypotheses about the system state, while others do~not. In this paper, we present a novel approach to find, for non-deterministic systems modeled as constraints over variables, tests that allow to distinguish among the hypotheses as good as possible. The idea is to assess the quality of a test by determining the ratio of distinguishing (good) and not distinguishing (bad) outcomes. This measure refines previous notions proposed in the literature on model-based testing and can be computed using model counting techniques. We propose and analyze a greedy-type algorithm to solve this test optimization problem, using existing model counters as a building block. We give preliminary experimental results of our method, and discuss possible improvements.}, language = {en} } @misc{AchterbergHeinzKoch, author = {Achterberg, Tobias and Heinz, Stefan and Koch, Thorsten}, title = {Counting solutions of integer programs using unrestricted subtree detection}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10632}, number = {08-09}, abstract = {In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.}, language = {en} } @misc{BertholdHeinzPfetsch, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Solving Pseudo-Boolean Problems with SCIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10671}, number = {08-12}, abstract = {Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.}, language = {en} } @misc{HarksHeinzPfetsch, author = {Harks, Tobias and Heinz, Stefan and Pfetsch, Marc}, title = {Competitive Online Multicommodity Routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9212}, number = {06-27}, abstract = {We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is \$4K/2+K\$-competitive, where \$K\$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.}, language = {en} } @misc{HarksHeinzPfetsch, author = {Harks, Tobias and Heinz, Stefan and Pfetsch, Marc}, title = {Competitive Online Multicommodity Routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9599}, number = {07-16}, abstract = {In this paper we study online multicommodity routing problems in networks, in which commodities have to be routed sequentially. The flow of each commodity can be split on several paths. Arcs are equipped with load dependent price functions defining routing costs, which have to be minimized. We discuss a greedy online algorithm that routes each commodity by minimizing a convex cost function that only depends on the demands previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is 4K2 (1+K)2 -competitive, where K is the number of commodities. For the single-source single-destination case, this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.}, language = {en} } @misc{HeinzKrumkeMegowetal., author = {Heinz, Stefan and Krumke, Sven and Megow, Nicole and Rambau, J{\"o}rg and Tuchscherer, Andreas and Vredeveld, Tjark}, title = {The Online Target Date Assignment Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8945}, number = {05-61}, abstract = {Many online problems encountered in real-life involve a two-stage decision process: upon arrival of a new request, an irrevocable first-stage decision (the assignment of a specific resource to the request) must be made immediately, while in a second stage process, certain ``subinstances'' (that is, the instances of all requests assigned to a particular resource) can be solved to optimality (offline) later. We introduce the novel concept of an \emph{Online Target Date Assignment Problem} (\textsc{OnlineTDAP}) as a general framework for online problems with this nature. Requests for the \textsc{OnlineTDAP} become known at certain dates. An online algorithm has to assign a target date to each request, specifying on which date the request should be processed (e.\,g., an appointment with a customer for a washing machine repair). The cost at a target date is given by the \emph{downstream cost}, the optimal cost of processing all requests at that date w.\,r.\,t.\ some fixed downstream offline optimization problem (e.\,g., the cost of an optimal dispatch for service technicians). We provide general competitive algorithms for the \textsc{OnlineTDAP} independently of the particular downstream problem, when the overall objective is to minimize either the sum or the maximum of all downstream costs. As the first basic examples, we analyze the competitive ratios of our algorithms for the par ticular academic downstream problems of bin-packing, nonpreemptive scheduling on identical parallel machines, and routing a traveling salesman.