TY - CHAP A1 - Dalitz, Wolfgang A1 - Chrapary, Hagen T1 - Software Products, Software Versions, Archiving of Software, and swMATH T2 - Mathematical Software – ICMS 2018 N2 - Management of software information is difficult for various reasons. First, software typically cannot be reduced to a single object: information about software is an aggregate of software code, APIs, documentation, installations guides, tutorials, user interfaces, test data, dependencies on hardware and other software, etc. Moreover, secondary information about software, especially use cases and experience with employing the software, is important to communicate. Second, typically named software, which we term here a `software product', is taken to stand for all versions of the software which can have different features and properties and may produced different results from the same input data. Software production is a dynamic process and software development is, increasingly, widely distributed. Therefore GitHub, GitLab, Bitbucket and other platforms for sharing are used. Information about software is alos provided in different locations, on websites, repositories, portals, etc. Each resource provides information about software from a particular point of view, but the information is often not linked together. Therefore swMATH has developed a conception which covers portals and a search engines for mathematical software, persistent and citable landing pages for specific software, and a method for software archiving. Based on the publication-based approach, swMATH collects and analyses semi-automatically the existing information about mathematical software found on the Web and makes it available in a user-oriented way. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-96418-8_15 SP - 123 EP - 127 ER - TY - CHAP A1 - Dalitz, Wolfgang A1 - Chrapary, Hagen A1 - Sperber, Wolfram T1 - Software Knowledge Management and swMATH T2 - Fachgruppe Didaktik der Mathematik der Universität Paderborn N2 - Mathematische Software ist heute ein weitverbreitetes Werkzeug in der Forschung, aber auch in der mathematischen Bildung. Die Anzahl mathematischer Softwareprodukte wächst, nicht zuletzt durch die Anforderungen der Anwender, stark. Anders als für mathematische Publikationen sind für das Management mathematischer Software viele Fragen offen und werden noch diskutiert, etwa die Standardisierung von Software Zitationen. Der Aufbau einer effizienten Infrastruktur für Software ist eine notwendige Voraussetzung für die Überprüfung von Forschungsergebnissen, die mittels Software erzielt worden sind und wichtig für die Entscheidung, ob eine bestimmte Software zur Lösung eines Problems verwendet werden soll. Das swMATH [1] Portal gibt einen weitgehend vollständigen Überblick über die existierende mathematische Software. Es ist ein Dienst entstanden, der automatisiert die im Web vorhandenen Informationen zu einer Software identifiziert, auswertet und verfügbar macht. Der Dienst soll insbesondere durch die Verknüpfung mit anderen Quellen, etwa dem Internet Archive, persistente Informationen über ein Software Produkt und dessen Versionen liefern. Y1 - 2018 U6 - https://doi.org/10.17877/DE290R-19281 SP - 401 EP - 404 ER - TY - JOUR A1 - Chrapary, Hagen A1 - Dalitz, Wolfgang A1 - Neun, Winfried A1 - Sperber, Wolfram T1 - Design, Concepts, and State of the Art of the swMATH Service JF - Mathematics in Computer Science N2 - In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context. Y1 - 2017 U6 - https://doi.org/10.1007/s11786-017-0305-5 VL - 11 IS - 3-4 SP - 469 EP - 481 ER - TY - JOUR A1 - Chrapary, Hagen A1 - Dalitz, Wolfgang A1 - Sperber, Wolfram T1 - swMATH - Challenges, Next Steps, and Outlook JF - CICM-WS-WIP 2016, Workshop and Work in Progress Papers at CICM 2016 N2 - swMATH is currently one of the most comprehensive specialized information services and search engines for Mathematical SoftWare (MSW). It was the intention of the project to support the user community by providing infor- mation about MSW and searching relevant MSW. Currently swMATH lists infor- mation of more than 13,000 items and 120,000 publications which refer to MSW. Maintaining and updating of the service is mainly done automatically, the num- ber of requests is permanently increasing. This sounds like a perfect solution. But swMATH is only a first step to a powerful information system on mathematical research data. This talk addresses some open problems for the further develop- ment of the swMATH service. It is shown that some problems for swMATH lead to central questions for the information management of mathematical research data, especially for MSW. This contains an extended content analysis of MSW, versioning and citation standard of MSW, a typing of the swMATH resources and the presentation of context information and high-quality control within the swMATH service. Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0074-1785-8 VL - Vol-1785 SP - 107 EP - 116 ER - TY - GEN ED - Dalitz, Wolfgang T1 - alsoMATH - A Database for Mathematical Algorithms and Software N2 - Mathematical publications are an important resource for the devel- opment of machine-based methods for mathematical knowledge man- agement. This article describes the publication-based approach to improve the information and the access to two important classes of mathematical research, mathematical software and mathematical algo- rithms. The publication-based approach is based on analyzing links and the structure of mathematical publications. It has been used to build the swMATH service which provides comprehensive information about mathematical software and algorithms. Y1 - 2019 U6 - https://doi.org/http://cl-informatik.uibk.ac.at/cek/cicm-wip-tentative/ VL - 2019 PB - Cezary Kaliszyk ER - TY - JOUR A1 - Eifler, Leon A1 - Gleixner, Ambros