TY - GEN A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 N2 - 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. T3 - ZIB-Report - 10-31 KW - Mixed Integer Programming KW - Problem Instances KW - IP KW - MIP KW - MIPLIB Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12953 ER - TY - GEN A1 - Koch, Thorsten A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - What could a million CPUs do to solve Integer Programs? N2 - Given the steady increase in cores per CPU, it is only a matter of time until supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments. T3 - ZIB-Report - 11-40 Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14222 SN - 1438-0064 ER - TY - CHAP A1 - Miltenberger, Matthias A1 - Ralphs, Ted A1 - Steffy, Daniel T1 - Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization T2 - Operations Research Proceedings 2017 N2 - We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6 SP - 151 EP - 157 PB - Springer International Publishing ER - TY - GEN A1 - Miltenberger, Matthias A1 - Ralphs, Ted A1 - Steffy, Daniel T1 - Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization T2 - Operations Research Proceedings 2017 N2 - We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct. T3 - ZIB-Report - 17-43 KW - Mixed Integer Programming KW - Linear Programming KW - Algorithm Analysis Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64645 SN - 1438-0064 ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten T1 - Parallel Solvers for Mixed Integer Linear Programming N2 - In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures. T3 - ZIB-Report - 16-74 KW - parallel computing KW - integer programming KW - branch-and-bound KW - supercomputing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62239 SN - 1438-0064 ER - TY - JOUR A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 JF - Mathematical Programming Computation Y1 - 2011 UR - http://mpc.zib.de/index.php/MPC/article/view/56 U6 - https://doi.org/10.1007/s12532-011-0025-9 VL - 3 IS - 2 SP - 103 EP - 163 ER - TY - JOUR A1 - Koch, Thorsten A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - Could we use a million cores to solve an integer program? JF - Mathematical Methods of Operations Research Y1 - 2012 U6 - https://doi.org/10.1007/s00186-012-0390-9 VL - 76 IS - 1 SP - 67 EP - 93 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 - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten ED - Hamadi, Youssef T1 - Parallel Solvers for Mixed Integer Linear Optimization T2 - Handbook of Parallel Constraint Reasoning Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-63516-3_8 SP - 283 EP - 336 PB - Springer Nature ER - TY - GEN A1 - Maher, Stephen J. A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - Assessing the Effectiveness of (Parallel) Branch-and-bound Algorithms N2 - Empirical studies are fundamental in assessing the effectiveness of implementations of branch-and-bound algorithms. The complexity of such implementations makes empirical study difficult for a wide variety of reasons. Various attempts have been made to develop and codify a set of standard techniques for the assessment of optimization algorithms and their software implementations; however, most previous work has been focused on classical sequential algorithms. Since parallel computation has become increasingly mainstream, it is necessary to re-examine and modernize these practices. In this paper, we propose a framework for assessment based on the notion that resource consumption is at the heart of what we generally refer to as the “effectiveness” of an implementation. The proposed framework carefully distinguishes between an implementation’s baseline efficiency, the efficacy with which it utilizes a fixed allocation of resources, and its scalability, a measure of how the efficiency changes as resources (typically additional computing cores) are added or removed. Efficiency is typically applied to sequential implementations, whereas scalability is applied to parallel implementations. Efficiency and scalability are both important contributors in determining the overall effectiveness of a given parallel implementation, but the goal of improved efficiency is often at odds with the goal of improved scalability. Within the proposed framework, we review the challenges to effective evaluation and discuss the strengths and weaknesses of existing methods of assessment. T3 - ZIB-Report - 19-03 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74702 ER - TY - JOUR A1 - Bolusani, Suresh A1 - Ralphs, Ted K. T1 - a framework for generalized Benders' decomposition and its applications to multilevel optimization JF - Mathematical Programming Y1 - 2022 ER -