}, language = {en} } @misc{Heinz, type = {Master Thesis}, author = {Heinz, Stefan}, title = {Policies for Online Target Date Assignment Problems: Competitive Analysis versus Expected Performance}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9933}, school = {Zuse Institute Berlin (ZIB)}, language = {en} } @misc{HarksHeinzPfetschetal., author = {Harks, Tobias and Heinz, Stefan and Pfetsch, Marc and Vredeveld, Tjark}, title = {Online Multicommodity Routing with Time Windows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9654}, number = {07-22}, abstract = {We consider a multicommodity routing problem, where demands are released \emph{online} and have to be routed in a network during specified time windows. The objective is to minimize a time and load dependent convex cost function of the aggregate arc flow. First, we study the fractional routing variant. We present two online algorithms, called Seq and Seq\$^2\$. Our first main result states that, for cost functions defined by polynomial price functions with nonnegative coefficients and maximum degree~\$d\$, the competitive ratio of Seq and Seq\$^2\$ is at most \$(d+1)^{d+1}\$, which is tight. We also present lower bounds of \$(0.265\,(d+1))^{d+1}\$ for any online algorithm. In the case of a network with two nodes and parallel arcs, we prove a lower bound of \$(2-\frac{1}{2} \sqrt{3})\$ on the competitive ratio for Seq and Seq\$^2\$, even for affine linear price functions. Furthermore, we study resource augmentation, where the online algorithm has to route less demand than the offline adversary. Second, we consider unsplittable routings. For this setting, we present two online algorithms, called U-Seq and U-Seq\$^2\$. We prove that for polynomial price functions with nonnegative coefficients and maximum degree~\$d\$, the competitive ratio of U-Seq and U-Seq\$^2\$ is bounded by \$O{1.77^d\,d^{d+1}}\$. We present lower bounds of \$(0.5307\,(d+1))^{d+1}\$ for any online algorithm and \$(d+1)^{d+1}\$ for our algorithms. Third, we consider a special case of our framework: online load balancing in the \$\ell_p\$-norm. For the fractional and unsplittable variant of this problem, we show that our online algorithms are \$p\$ and \$O{p}\$ competitive, respectively. Such results where previously known only for scheduling jobs on restricted (un)related parallel machines.}, language = {en} } @misc{KochAchterbergAndersenetal.2010, author = {Koch, Thorsten and Achterberg, Tobias and Andersen, Erling and Bastert, Oliver and Berthold, Timo and Bixby, Robert E. and Danna, Emilie and Gamrath, Gerald and Gleixner, Ambros and Heinz, Stefan and Lodi, Andrea and Mittelmann, Hans and Ralphs, Ted and Salvagnin, Domenico and Steffy, Daniel and Wolter, Kati}, title = {MIPLIB 2010}, doi = {10.1007/s12532-011-0025-9}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12953}, number = {10-31}, year = {2010}, abstract = {This paper reports on the fifth version of the Mixed Integer Programming Library. The MIPLIB 2010 is the first MIPLIB release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today's codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.}, language = {en} } @misc{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten}, title = {ParaSCIP - a parallel extension of SCIP}, doi = {10.1007/978-3-642-24025-6_12}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11921}, number = {10-27}, abstract = {Mixed integer programming (MIP) has become one of the most important techniques in Operations Research and Discrete Optimization. SCIP (Solving Constraint Integer Programs) is currently one of the fastest non-commercial MIP solvers. It is based on the branch-and-bound procedure in which the problem is recursively split into smaller subproblems, thereby creating a so-called branching tree. We present ParaSCIP, an extension of SCIP, which realizes a parallelization on a distributed memory computing environment. ParaSCIP uses SCIP solvers as independently running processes to solve subproblems (nodes of the branching tree) locally. This makes the parallelization development independent of the SCIP development. Thus, ParaSCIP directly profits from any algorithmic progress in future versions of SCIP. Using a first implementation of ParaSCIP, we were able to solve two previously unsolved instances from MIPLIB2003, a standard test set library for MIP solvers. For these computations, we used up to 2048 cores of the HLRN~II supercomputer.}, language = {en} } @misc{BertholdHeinzSchulz, author = {Berthold, Timo and Heinz, Stefan and Schulz, Jens}, title = {An approximative Criterion for the Potential of Energetic Reasoning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12655}, number = {11-12}, abstract = {Energetic reasoning is one of the most powerful propagation algorithms in cumulative scheduling. In practice, however, it is not commonly used because it has a high running time and its success highly depends on the tightness of the variable bounds. In order to speed up energetic reasoning, we provide an easy-to-check necessary condition for energetic reasoning to detect infeasibilities. We present an implementation of energetic reasoning that employs this condition and that can be parametrically adjusted to handle the trade-off between solving time and propagation overhead. Computational results on instances from the PSPLIB are provided. These results show that using this condition decreases the running time by more than a half, although more search nodes need to be explored.