@article{HoppmannBaumHenningsZitteletal.2021, author = {Hoppmann-Baum, Kai and Hennings, Felix and Zittel, Janina and Gotzes, Uwe and Spreckelsen, Eva-Maria and Spreckelsen, Klaus and Koch, Thorsten}, title = {An Optimization Approach for the Transient Control of Hydrogen Transport Networks}, journal = {Mathematical Methods of Operations Research}, number = {Special Issue on Energy Networks}, year = {2021}, language = {en} } @misc{WitzigGleixner2019, author = {Witzig, Jakob and Gleixner, Ambros}, title = {Conflict-Driven Heuristics for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1287/ijoc.2020.0973}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72204}, year = {2019}, abstract = {Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.}, language = {en} } @misc{HendelMiltenbergerWitzig2018, author = {Hendel, Gregor and Miltenberger, Matthias and Witzig, Jakob}, title = {Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69563}, year = {2018}, abstract = {State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics as well as Simplex pricing strategies. For each class we propose a selection strategy that is updated based on the observed runtime behavior, aiming to ultimately select only the best algorithms for a given instance. We review several common strategies for such a selection scenario under uncertainty, also known as Multi Armed Bandit Problem. In order to apply those bandit strategies, we carefully design reward functions to rank and compare each individual heuristic or pricing algorithm within its respective class. Finally, we discuss the computational benefits of using the proposed adaptive selection within the \scip Optimization Suite on publicly available MIP instances.}, language = {en} } @misc{GamrathKochMartinetal.2013, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in Presolving for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/s12532-015-0083-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42530}, year = {2013}, abstract = {Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice.}, language = {en} } @incollection{GamrathBertholdHeinzetal.2015, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-Based Primal Heuristics for Mixed Integer Programming}, 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}, year = {2015}, 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} } @misc{WitzigBertholdHeinz2016, 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}, year = {2016}, 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{GleixnerMaherMuelleretal.2017, author = {Gleixner, Ambros and Maher, Stephen J. and M{\"u}ller, Benjamin and Pedroso, Jo{\~a}o Pedro}, title = {Exact Methods for Recursive Circle Packing}, doi = {10.1007/s10479-018-3115-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62039}, year = {2017}, abstract = {Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig-Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a "price-and-verify" algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.}, language = {en} } @misc{CheungGleixnerSteffy2016, author = {Cheung, Kevin K. H. and Gleixner, Ambros and Steffy, Daniel}, title = {Verifying Integer Programming Results}, issn = {1438-0064}, doi = {10.1007/978-3-319-59250-3_13}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61044}, year = {2016}, abstract = {Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certificate format is designed with simplicity in mind and is composed of a list of statements that can be sequentially verified using a limited number of simple yet powerful inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of mixed-integer linear programming instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.}, language = {en} } @article{RehfeldtKoch2019, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem}, volume = {29}, journal = {SIAM Journal on Optimization}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/17M1145963}, pages = {369 -- 398}, year = {2019}, abstract = {Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced.}, language = {en} } @misc{FujisawaShinanoWaki2015, author = {Fujisawa, Katsuki and Shinano, Yuji and Waki, Hayato}, title = {Optimization in the Real World}, volume = {13}, journal = {Mathematics for Industry (MFI)}, publisher = {Springer Tokyo Heidelberg New York Dordrecht London}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2}, year = {2015}, language = {en} } @inproceedings{BreuerBussieckCaoetal.2018, author = {Breuer, Thomas and Bussieck, Michael and Cao, Karl-Kien and Cebulla, Felix and Fiand, Frederik and Gils, Hans Christian and Gleixner, Ambros and Khabi, Dmitry and Koch, Thorsten and Rehfeldt, Daniel and Wetzel, Manuel}, title = {Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_85}, pages = {641 -- 647}, year = {2018}, abstract = {Current linear energy system models (ESM) acquiring to provide sufficient detail and reliability frequently bring along problems of both high intricacy and increasing scale. Unfortunately, the size and complexity of these problems often prove to be intractable even for commercial state-of-the-art linear programming solvers. This article describes an interdisciplinary approach to exploit the intrinsic structure of these large-scale linear problems to be able to solve them on massively parallel high-performance computers. A key aspect are extensions to the parallel interior-point solver PIPS-IPM originally developed for stochastic optimization problems. Furthermore, a newly developed GAMS interface to the solver as well as some GAMS language extensions to model block-structured problems will be described.