TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack – A solver for STP and variants with parallelization extensions JF - Mathematical Programming Computation N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/s12532-016-0114-x VL - 9 IS - 2 SP - 231 EP - 296 ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - 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. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 SN - 1438-0064 ER - TY - CHAP A1 - Gamrath, Gerald A1 - Schubert, Christoph T1 - Measuring the impact of branching rules for mixed-integer programming T2 - Operations Research Proceedings 2017 N2 - Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_23 SP - 165 EP - 170 PB - Springer International Publishing ER - TY - GEN A1 - Gleixner, Ambros A1 - Bastubbe, Michael A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Schubert, Christoph A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Walter, Matthias A1 - Wegscheider, Fabian A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 6.0 N2 - 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. T3 - ZIB-Report - 18-26 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69361 SN - 1438-0064 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming JF - Journal of Computational Mathematics N2 - The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP. Y1 - 2019 U6 - https://doi.org/10.4208/jcm.1905-m2019-0055 VL - 37 SP - 866 EP - 888 ER - TY - GEN A1 - Berthold, Timo A1 - Gamrath, Gerald A1 - Salvagnin, Domenico T1 - Exploiting Dual Degeneracy in Branching N2 - 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 common methods like most infeasible branching, strong branching, pseudocost branching, and their hybrids, but we also propose a novel branching rule called cloud diameter branching. We show that dual degeneracy, a requirement for alternative LP optima, is present for many instances from common MIP test sets. Computational experiments show significant improvements in the quality of branching decisions as well as reduced branching effort when using our modifications of existing branching rules. We discuss different ways to generate a cloud of solutions and present extensive computational results showing that through a careful implementation, cloud modifications can speed up full strong branching by more than 10 % on standard test sets. Additionally, by exploiting degeneracy, we are also able to improve the state-of-the-art hybrid branching rule and reduce the solving time on affected instances by almost 20 % on average. T3 - ZIB-Report - 19-17 KW - mixed integer programming KW - branching rule KW - search strategy KW - dual degeneracy Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73028 SN - 1438-0064 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-driven fix-and-propagate heuristics for mixed integer programming JF - Mathematical Programming Computation N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60 % of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-019-00159-1 VL - 11 IS - 4 SP - 675 EP - 702 PB - Springer CY - Berlin Heidelberg ER - TY - GEN A1 - Gamrath, Gerald A1 - Anderson, Daniel A1 - Bestuzheva, Ksenia A1 - Chen, Wei-Kun A1 - Eifler, Leon A1 - Gasse, Maxime A1 - Gemander, Patrick A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Halbig, Katrin A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Le Bodic, Pierre A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Miltenberger, Matthias A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Tawfik, Christine A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 7.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders’ decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders’ decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 20-10 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78023 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 -