}, language = {en} } @misc{HeinzSchulz, author = {Heinz, Stefan and Schulz, Jens}, title = {Explanations for the Cumulative Constraint: an Experimental Study}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12668}, number = {11-13}, abstract = {In cumulative scheduling, conflict analysis seems to be one of the key ingredients to solve such problems efficiently. Thereby, the computational complexity of explanation algorithms plays an important role. Even more when we are faced with a backtracking system where explanations need to be constructed on the fly. In this paper we present extensive computational results to analyze the impact of explanation algorithms for the cumulative constraint in a backward checking system. The considered explanation algorithms differ in their quality and computational complexity. We present results for the domain propagation algorithms time-tabling, edge-finding, and energetic reasoning.}, language = {en} } @misc{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Solving Resource Allocation/Scheduling Problems with Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12691}, number = {11-14}, abstract = {Constraint Integer Programming (CIP) is a generalization of mixed-integer programming (MIP) in the direction of constraint programming (CP) allowing the inference techniques that have traditionally been the core of \P to be integrated with the problem solving techniques that form the core of complete MIP solvers. In this paper, we investigate the application of CIP to scheduling problems that require resource and start-time assignments to satisfy resource capacities. The best current approach to such problems is logic-based Benders decomposition, a manual decomposition method. We present a CIP model and demonstrate that it achieves performance competitive to the decomposition while out-performing the standard MIP and CP formulations.}, language = {en} } @misc{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14660}, number = {12-05}, abstract = {Despite the success of constraint programming (CP) for scheduling, the much wider penetration of mixed integer programming (MIP) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems.}, language = {en} } @misc{HeinzSchulzBeck, author = {Heinz, Stefan and Schulz, Jens and Beck, J. Christopher}, title = {Using dual presolving reductions to reformulate cumulative constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16321}, abstract = {Dual presolving reductions are a class of reformulation techniques that remove feasible or even optimal solutions while guaranteeing that at least one optimal solution remains, as long as the original problem was feasible. Presolving and dual reductions are important components of state-of-the-art mixed-integer linear programming solvers. In this paper, we introduce them both as unified, practical concepts in constraint programming solvers. Building on the existing idea of variable locks, we formally define and justify the use of dual information for cumulative constraints during a presolving phase of a solver. In particular, variable locks are used to decompose cumulative constraints, detect irrelevant variables, and infer variable assignments and domain reductions. Since the computational complexity of propagation algorithms typically depends on the number of variables and/or domain size, such dual reductions are a source of potential computational speed-up. Through experimental evidence on resource constrained project scheduling problems, we demonstrate that the conditions for dual reductions are present in well-known benchmark instances and that a substantial proportion of them can be solved to optimality in presolving -- without search. While we consider this result very promising, we do not observe significant change in overall run-time from the use of our novel dual reductions.}, language = {en} } @misc{HeinzKuBeck, author = {Heinz, Stefan and Ku, Wen-Yang and Beck, J. Christopher}, title = {Recent improvements using constraint integer programming for resource allocation and scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17676}, abstract = {Recently, we compared the performance of mixed-integer programming (MIP), constraint programming (CP), and constraint integer programming (CIP) to a state-of-the-art logic-based Benders manual decomposition (LBBD) for a resource allocation/scheduling problem. For a simple linear relaxation, the LBBD and CIP models deliver comparable performance with MIP also performing well. Here we show that algorithmic developments in CIP plus the use of an existing tighter relaxation substantially improve one of the CIP approaches. Furthermore, the use of the same relaxation in LBBD and MIP models significantly improves their performance. While such a result is known for LBBD, to the best of our knowledge, the other results are novel. Our experiments show that both CIP and MIP approaches are competitive with LBBD in terms of the number of problems solved to proven optimality, though MIP is about three times slower on average. Further, unlike the LBBD and CIP approaches, the MIP model is able to obtain provably high-quality solutions for all problem instances.