}, language = {en} } @article{FuriniTraversiBelottietal.2019, author = {Furini, Fabio and Traversi, Emiliano and Belotti, Pietro and Frangioni, Antonio and Gleixner, Ambros and Gould, Nick and Liberti, Leo and Lodi, Andrea and Misener, Ruth and Mittelmann, Hans and Sahinidis, Nikolaos V. and Vigerske, Stefan and Wiegele, Angelika}, title = {QPLIB: A Library of Quadratic Programming Instances}, volume = {11}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-018-0147-4}, pages = {237 -- 265}, year = {2019}, abstract = {This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.}, language = {en} } @phdthesis{Pulaj2017, author = {Pulaj, Jonad}, title = {Cutting Planes for Union-Closed Families}, year = {2017}, abstract = {Frankl's (union-closed sets) conjecture states that for any nonempty finite union-closed (UC) family of distinct sets there exists an element in at least half of the sets. Poonen's Theorem characterizes the existence of weights which determine whether a given UC family ensures Frankl's conjecture holds for all UC families which contain it. The weight systems are nontrivial to identify for a given UC family, and methods to determine such weight systems have led to several other open questions and conjectures regarding structures in UC families. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen's Theorem using computational integer programming coupled with redundant verification routines that ensure correctness. We find over one hundred previously unknown families of sets which ensure Frankl's conjecture holds for all families that contain any of them. This improves significantly on all previous results of the kind. Our framework allows us to answer several open questions and conjectures regarding structural properties of UC families, including proving the 3-sets conjecture of Morris from 2006 which characterizes the minimum number of 3-sets that ensure Frankl's conjecture holds for all families that contain them. Furthermore, our method provides a general algorithmic road-map for improving other known results and uncovering structures in UC families.}, language = {en} } @inproceedings{CheungGleixnerSteffy2017, author = {Cheung, Kevin K. H. and Gleixner, Ambros and Steffy, Daniel}, title = {Verifying Integer Programming Results}, volume = {10328}, booktitle = {F. Eisenbrand and J. Koenemann, eds., Integer Programming and Combinatorial Optimization: 19th International Conference, IPCO 2017}, doi = {10.1007/978-3-319-59250-3_13}, pages = {148 -- 160}, year = {2017}, abstract = {Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.}, language = {en} } @inproceedings{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {SCIP-Jack—a solver for STP and variants with parallelization extensions: An update}, booktitle = {Operations Research Proceedings 2017}, pages = {191 -- 196}, year = {2018}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. Although the different Steiner tree problem variants are usually strongly related, solution approaches employed so far have been prevalently problem-specific. Against this backdrop, the solver SCIP-Jack was created as a general-purpose framework that can be used to solve the classical Steiner tree problem and 11 of its variants. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. Furthermore, SCIP-Jack includes various newly developed algorithmic components such as preprocessing routines and heuristics. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. After the introduction of SCIP-Jack at the 2014 DIMACS Challenge on Steiner problems, the overall performance of the solver has considerably improved. This article provides an overview on the current state.}, language = {en} } @article{VierhausFuegenschuhGottwaldetal.2017, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin and Gottwald, Robert Lion and Gr{\"o}sser, Stefan}, title = {Using white-box nonlinear optimization methods in system dynamics policy improvement}, volume = {33}, journal = {System Dynamics Review}, number = {2}, doi = {10.1002/sdr.1583}, pages = {138 -- 168}, year = {2017}, abstract = {We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published "towards a global equilibrium" run with equal cost of intervention.}, language = {en} } @inproceedings{SchadeSchlechteWitzig2018, author = {Schade, Stanley and Schlechte, Thomas and Witzig, Jakob}, title = {Structure-based Decomposition for Pattern-Detection for Railway Timetables}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_95}, pages = {715 -- 721}, year = {2018}, abstract = {We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers.}, language = {en} } @masterthesis{Wischlinsky2017, type = {Bachelor Thesis}, author = {Wischlinsky, William}, title = {Feasibility-based bound tightening via linear programming}, year = {2017}, language = {en} } @misc{GleixnerBastubbeEifleretal.2018, author = {Gleixner, Ambros and Bastubbe, Michael and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Schubert, Christoph and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Walter, Matthias and Wegscheider, Fabian and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 6.