TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - MIPLIB 2003 N2 - 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. T3 - ZIB-Report - 05-28 KW - Mathematical Programming KW - Mixed Integer Programming KW - IP KW - MIP KW - Optimization KW - Instances Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8625 ER - TY - GEN A1 - Achterberg, Tobias T1 - Conflict Analysis in Mixed Integer Programming N2 - 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\%. T3 - ZIB-Report - 05-19 KW - mixed integer programming KW - branch and cut KW - conflict analysis KW - SAT Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8537 ER - TY - GEN A1 - Achterberg, Tobias A1 - Grötschel, Martin A1 - Koch, Thorsten T1 - Software for Teaching Modeling of Integer Programming Problems N2 - 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. T3 - ZIB-Report - 06-23 KW - Integer Programming KW - Modelling KW - MIP-Solver KW - Algebraic Modelling Languages KW - Teaching Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9176 ER - TY - JOUR A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - MIPLIB 2003 JF - Operations Research Letters Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/862/ U6 - https://doi.org/10.1016/j.orl.2005.07.009 VL - 34 IS - 4 SP - 361 EP - 372 PB - Elsevier / North-Holland ER - TY - CHAP A1 - Achterberg, Tobias A1 - Heinz, Stefan A1 - Koch, Thorsten ED - Perron, Laurent ED - Trick, Michael T1 - Counting Solutions of Integer Programs Using Unrestricted Subtree Detection T2 - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 5th International Conference, CPAIOR 2008 Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2008/1092/ VL - 5015 SP - 278 EP - 282 PB - Springer ER - TY - CHAP A1 - Eisenblätter, Andreas A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Achterberg, Tobias A1 - Fügenschuh, Armin A1 - Koster, Arie M.C.A. A1 - Wegel, Oliver A1 - Wessäly, Roland ED - Anandalingam, G. ED - Raghavan, S. T1 - Modelling Feasible Network Configurations for UMTS T2 - Telecommunications Network Design and Management Y1 - 2003 UR - http://opus.kobv.de/zib/volltexte/2002/684/ PB - Kluver ER - TY - JOUR A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Branching Rules Revisited JF - Operations Research Letters Y1 - 2005 UR - http://opus.kobv.de/zib/volltexte/2004/789/ U6 - https://doi.org/10.1016/j.orl.2004.04.002 VL - 33 IS - 1 SP - 42 EP - 54 PB - Elsevier / North-Holland ER - TY - JOUR A1 - Achterberg, Tobias A1 - Bixby, Robert E. A1 - Gu, Zonghao A1 - Rothberg, Edward A1 - Weninger, Dieter T1 - Presolve Reductions in Mixed Integer Programming JF - INFORMS Journal on Computing N2 - 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. Y1 - 2019 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores N2 - 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. T3 - ZIB-Report - 15-53 KW - Mixed Integer Programming KW - Parallel processing KW - Node merging KW - Racing ParaSCIP KW - Ubiquity Generator Framework KW - MIPLIB Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56404 SN - 1438-0064 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Gamrath, Gerald A1 - Achterberg, Tobias A1 - Bastubbe, Michael A1 - Berthold, Timo A1 - Christophel, Philipp M. A1 - Jarck, Kati A1 - Koch, Thorsten A1 - Linderoth, Jeff A1 - Lübbecke, Marco A1 - Mittelmann, Hans A1 - Ozyurt, Derya A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Shinano, Yuji T1 - MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library JF - Mathematical Programming Computation N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1007/s12532-020-00194-3 VL - 13 IS - 3 SP - 443 EP - 490 ER -