}, language = {en} } @misc{HeinzSchlechteStephanetal., author = {Heinz, Stefan and Schlechte, Thomas and Stephan, R{\"u}diger and Winkler, Michael}, title = {Solving steel mill slab design problems}, issn = {1438-0064}, doi = {10.1007/s10601-011-9113-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14089}, number = {11-38}, abstract = {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. The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. 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. 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.}, language = {en} } @inproceedings{HeinzKrumkeMegowetal.2006, author = {Heinz, Stefan and Krumke, Sven and Megow, Nicole and Rambau, J{\"o}rg and Tuchscherer, Andreas and Vredeveld, Tjark}, title = {The Online Target Date Assignment Problem}, series = {Proc. 3rd Workshop on Approximation and Online Algorithms}, volume = {3879}, booktitle = {Proc. 3rd Workshop on Approximation and Online Algorithms}, editor = {Erlebach, Thomas and Persiano, Giuseppe}, publisher = {Springer}, pages = {230 -- 243}, year = {2006}, language = {en} } @article{HeinzKaibelPeinhardtetal.2006, author = {Heinz, Stefan and Kaibel, Volker and Peinhardt, Matthias and Rambau, J{\"o}rg and Tuchscherer, Andreas}, title = {LP-Based Local Approximation for Markov Decision Problems}, number = {343}, publisher = {Matheon}, year = {2006}, language = {en} } @misc{GamrathBertholdHeinzetal., author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, issn = {1438-0064}, doi = {10.1007/s12532-019-00159-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65387}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early in the solving process and help to solve instances to optimality faster. In this paper, we present a scheme for primal start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved as an LP and the solution is rounded. If the rounded solution did not provide a feasible solution already, a sub-MIP is solved for the neighborhood defined by the variable fixings performed in the first phase. The global structures help to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about three out of five instances and therewith help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.}, language = {en} } @article{HeinzSchlechteStephanetal., author = {Heinz, Stefan and Schlechte, Thomas and Stephan, R{\"u}diger and Winkler, Michael}, title = {Solving steel mill slab design problems}, series = {Constraints}, volume = {17}, journal = {Constraints}, number = {1}, doi = {10.1007/s10601-011-9113-8}, pages = {39 -- 50}, abstract = {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.}, language = {en} } @incollection{GamrathBertholdHeinzetal., author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-Based Primal Heuristics for Mixed Integer Programming}, series = {Optimization in the Real World}, volume = {13}, booktitle = {Optimization in the Real World}, publisher = {Springer Japan}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_3}, pages = {37 -- 53}, abstract = {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.}, language = {en} } @inproceedings{BertholdFarmerHeinzetal., author = {Berthold, Timo and Farmer, James and Heinz, Stefan and Perregaard, Michael}, title = {Parallelization of the FICO Xpress-Optimizer}, series = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, doi = {10.1007/978-3-319-42432-3_31}, pages = {251 -- 258}, language = {en} } @inproceedings{ShinanoBertholdHeinz, author = {Shinano, Yuji and Berthold, Timo and Heinz, Stefan}, title = {A First Implementation of ParaXpress: Combining Internal and External Parallelization to Solve MIPs on Supercomputers}, series = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, doi = {10.1007/978-3-319-42432-3_38}, pages = {308 -- 316}, language = {en} } @inproceedings{BertholdGleixnerHeinzetal.2012, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Koch, Thorsten and Shinano, Yuji}, title = {SCIP Optimization Suite を利用した 混合整数(線形/非線形) 計画問題の解法}, series = {Proceedings of the 24th RAMP symposium. The Operations Society of Japan, RAMP: Research Association of Mathematical Programming}, booktitle = {Proceedings of the 24th RAMP symposium. The Operations Society of Japan, RAMP: Research Association of Mathematical Programming}, pages = {165 -- 192}, year = {2012}, abstract = {この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる.}, language = {ja} } @inproceedings{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling}, series = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012)}, volume = {7298}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012)}, pages = {211 -- 227}, language = {en} } @inproceedings{BertholdHeinzSchulz, author = {Berthold, Timo and Heinz, Stefan and Schulz, Jens}, title = {An approximative Criterion for the Potential of Energetic Reasoning}, series = {Theory and Practice of Algorithms in (Computer) Systems}, volume = {6595}, booktitle = {Theory and Practice of Algorithms in (Computer) Systems}, pages = {229 -- 239}, language = {en} } @inproceedings{HeinzSchulz, author = {Heinz, Stefan and Schulz, Jens}, title = {Explanations for the Cumulative Constraint: An Experimental