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69361}, year = {2018}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.}, language = {en} } @misc{WeberSagerGleixner2018, author = {Weber, Tobias and Sager, Sebastian and Gleixner, Ambros}, title = {Solving Quadratic Programs to High Precision using Scaled Iterative Refinement}, issn = {1438-0064}, doi = {10.1007/s12532-019-00154-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68152}, year = {2018}, abstract = {Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and M{\´e}sz{\´a}ros benchmark library.}, language = {en} } @article{WeberSagerGleixner2019, author = {Weber, Tobias and Sager, Sebastian and Gleixner, Ambros}, title = {Solving Quadratic Programs to High Precision using Scaled Iterative Refinement}, volume = {11}, journal = {Mathematical Programming Computation}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/s12532-019-00154-6}, pages = {421 -- 455}, year = {2019}, abstract = {Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and M{\´e}sz{\´a}ros benchmark library.}, 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}, volume = {3}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-011-0025-9}, pages = {103 -- 163}, year = {2011}, language = {en} } @article{Gamrath2013, author = {Gamrath, Gerald}, title = {Improving strong branching by propagation}, volume = {7874}, journal = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems}, editor = {Gomes, Carla and Sellmann, Meinolf}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/978-3-642-38171-3_25}, pages = {347 -- 354}, year = {2013}, abstract = {Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers. It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time.}, language = {en} } @inproceedings{FuegenschuhHillerHumpolaetal.2011, author = {F{\"u}genschuh, Armin and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Schwarz, Robert and Schweiger, Jonas and Szabo, Jacint}, title = {Gas Network Topology Optimization for Upcoming Market Requirements}, booktitle = {International Conference on the European Energy Market (EEM)}, doi = {10.1109/EEM.2011.5953035}, pages = {346 -- 351}, year = {2011}, abstract = {Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed.}, language = {en} } @article{Gamrath2014, author = {Gamrath, Gerald}, title = {Improving strong branching by domain propagation}, volume = {2}, journal = {EURO Journal on Computational Optimization}, number = {3}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {10.1007/s13675-014-0021-8}, pages = {99 -- 122}, year = {2014}, abstract = {One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique MIP solvers usually apply at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, the state-of-the-art hybrid branching rule can be improved this way as well. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013.}, language = {en} } @inproceedings{HeinzSchulz2011, author = {Heinz, Stefan and Schulz, Jens}, title = {Explanations for the Cumulative Constraint: An Experimental Study}, volume = {6630}, booktitle = {Experimental Algorithms}, pages = {400 -- 409}, year = {2011}, language = {en} } @article{GleixnerHeldHuangetal.2012, author = {Gleixner, Ambros and Held, Harald and Huang, Wei and Vigerske, Stefan}, title = {Towards globally optimal operation of water supply networks}, volume = {2}, journal = {Numerical Algebra, Control and Optimization}, number = {4}, doi = {10.3934/naco.2012.2.695}, pages = {695 -- 711}, year = {2012}, abstract = {This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.}, 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}, 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} } @article{BertholdGleixnerHeinzetal.2012, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {Analyzing the computational impact of MIQCP solver components}, volume = {2}, journal = {Numerical Algebra, Control and Optimization}, number = {4}, doi = {10.3934/naco.2012.2.739}, pages = {739 -- 748}, year = {2012}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @inproceedings{HeinzBeck2012, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling}, volume = {7298}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012)}, pages = {211 -- 227}, year = {2012}, language = {en} } @inproceedings{BertholdHeinzSchulz2011, author = {Berthold, Timo and Heinz, Stefan and Schulz, Jens}, title = {An approximative Criterion for the Potential of Energetic Reasoning}, volume = {6595}, booktitle = {Theory and Practice of Algorithms in (Computer) Systems}, pages = {229 -- 239}, year = {2011}, language = {en} } @inproceedings{HendelBertholdAchterberg2011, author = {Hendel, Gregor and Berthold, Timo and Achterberg, Tobias}, title = {Rounding and Propagation Heuristics for Mixed Integer Programming}, booktitle = {Operations Research Proceedings 2011}, pages = {71 -- 76}, year = {2011}, abstract = {Primal heuristics are an important component of state-of-the-art codes for mixed integer programming. In this paper, we focus on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation). We give an overview of eight different approaches. To assess the impact of these primal heuristics on the ability to find feasible solutions, in particular early during search, we introduce a new performance measure, the primal integral. Computational experiments evaluate this and other measures on MIPLIB~2010 benchmark instances.