TY - JOUR A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - MILP. Try. Repeat. JF - Proceedings of the 13th International Conference on the Practice and Theory of Automated Timetabling - PATAT 2021 Y1 - 2021 VL - 2 ER - TY - GEN A1 - Koch, Thorsten A1 - Berthold, Timo A1 - Pedersen, Jaap A1 - Vanaret, Charlie T1 - Progress in Mathematical Programming Solvers from 2001 to 2020 N2 - This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time. T3 - ZIB-Report - 21-20 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82779 SN - 1438-0064 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 - TY - JOUR A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - 制約整数計画ソルバ SCIP の並列化 JF - 統計数理 N2 - 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. N2 - The paradigm of constraint integer programming (CIP) combines modeling and solving techniques from the fields of constraint programming (CP), mixed-integer programming (MIP) and satisfability problem (SAT). This paradigm allows us to address a wide range of optimization problems. SCIP is an implementation of the idea of CIP and is now being continuously extended by a group of researchers centered at Zuse Institute Berlin (ZIB). This paper introduces two parallel extensions of SCIP. One is ParaSCIP, which is intended to run on a large scale distributed memory computing environment, and the other is FiberSCIP, intended to run on a shared memory computing environment. ParaSCIP has been run successfully on the HLRN II supercomputer utilizing up to 7,168 cores to solve a single difficult MIP. It has also been tested on an ISM supercomputer (Fujitsu PRIMERGY RX200S5 using up to 512 cores). The previously unsolved instance dg012142 from MIPLIB2010 was solved by using the ISM supercomputer. Y1 - 2013 UR - https://www.ism.ac.jp/editsec/toukei/pdf/61-1-047.pdf VL - 61 IS - 1 SP - 47 EP - 78 ER - TY - CHAP A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-33271-5_4 VL - 13884 SP - 52 EP - 68 PB - Springer ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. T3 - ZIB-Report - 22-28 KW - cut selection KW - anlalytic center KW - mixed-integer programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89065 SN - 1438-0064 ER - TY - JOUR A1 - Koch, Thorsten A1 - Berthold, Timo A1 - Pedersen, Jaap A1 - Vanaret, Charlie T1 - Progress in mathematical programming solvers from 2001 to 2020 JF - EURO Journal on Computational Optimization N2 - This study investigates the progress made in lp and milp solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving lp/milp, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for lp and around 50 for milp, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time. Y1 - 2022 U6 - https://doi.org/10.1016/j.ejco.2022.100031 VL - 10 SP - 100031 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores N2 - 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. T3 - ZIB-Report - 20-16 KW - Mixed Integer Programming, Parallel processing, Node merging, Racing, ParaSCIP, Ubiquity Generator Framework, MIPLIB Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78393 SN - 1438-0064 ER -