@misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching on History Information}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6990}, number = {02-32}, abstract = {Mixed integer programs (\$MIPs\$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in \$SIP\$, a state-of-the-art \$MIP\$ solver. We give computational results that show the superiority of the new strategy.}, language = {en} } @misc{AchterbergBerthold, author = {Achterberg, Tobias and Berthold, Timo}, title = {Improving the Feasibility Pump}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8754}, number = {05-42}, abstract = {The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modification of the algorithm in order to find better solutions. Extensive computational results show the success of this variant: in 89 out of 121 MIP instances the modified version produces improved solutions in comparison to the original Feasibility Pump.}, language = {en} } @misc{Achterberg, author = {Achterberg, Tobias}, title = {SCIP - a framework to integrate Constraint and Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7947}, number = {04-19}, abstract = {Constraint Programs and Mixed Integer Programs are closely related optimization problems originating from different scientific areas. Today's state-of-the-art algorithms of both fields have several strategies in common, in particular the branch-and-bound process to recursively divide the problem into smaller sub problems. On the other hand, the main techniques to process each sub problem are different, and it was observed that they have complementary strenghts. We propose a programming framework {\sffamily SCIP} that integrates techniques from both fields in order to exploit the strenghts of both, Constraint Programming and Mixed Integer Programming. In contrast to other proposals of recent years to combine both fields, {\sffamily SCIP} does not focus on easy implementation and rapid prototyping, but is tailored towards expert users in need of full, in-depth control and high performance.}, language = {en} } @misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching rules revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7886}, number = {04-13}, abstract = {Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.}, language = {en} } @phdthesis{Achterberg, author = {Achterberg, Tobias}, title = {Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11129}, abstract = {This thesis introduces the novel paradigm of "constraint integer programming" (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.}, language = {en} } @misc{AchterbergBertholdKochetal., author = {Achterberg, Tobias and Berthold, Timo and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: a New Approach to Integrate CP and MIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10520}, number = {08-01}, 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 from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two 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 employ the CIP framework to solve chip design verification problems, which involve some highly non-linear 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 non-linear constraints by employing constraint programming techniques.}, 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{AchterbergKochTuchscherer, author = {Achterberg, Tobias and Koch, Thorsten and Tuchscherer, Andreas}, title = {On the Effects of Minor Changes in Model Formulations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10808}, number = {08-29}, abstract = {Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not.}, 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{AchterbergGroetschelKoch, author = {Achterberg, Tobias and Gr{\"o}tschel, Martin and Koch, Thorsten}, title = {Software for Teaching Modeling of Integer Programming Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9176}, number = {06-23}, abstract = {Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.}, language = {en} } @misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {MIPLIB 2003}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8625}, number = {05-28}, abstract = {This paper reports on the fourth version of the Mixed Integer Programming Library. Since ({\sc miplib}) is to provide a concise set of challenging problems, it became necessary to purge instances that became too easy. We present an overview of the 27 new problems and statistical data for all 60 instances.}, language = {en} } @misc{AchterbergBrinkmannWedler, author = {Achterberg, Tobias and Brinkmann, Raik and Wedler, Markus}, title = {Property Checking with Constraint Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10376}, number = {07-37}, abstract = {We address the property checking problem for SoC design verification at the register transfer level (RTL) by integrating techniques from integer programming, constraint programming, and SAT solving. Specialized domain propagation and preprocessing algorithms for individual RTL operations extend a general constraint integer programming framework. Conflict clauses are learned by analyzing infeasible LPs and deductions, and by employing reverse propagation. Experimental results show that our approach outperforms SAT techniques for proving the validity of properties on circuits containing arithmetics.}, 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{AchterbergRaack, author = {Achterberg, Tobias and Raack, Christian}, title = {The MCF-Separator -- Detecting and Exploiting Multi-Commodity Flow Structures in MIPs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11592}, number = {09-38}, abstract = {Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.}, language = {en} } @article{AchterbergGroetschelKoch2006, author = {Achterberg, Tobias and Gr{\"o}tschel, Martin and Koch, Thorsten}, title = {Teaching MIP Modeling and Solving}, series = {OR/MS Today}, volume = {33}, journal = {OR/MS Today}, number = {6}, pages = {14 -- 15}, year = {2006}, language = {en} } @misc{AchterbergBertholdHendel, author = {Achterberg, Tobias and Berthold, Timo and Hendel, Gregor}, title = {Rounding and Propagation Heuristics for Mixed Integer Programming}, doi = {10.1007/978-3-642-29210-1_12}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13255}, number = {11-29}, 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} } @article{AchterbergRaack2010, author = {Achterberg, Tobias and Raack, Christian}, title = {The MCF-Separator - Detecting and Exploiting Multi-Commodity Flows in MIPs}, series = {Mathematical Programming C}, journal = {Mathematical Programming C}, number = {2}, pages = {125 -- 165}, year = {2010}, language = {en} } @inproceedings{HendelBertholdAchterberg, author = {Hendel, Gregor and Berthold, Timo and Achterberg, Tobias}, title = {Rounding and Propagation Heuristics for Mixed Integer Programming}, series = {Operations Research Proceedings 2011}, booktitle = {Operations Research Proceedings 2011}, pages = {71 -- 76}, 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} } @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} } @inproceedings{EisenblaetterKochMartinetal.2003, author = {Eisenbl{\"a}tter, Andreas and Koch, Thorsten and Martin, Alexander and Achterberg, Tobias and F{\"u}genschuh, Armin and Koster, Arie M.C.A. and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Modelling Feasible Network Configurations for UMTS}, series = {Telecommunications Network Design and Management}, booktitle = {Telecommunications Network Design and Management}, editor = {Anandalingam, G. and Raghavan, S.