Study}, series = {Experimental Algorithms}, volume = {6630}, booktitle = {Experimental Algorithms}, pages = {400 -- 409}, language = {en} } @inproceedings{AchterbergHeinzKoch2008, author = {Achterberg, Tobias and Heinz, Stefan and Koch, Thorsten}, title = {Counting Solutions of Integer Programs Using Unrestricted Subtree Detection}, series = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 5th International Conference, CPAIOR 2008}, volume = {5015}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 5th International Conference, CPAIOR 2008}, editor = {Perron, Laurent and Trick, Michael}, publisher = {Springer}, pages = {278 -- 282}, year = {2008}, language = {en} } @article{KochAchterbergAndersenetal.2011, author = {Koch, Thorsten and Achterberg, Tobias and Andersen, Erling and Bastert, Oliver and Berthold, Timo and Bixby, Robert E. and Danna, Emilie and Gamrath, Gerald and Gleixner, Ambros and Heinz, Stefan and Lodi, Andrea and Mittelmann, Hans and Ralphs, Ted and Salvagnin, Domenico and Steffy, Daniel and Wolter, Kati}, title = {MIPLIB 2010}, series = {Mathematical Programming Computation}, volume = {3}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-011-0025-9}, pages = {103 -- 163}, year = {2011}, language = {en} } @inproceedings{ShinanoAchterbergBertholdetal.2012, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten}, title = {ParaSCIP: a parallel extension of SCIP}, series = {Competence in High Performance Computing 2010}, booktitle = {Competence in High Performance Computing 2010}, editor = {Bischof, Christian and Hegering, Heinz-Gerd and Nagel, Wolfgang and Wittum, Gabriel}, publisher = {Springer}, doi = {10.1007/978-3-642-24025-6_12}, pages = {135 -- 148}, year = {2012}, language = {en} } @misc{BertholdGleixnerHeinzetal., author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Koch, Thorsten and Shinano, Yuji}, title = {SCIP Optimization Suite を利用した 混合整数(線形/非線形) 計画問題の解法}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15598}, abstract = {この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる.}, language = {ja} } @misc{BertholdGamrathGleixneretal., author = {Berthold, Timo and Gamrath, Gerald and Gleixner, Ambros and Heinz, Stefan and Koch, Thorsten and Shinano, Yuji}, title = {Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15654}, abstract = {This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how these can be used in concert to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview of available interfaces, and outline plans for future development.}, language = {en} } @inproceedings{BertholdHeinzLuebbeckeetal.2010, author = {Berthold, Timo and Heinz, Stefan and L{\"u}bbecke, Marco and M{\"o}hring, Rolf and Schulz, Jens}, title = {A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling}, series = {Proc. of CPAIOR 2010}, volume = {6140}, booktitle = {Proc. of CPAIOR 2010}, editor = {Lodi, Andrea and Milano, Michela and Toth, Paolo}, publisher = {Springer}, pages = {313 -- 317}, year = {2010}, language = {en} } @inproceedings{BertholdHeinzPfetsch2009, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Nonlinear pseudo-Boolean optimization}, series = {Theory and Applications of Satisfiability Testing - SAT 2009}, volume = {5584}, booktitle = {Theory and Applications of Satisfiability Testing - SAT 2009}, editor = {Kullmann, Oliver}, publisher = {Springer}, pages = {441 -- 446}, year = {2009}, language = {en} } @inproceedings{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores}, series = {Proc. of 30th IEEE International Parallel \& Distributed Processing Symposium}, booktitle = {Proc. of 30th IEEE International Parallel \& Distributed Processing Symposium}, doi = {10.1109/IPDPS.2016.56}, abstract = {This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.}, language = {en} } @inproceedings{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Hard MIPLIP2003 Problems with ParaSCIP on Supercomputers: An Update}, series = {IPDPSW'14 Proceedings of the 2014 IEEE, International Parallel \& Distributed Processing Symposium Workshops}, booktitle = {IPDPSW'14 Proceedings of the 2014 IEEE, International Parallel \& Distributed Processing Symposium Workshops}, editor = {IEEE,}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, isbn = {978-1-4799-4117-9}, doi = {10.1109/IPDPSW.2014.174}, pages = {1552 -- 1561}, language = {en} } @article{GessatZachowBurgertetal.2007, author = {Gessat, Michael and Zachow, Stefan and Burgert, Oliver and Lemke, Heinz}, title = {Geometric Meshes in Medical Applications - Steps towards a specification of Geometric Models in DICOM}, series = {Int. J. of Computer Assisted Radiology and Surgery (CARS)}, journal = {Int. J. of Computer Assisted Radiology and Surgery (CARS)}, doi = {10.1007/s11548-007-0112-6}, pages = {440 -- 442}, year = {2007}, language = {en} } @misc{GamrathBertholdHeinzetal., author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-based primal heuristics for mixed integer programming}, issn = {1438-0064}, doi = {http://dx.doi.org/10.1007/978-4-431-55420-2_3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55518}, abstract = {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.