}, language = {en} } @misc{BertholdSalvagnin2013, author = {Berthold, Timo and Salvagnin, Domenico}, title = {Cloud branching}, volume = {7874}, journal = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems}, editor = {Gomes, Carla and Sellmann, Meinolf}, publisher = {Springer}, doi = {10.1007/978-3-642-38171-3_3}, pages = {28 -- 43}, year = {2013}, abstract = {Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the current LP relaxation. These strategies naturally extend state-of-the-art methods like strong branching, pseudocost branching, and their hybrids. We show that by exploiting dual degeneracy, and thus multiple alternative optimal solutions, it is possible to enhance traditional methods. We present preliminary computational results, applying the newly proposed strategy to full strong branching, which is known to be the MIP branching rule leading to the fewest number of search nodes. It turns out that cloud branching can reduce the mean running time by up to 30\% on standard test sets.}, language = {en} } @article{HeinzSchlechteStephanetal.2012, author = {Heinz, Stefan and Schlechte, Thomas and Stephan, R{\"u}diger and Winkler, Michael}, title = {Solving steel mill slab design problems}, volume = {17}, journal = {Constraints}, number = {1}, doi = {10.1007/s10601-011-9113-8}, pages = {39 -- 50}, year = {2012}, 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} } @article{BertholdGleixner2014, author = {Berthold, Timo and Gleixner, Ambros}, title = {Undercover: a primal MINLP heuristic exploring a largest sub-MIP}, volume = {144}, journal = {Mathematical Programming}, number = {1-2}, doi = {10.1007/s10107-013-0635-2}, pages = {315 -- 346}, year = {2014}, abstract = {We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers.}, language = {en} } @article{AchterbergBerthold2007, author = {Achterberg, Tobias and Berthold, Timo}, title = {Improving the Feasibility Pump}, volume = {Special Issue 4}, journal = {Discrete Optimization}, number = {1}, pages = {77 -- 86}, year = {2007}, language = {en} } @article{Berthold2008, author = {Berthold, Timo}, title = {Heuristiken im Branch-and-Cut-Framework SCIP}, journal = {OR News}, number = {32}, pages = {24 -- 25}, year = {2008}, language = {en} } @misc{ShinanoHeinzVigerskeetal.2013, author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, issn = {1438-0064}, doi = {10.1287/ijoc.2017.0762}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42595}, year = {2013}, abstract = {Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated.}, language = {en} } @misc{Gamrath2013, author = {Gamrath, Gerald}, title = {Improving strong branching by domain propagation}, issn = {1438-0064}, doi = {10.1007/s13675-014-0021-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42546}, year = {2013}, abstract = {One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique usually used at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, also the state-of-the-art hybrid branching rule can be improved this way. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013.}, language = {en} } @misc{GamrathMelchioriBertholdetal.2015, author = {Gamrath, Gerald and Melchiori, Anna and Berthold, Timo and Gleixner, Ambros and Salvagnin, Domenico}, title = {Branching on multi-aggregated variables}, issn = {1438-0064}, doi = {10.1007/978-3-319-18008-3_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53829}, year = {2015}, abstract = {In mixed-integer programming, the branching rule is a key component to a fast convergence of the branch-and-bound algorithm. The most common strategy is to branch on simple disjunctions that split the domain of a single integer variable into two disjoint intervals. Multi-aggregation is a presolving step that replaces variables by an affine linear sum of other variables, thereby reducing the problem size. While this simplification typically improves the performance of MIP solvers, it also restricts the degree of freedom in variable-based branching rules. We present a novel branching scheme that tries to overcome the above drawback by considering general disjunctions defined by multi-aggregated variables in addition to the standard disjunctions based on single variables. This natural idea results in a hybrid between variable- and constraint-based branching rules. Our implementation within the constraint integer programming framework SCIP incorporates this into a full strong branching rule and reduces the number of branch-and-bound nodes on a general test set of publicly available benchmark instances. For a specific class of problems, we show that the solving time decreases significantly.}, language = {en} } @misc{WitzigGamrathHiller2015, author = {Witzig, Jakob and Gamrath, Gerald and Hiller, Benjamin}, title = {Reoptimization Techniques in MIP Solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-20086-6_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54375}, year = {2015}, abstract = {Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to ``warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.