}, publisher = {Kluver}, year = {2003}, language = {en} } @article{AchterbergKochMartin2005, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching Rules Revisited}, series = {Operations Research Letters}, volume = {33}, journal = {Operations Research Letters}, number = {1}, publisher = {Elsevier / North-Holland}, doi = {10.1016/j.orl.2004.04.002}, pages = {42 -- 54}, year = {2005}, language = {en} } @article{AchterbergKochMartin2006, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {MIPLIB 2003}, series = {Operations Research Letters}, volume = {34}, journal = {Operations Research Letters}, number = {4}, publisher = {Elsevier / North-Holland}, doi = {10.1016/j.orl.2005.07.009}, pages = {361 -- 372}, year = {2006}, language = {en} } @inproceedings{AchterbergBertholdKochetal.2008, author = {Achterberg, Tobias and Berthold, Timo and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: A New Approach to Integrate CP and MIP}, 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}, doi = {10.1007/978-3-540-68155-7_4}, pages = {6 -- 20}, year = {2008}, language = {en} } @article{AchterbergBerthold2007, author = {Achterberg, Tobias and Berthold, Timo}, title = {Improving the Feasibility Pump}, series = {Discrete Optimization}, volume = {Special Issue 4}, journal = {Discrete Optimization}, number = {1}, pages = {77 -- 86}, year = {2007}, language = {en} } @inproceedings{AchterbergBerthold2009, author = {Achterberg, Tobias and Berthold, Timo}, title = {Hybrid Branching}, series = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 6th International Conference, CPAIOR 2009}, volume = {5547}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 6th International Conference, CPAIOR 2009}, editor = {van Hoeve, Willem and Hooker, John}, publisher = {Springer}, pages = {309 -- 311}, 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{GleixnerHendelGamrathetal., author = {Gleixner, Ambros and Hendel, Gregor and Gamrath, Gerald and Achterberg, Tobias and Bastubbe, Michael and Berthold, Timo and Christophel, Philipp M. and Jarck, Kati and Koch, Thorsten and Linderoth, Jeff and L{\"u}bbecke, Marco and Mittelmann, Hans and Ozyurt, Derya and Ralphs, Ted and Salvagnin, Domenico and Shinano, Yuji}, title = {MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library}, series = {Mathematical Programming Computation}, volume = {13}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-020-00194-3}, pages = {443 -- 490}, abstract = {We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data.}, language = {en} } @article{AchterbergBixbyGuetal., author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, series = {INFORMS Journal on Computing}, journal = {INFORMS Journal on Computing}, abstract = {Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.}, language = {en} } @misc{AchterbergBixbyGuetal., author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60370}, abstract = {Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.}, language = {en} } @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} } @phdthesis{Achterberg, author = {Achterberg, Tobias}, title = {Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-16117}, abstract = {This thesis introduces the novel paradigm of constraint integer programming (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.}, language = {en} } @misc{Achterberg, author = {Achterberg, Tobias}, title = {Conflict Analysis in Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8537}, number = {05-19}, abstract = {Conflict analysis for infeasible subproblems is one of the key ingredients in modern SAT solvers to cope with large real-world instances. In contrast, it is common practice for today's mixed integer programming solvers to just discard infeasible subproblems and the information they reveal. In this paper we try to remedy this situation by generalizing the SAT infeasibility analysis to mixed integer programming. We present heuristics for branch-and-cut solvers to generate valid inequalities from the current infeasible subproblem and the associated branching information. SAT techniques can then be used to strengthen the resulting cuts. We performed computational experiments which show the potential of our method: On feasible MIP instances, the number of required branching nodes was reduced by 50\\% in the geometric mean. However, the total solving time increased by 15\\%. on infeasible MIPs arising in the context of chip verification, the number of nodes was reduced by 90\\%, thereby reducing the solving time by 60\\%.}, 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} } @inproceedings{BestuzhevaGleixnerAchterberg, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Achterberg, Tobias}, title = {Efficient Separation of RLT Cuts for Implicit and Explicit Bilinear Products}, series = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, volume = {13904}, booktitle = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-32726-1_2}, pages = {14 -- 28}, abstract = {The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and improve the performance of RLT for bilinear product relations. First, a method for detecting bilinear product relations implicitly contained in mixed-integer linear programs is developed based on analyzing linear constraints with binary variables, thus enabling the application of bilinear RLT to a new class of problems. Our second contribution addresses the high computational cost of RLT cut separation, which presents one of the major difficulties in applying RLT efficiently in practice. We propose a new RLT cutting plane separation algorithm which identifies combinations of linear constraints and bound factors that are expected to yield an inequality that is violated by the current relaxation solution. A detailed computational study based on implementations in two solvers evaluates the performance impact of the proposed methods.}, language = {en} }