}, language = {en} } @article{BertholdFarmerHeinzetal., author = {Berthold, Timo and Farmer, James and Heinz, Stefan and Perregaard, Michael}, title = {Parallelization of the FICO Xpress Optimizer}, series = {Optimization Methods and Software}, volume = {33}, journal = {Optimization Methods and Software}, number = {3}, doi = {10.1080/10556788.2017.1333612}, pages = {518 -- 529}, abstract = {Computing hardware has mostly thrashed out the physical limits for speeding up individual computing cores. Consequently, the main line of progress for new hardware is growing the number of computing cores within a single CPU. This makes the study of efficient parallelization schemes for computation-intensive algorithms more and more important. A natural precondition to achieving reasonable speedups from parallelization is maintaining a high workload of the available computational resources. At the same time, reproducibility and reliability are key requirements for software that is used in industrial applications. In this paper, we present the new parallelization concept for the state-of-the-art MIP solver FICO Xpress-Optimizer. MIP solvers like Xpress are expected to be deterministic. This inevitably results in synchronization latencies which render the goal of a satisfying workload a challenge in itself. We address this challenge by following a partial information approach and separating the concepts of simultaneous tasks and independent threads from each other. Our computational results indicate that this leads to a much higher CPU workload and thereby to an improved, almost linear, scaling on modern high-performance CPUs. As an added value, the solution path that Xpress takes is not only deterministic in a fixed environment, but also, to a certain extent, thread-independent. This paper is an extended version of Berthold et al. [Parallelization of the FICO Xpress-Optimizer, in Mathematical Software - ICMS 2016: 5th International Conference, G.-M. Greuel, T. Koch, P. Paule, and A. Sommere, eds., Springer International Publishing, Berlin, 2016, pp. 251-258] containing more detailed technical descriptions, illustrative examples and updated computational results.}, language = {en} } @article{GamrathBertholdHeinzetal., author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, series = {Mathematical Programming Computation}, volume = {11}, journal = {Mathematical Programming Computation}, number = {4}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {10.1007/s12532-019-00159-1}, pages = {675 -- 702}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60 \% of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.}, language = {en} } @article{ShinanoBertholdHeinz, author = {Shinano, Yuji and Berthold, Timo and Heinz, Stefan}, title = {ParaXpress: An Experimental Extension of the FICO Xpress-Optimizer to Solve Hard MIPs on Supercomputers}, series = {Optimization Methods \& Software}, volume = {33}, journal = {Optimization Methods \& Software}, number = {3}, doi = {10.1080/10556788.2018.1428602}, pages = {530 -- 539}, abstract = {The Ubiquity Generator (UG) is a general framework for the external parallelization of mixed integer programming (MIP) solvers. In this paper, we present ParaXpress, a distributed memory parallelization of the powerful commercial MIP solver FICO Xpress. Besides sheer performance, an important feature of Xpress is that it provides an internal parallelization for shared memory systems. When aiming for a best possible performance of ParaXpress on a supercomputer, the question arises how to balance the internal Xpress parallelization and the external parallelization by UG against each other. We provide computational experiments to address this question and we show computational results for running ParaXpress on a Top500 supercomputer, using up to 43,344 cores in parallel.}, language = {en} } @article{BoltzeHoellerlKubereketal., author = {Boltze, Julia and H{\"o}llerl, Annika and Kuberek, Monika and Lohrum, Stefan and Pampel, Heinz and Putnings, Markus and Retter, Regina and Rusch, Beate and Sch{\"a}ffler, Hildegard and S{\"o}llner, Konstanze}, title = {DeepGreen: Eine Infrastruktur f{\"u}r die Open-Access-Transformation}, series = {O-Bib. Das Offene Bibliotheksjournal}, volume = {9}, journal = {O-Bib. Das Offene Bibliotheksjournal}, number = {1}, doi = {10.5282/o-bib/5764}, abstract = {Mit DeepGreen wurde eine Infrastruktur aufgebaut und etabliert, die Zeitschriftenartikel von wissenschaftlichen Verlagen abholt und berechtigten Bibliotheken zur Ver{\"o}ffentlichung in ihren Repositorien sendet. DeepGreen unterst{\"u}tzt Bibliotheken als Dienstleister f{\"u}r Hochschulen, außeruniversit{\"a}re Einrichtungen und die dort t{\"a}tigen Wissenschaftler*innen, Publikationen auf Open-Access-Repositorien frei zug{\"a}nglich zu machen und f{\"o}rdert das Zusammenspiel von wissenschaftlichen Einrichtungen und Verlagen. DeepGreen wurde von Januar 2016 bis Juni 2021 von der Deutschen Forschungsgemeinschaft gef{\"o}rdert und wird nun vom Kooperativen Bibliotheksverbund Berlin-Brandenburg, von der Bayerischen Staatsbibliothek und von der Universit{\"a}tsbibliothek Erlangen-N{\"u}rnberg in arbeitsteiliger Eigenleistung f{\"u}r zwei Jahre weiterbetrieben. Der vorliegende Beitrag beleuchtet vielf{\"a}ltige Aspekte bei der Realisierung von DeepGreen und geht auf die Perspektiven dieser zentralen Open-Access-Infrastruktur f{\"u}r deutsche Wissenschaftseinrichtungen ein.