@misc{AchterbergBertholdHeinzetal.2008, 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}, year = {2008}, 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{GamrathKochRehfeldtetal.2014, author = {Gamrath, Gerald and Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A massively parallel STP solver}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52293}, year = {2014}, abstract = {In this article we describe the impact from embedding a 15 year old model for solving the Steiner tree problem in graphs in a state-of-the-art MIP-Framework, making the result run in a massively parallel environment and extending the model to solve as many variants as possible. We end up with a high-perfomance solver that is capable of solving previously unsolved instances and, in contrast to its predecessor, is freely available for academic research.}, language = {en} } @misc{KochMartinPfetsch2013, author = {Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Progress in Academic Computational Integer Programming}, journal = {Facets of Combinatorial Optimization}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_19}, pages = {483 -- 506}, year = {2013}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, issn = {1438-0064}, doi = {10.4171/137}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49947}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {135 -- 146}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @article{CookKochSteffyetal.2013, author = {Cook, William and Koch, Thorsten and Steffy, Daniel and Wolter, Kati}, title = {A hybrid branch-and-bound approach for exact rational mixed-integer programming}, volume = {5}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-013-0055-6}, pages = {305 -- 344}, year = {2013}, abstract = {We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances.}, language = {en} } @misc{RalphsShinanoBertholdetal.2016, author = {Ralphs, Ted and Shinano, Yuji and Berthold, Timo and Koch, Thorsten}, title = {Parallel Solvers for Mixed Integer Linear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62239}, year = {2016}, abstract = {In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.}, language = {en} } @inproceedings{ShinanoAchterbergBertholdetal.2014, 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}, 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}, year = {2014}, language = {en} } @misc{BertholdHendelKoch2016, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {The Three Phases of MIP Solving}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1392519}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61607}, year = {2016}, abstract = {Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points.}, language = {en} } @misc{HillerKochScheweetal.2017, author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61931}, year = {2017}, abstract = {Since 2005, the gas market in the European Union is liberalized and the trading of natural gas is decoupled from its transport. The transport is done by so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer maximum independent capacities at each entry and exit such that the resulting gas flows can be realized by the network without compromising security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This paper gives an overview of the toolset for evaluating gas network capacities that has been developed within the ForNe project, a joint research project of seven research partners initiated by Open Grid Europe, Germany's biggest TSO. While most of the relevant mathematics is described in the book "Evaluating Gas Network Capacities", this article sketches the system as a whole, describes some developments that have taken place recently, and gives some details about the current implementation.}, language = {en} } @article{GamrathKochMartinetal.2015, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in presolving for mixed integer programming}, volume = {7}, journal = {Mathematical Programming Computation}, number = {4}, doi = {10.1007/s12532-015-0083-5}, pages = {367 -- 398}, year = {2015}, abstract = {This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 \% on affected instances while not degrading the performance on the remaining problems.}, language = {en} }