}, language = {en} } @misc{MaherFischerGallyetal.2017, author = {Maher, Stephen J. and Fischer, Tobias and Gally, Tristan and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Robert Lion and Hendel, Gregor and Koch, Thorsten and L{\"u}bbecke, Marco and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 4.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62170}, year = {2017}, abstract = {The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.}, language = {en} } @article{YokoyamaShinanoTaniguchietal.2015, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation}, volume = {92}, journal = {Energy Conversion and Management}, doi = {10.1016/j.enconman.2014.12.020}, pages = {92 -- 104}, year = {2015}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation variables is proposed to solve the optimal design problem of energy supply systems efficiently: At the upper level, the optimal values of design variables are searched by the branch and bound method; At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively during the search at the upper level; Lower bounds for the optimal value of the objective function to be minimized are evaluated, and are utilized for the bounding operations at both the levels. This method is implemented into open and commercial MILP solvers. Illustrative and practical case studies on the optimal design of cogeneration systems are conducted, and the validity and effectiveness of the proposed method are clarified.}, language = {en} } @incollection{YokoyamaShinano2015, author = {Yokoyama, Ryohei and Shinano, Yuji}, title = {MILP Approaches to Optimal Design and Operation of Distributed Energy Systems}, volume = {Volume 13}, booktitle = {Optimization in the Real World}, publisher = {Springer}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_9}, pages = {157 -- 176}, year = {2015}, abstract = {Energy field is one of the practical areas to which optimization can contribute significantly. In this chapter, the application of mixed-integer linear programming (MILP) approaches to optimal design and operation of distributed energy systems is described. First, the optimal design and operation problems are defined, and relevant previous work is reviewed. Then, an MILP method utilizing the hierarchical relationship between design and operation variables is presented. In the optimal design problem, integer variables are used to express the types, capacities, numbers, operation modes, and on/off states of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. The presented method can change the enumeration tree for the branching and bounding procedures, and can search the optimal solution very efficiently. Finally, future work in relation to this method is described.}, language = {en} } @masterthesis{Wyczisk2016, type = {Bachelor Thesis}, author = {Wyczisk, Christopher}, title = {Portfoliooptimierung mittels mathematischer Optimierung}, year = {2016}, language = {de} } @misc{GamrathFischerGallyetal.2016, author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, year = {2016}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, language = {en} } @misc{BallersteinMichaelsVigerske2013, author = {Ballerstein, Martin and Michaels, Dennis and Vigerske, Stefan}, title = {Linear Underestimators for bivariate functions with a fixed convexity behavior}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17641}, year = {2013}, abstract = {This is a technical report for the SCIP constraint handler cons_bivariate. We describe a cut-generation algorithm for a class of bivariate twice continuously differentiable functions with fixed convexity behavior over a box. Computational results comparing our cut-generation algorithms with state-of-the-art global optimization software on a series of randomly generated test instances are reported and discussed.}, language = {en} } @misc{BertholdHendel2013, author = {Berthold, Timo and Hendel, Gregor}, title = {Shift-And-Propagate}, issn = {1438-0064}, doi = {10.1007/s10732-014-9271-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17596}, year = {2013}, abstract = {For mixed integer programming, recent years have seen a growing interest in the design of general purpose primal heuristics for use inside complete solvers. Many of these heuristics rely on an optimal LP solution. Finding this may itself take a significant amount of time. The presented paper addresses this issue by the introduction of the Shift-And-Propagate heuristic. Shift-And-Propagate is a pre-root primal heuristic that does not require a previously found LP solution. It applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement of existing rounding and propagation heuristics.}, language = {en} } @article{GamrathKochMaheretal.2017, author = {Gamrath, Gerald and Koch, Thorsten and Maher, Stephen J. and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A solver for STP and variants with parallelization extensions}, volume = {9}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-016-0114-x}, pages = {231 -- 296}, year = {2017}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.}, language = {en} } @inproceedings{ShinanoBertholdHeinz2016, 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}, 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}, year = {2016}, language = {en} }