}, language = {de} } @misc{BertelmannKochCeynowaetal., author = {Bertelmann, Roland and Koch, Thorsten and Ceynowa, Klaus and S{\"o}llner, Konstanze and Christof, J{\"u}rgen and Rusch, Beate and Sch{\"a}ffler, Hildegard and Putnings, Markus and Pampel, Heinz and Kuberek, Monika and Boltze, Julia and Lohrum, Stefan and Retter, Regina and H{\"o}llerl, Annika and Faensen, Katja and Steffen, Ronald and Gross, Matthias and Hoffmann, Cornelia and Haoua, Marsa}, title = {DeepGreen: Etablierung und Weiterentwicklung rechtssicherer Workflows zur effizienten Umsetzung von Open-Access-Komponenten in Lizenzvereinbarungen f{\"u}r wissenschaftliche Publikationen - Abschlussbericht}, issn = {1438-0064}, doi = {10.12752/8542}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85420}, abstract = {DeepGreen wurde vom 01.08.2018 bis zum 30.06.2021 in einer zweiten Projektphase von der Deutschen Forschungsgemeinschaft (DFG) gef{\"o}rdert. DeepGreen unterst{\"u}tzt Bibliotheken als Dienstleister f{\"u}r Hochschulen, außeruniversit{\"a}re Forschungseinrichtungen und die dort t{\"a}tigen Wissenschaftler:innen dabei, Publikationen auf Open-Access-Repositorien frei zug{\"a}nglich zu machen und f{\"o}rdert das Zusammenspiel von wissenschaftlichen Einrichtungen und Verlagen. An der zweiten Projektphase waren der Kooperative Bibliotheksverbund Berlin-Brandenburg, die Bayerische Staatsbibliothek, der Bibliotheksverbund Bayern, die Universit{\"a}tsbibliotheken der Friedrich-Alexander-Universit{\"a}t Erlangen-N{\"u}rnberg und der Technischen Universit{\"a}t Berlin und das Helmholtz Open Science Office beteiligt. In dem Projekt wurde erfolgreich eine technische und organisatorische L{\"o}sung zur automatisierten Verteilung von Artikeldaten wissenschaftlicher Verlage an institutionelle und fachliche Repositorien entwickelt. In der zweiten Projektphase lag der Fokus auf der Erprobung der Datendrehscheibe in der Praxis und der Ausweitung auf weitere Datenabnehmer und weitere Verlage. Im Anschluss an die DFG-gef{\"o}rderte Projektlaufzeit ist DeepGreen in einen zweij{\"a}hrigen Pilotbetrieb {\"u}bergegangen. Ziel des Pilotbetriebs ist es, den {\"U}bergang in einen bundesweiten Real-Betrieb vorzubereiten.}, language = {de} } @misc{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving hard MIPLIB2003 problems with ParaSCIP on Supercomputers: An update}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42888}, abstract = {Contemporary supercomputers can easily provide years of CPU time per wall-clock hour. One challenge of today's software development is how to harness this wast computing power in order to solve really hard mixed integer programming instances. In 2010, two out of six open MIPLIB2003 instances could be solved by ParaSCIP in more than ten consecutive runs, restarting from checkpointing files. The contribution of this paper is threefold: For the first time, we present computational results of single runs for those two instances. Secondly, we provide new improved upper and lower bounds for all of the remaining four open MIPLIB2003 instances. Finally, we explain which new developments led to these results and discuss the current progress of ParaSCIP. Experiments were conducted on HLRNII, on HLRN III, and on the Titan supercomputer, using up to 35,200 cores.}, language = {en} } @misc{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78393}, abstract = {Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper, we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.}, language = {en} } @misc{ShinanoAchterbergBertholdetal., author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores}, issn = {1438-0064}, doi = {10.1109/IPDPS.2016.56}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56404}, abstract = {This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.}, language = {en} } @misc{HeinzKaibelPeinhardtetal., author = {Heinz, Stefan and Kaibel, Volker and Peinhardt, Matthias and Rambau, J{\"o}rg and Tuchscherer, Andreas}, title = {LP-Based Local Approximation for Markov Decision Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9131}, number = {06-20}, abstract = {The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an \$\varepsilon\$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.}, language = {en} } @misc{WitzigBertholdHeinz, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Experiments with Conflict Analysis in Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/978-3-319-59776-8_17}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61087}, abstract = {The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The result of the analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. The dual LP solution provides a set of multipliers that can be used to generate a single new globally valid linear constraint. The main contribution of this short paper is an empirical evaluation of two ways to combine both approaches. Experiments are carried out on general MIP instances from standard public test sets such as Miplib2010; the presented algorithms have been implemented within the non-commercial MIP solver SCIP. Moreover, we present a pool-based approach to manage conflicts which addresses the way a MIP solver traverses the search tree better than aging strategies known from SAT solving.}, language = {en} } @inproceedings{WitzigBertholdHeinz, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Experiments with Conflict Analysis in Mixed Integer Programming}, series = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017}, volume = {10335}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017}, publisher = {Springer}, doi = {10.1007/978-3-319-59776-8_17}, pages = {211 -- 222}, abstract = {The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The result of the analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. The dual LP solution provides a set of multipliers that can be used to generate a single new globally valid linear constraint. The main contribution of this short paper is an empirical evaluation of two ways to combine both approaches. Experiments are carried out on general MIP instances from standard public test sets such as Miplib2010; the presented algorithms have been implemented within the non-commercial MIP solver SCIP. Moreover, we present a pool-based approach to manage conflicts which addresses the way a MIP solver traverses the search tree better than aging strategies known from SAT solving.}, language = {en} } @misc{WitzigBertholdHeinz, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Computational Aspects of Infeasibility Analysis in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74962}, abstract = {The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. This method is called dual proof analysis. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide an intense computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first integrated approach to use both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set MIPLIB 2017; the presented algorithms have been implemented within the non-commercial MIP solver SCIP and the commercial MIP solver FICO Xpress.}, language = {en} } @misc{WitzigBertholdHeinz, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71170}, abstract = {Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part.}, language = {en} } @inproceedings{WitzigBertholdHeinz, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, series = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, volume = {11494}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_6}, pages = {84 -- 94}, abstract = {Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part.}, language = {en} } @inproceedings{KraemerHerrmannBoethetal., author = {Kr{\"a}mer, Martin and Herrmann, Karl-Heinz and Boeth, Heide and Tycowicz, Christoph von and K{\"o}nig, Christian and Zachow, Stefan and Ehrig, Rainald and Hege, Hans-Christian and Duda, Georg and Reichenbach, J{\"u}rgen}, title = {Measuring 3D knee dynamics using center out radial ultra-short echo time trajectories with a low cost experimental setup}, series = {ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada}, booktitle = {ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada}, language = {en} } @misc{BertelmannBoltzeCeynowaetal., author = {Bertelmann, Roland and Boltze, Julia and Ceynowa, Klaus and Christof, J{\"u}rgen and Faensen, Katja and Groß, Matthias and Hoffmann, Cornelia and Koch, Thorsten and Kuberek, Monika and Lohrum, Stefan and Pampel, Heinz and Putnings, Markus and Retter, Regina and Rusch, Beate and Sch{\"a}ffler, Hildegard and S{\"o}llner, Konstanze and Steffen, Ronald and Wannick, Eike}, title = {DeepGreen: Open-Access-Transformation in der Informationsinfrastruktur - Anforderungen und Empfehlungen, Version 1.0}, issn = {1438-0064}, doi = {10.12752/8150}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81503}, abstract = {DeepGreen ist ein Service, der es teilnehmenden institutionellen Open-Access-Repositorien,Open-Access-Fachrepositorien und Forschungsinformationssystemen erleichtert, f{\"u}r sie relevante Verlagspublikationen in zyklischer Abfolge mithilfe von Schnittstellen Open Access zur Verf{\"u}gung zu stellen. Die entsprechende Bandbreite an Relationen zwischen den Akteuren, diverse lizenzrechtliche Rahmenbedingungen sowie technische Anforderungen gestalten das Thema komplex. Ziel dieser Handreichung ist es, neben all diesen Themen, die begleitend beleuchtet werden, im Besonderen Empfehlungen f{\"u}r die reibungslose Nutzung der Daten{\"u}bertragung zu liefern. Außerdem werden mithilfe einer vorangestellten Workflow- Evaluierung Unterschiede und Besonderheiten in den Arbeitsschritten bei institutionellen Open-Access-Repositorien und Open-Access-Fachrepositorien aufgezeigt und ebenfalls mit Empfehlungen angereichert.}, language = {de} }