T1 - A Computational Status Update for Exact Rational Mixed Integer Programming JF - Integer Programming and Combinatorial Optimization: 22th International Conference, IPCO 2021 N2 - The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours. Y1 - 2021 U6 - https://doi.org/10.1007/978-3-030-73879-2_12 ER - TY - GEN A1 - Eifler, Leon A1 - Gleixner, Ambros T1 - A Computational Status Update for Exact Rational Mixed Integer Programming N2 - The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours. T3 - ZIB-Report - 21-04 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81298 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Witzig, Jakob T1 - Conflict Analysis for MINLP N2 - The generalization of MIP techniques to deal with nonlinear, potentially non-convex, constraints have been a fruitful direction of research for computational MINLP in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers towards the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared towards two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. T3 - ZIB-Report - 20-20 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78964 SN - 1438-0064 ER - TY - GEN A1 - Witzig, Jakob A1 - Berthold, Timo T1 - Conflict-Free Learning for Mixed Integer Programming N2 - Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set. T3 - ZIB-Report - 19-59 KW - mixed integer programming KW - conflict analysis KW - dual proof analysis KW - no-good learning KW - solution learning Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75338 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji T1 - UG - Ubiquity Generator Framework v1.0.0beta N2 - UG is a generic framework to parallelize branch-and-bound based solvers (e.g., MIP, MINLP, ExactIP) in a distributed or shared memory computing environment. It exploits the powerful performance of state-of-the-art "base solvers", such as SCIP, CPLEX, etc. without the need for base solver parallelization. UG framework, ParaSCIP(ug[SCIP,MPI]) and FiberSCIP (ug[SCIP,Pthreads]) are available as a beta version. v1.0.0: new documentation and cmake, generalization of ug framework, implementation of selfsplitrampup for fiber- and parascip, better memory and time limit handling. KW - parallelization framework KW - branch-and-bound parallelization KW - integer optimization Y1 - 2021 U6 - https://doi.org/10.12752/8521 ER - TY - CHAP A1 - Witzig, Jakob A1 - Berthold, Timo T1 - Conflict-Free Learning for Mixed Integer Programming T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020 N2 - Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set. Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-58942-4_34 IS - 12296 SP - 521 EP - 530 PB - Springer, Cham. 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 - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - On the exact solution of prize-collecting Steiner tree problems T3 - ZIB-Report - 20-11 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78174 SN - 1438-0064 ER - TY - GEN A1 - Hendel, Gregor A1 - Anderson, Daniel A1 - Le Bodic, Pierre A1 - Pfetsch, Marc T1 - Estimating the Size of Branch-And-Bound Trees N2 - This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP. T3 - ZIB-Report - 20-02 KW - mixed integer programming KW - machine learning KW - branch and bound KW - forecasting Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78144 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 - THES A1 - Eifler, Leon T1 - Algorithms and Certificates for Exact Mixed Integer Programming N2 - Mixed Integer Programming (MIP) is a powerful tool for solving optimization problems with discrete decisions. Although the problem class of mixed integer programs is NP-hard, MIP solvers have made significant progress in solving large-scale instances through decades of dedicated research and complex algorithmic improvements. In practice, virtually all algorithms to solve MIP problems are based on floating-point arithmetic due to its rapid computation times and robust numerical capabilities. Using error tolerances, MIP solvers avoid numerical issues and maintain a solution quality that is sufficient for most practical applications. There are, however, applications where exact solutions are required, such as when MIPs are employed as a tool in computer-assisted proofs. In such cases, exact, certified MIP solvers are a necessity. This thesis delves into the study and development of exact, certified mixed integer programming methods. The primary contribution of this thesis is an algorithmic framework for exact rational mixed integer programming. This framework incorporates safe dual bounding techniques, exact rational presolving, an exact repair step for heuristic solutions, and a novel exact Gomory mixed integer cut generator. We validate the effectiveness of our framework through experiments on a diverse set of benchmark instances. We take great care to measure the similarities and differences with corresponding techniques in the floating-point setting. Furthermore, we incorporate certification techniques into the framework to provide rigorous guarantees on the correctness of the computed solutions. We also provide a comprehensive algorithmic and computational study of the solver-independent verification of these certficates. We also present a framework for applying exact MIP as a tool for computer-assisted mathematics, using Chvátals conjecture as an illustrative example. Another significant contribution of this thesis is a new algorithm for solving linear programs exactly. This algorithm combines two state-of-the-art techniques for exact linear programming: precision boosting and LP iterative refinement. Combining these techniques can significantly improve the performance of exact linear programming solvers, and we prove that the algorithm is theoretically guaranteed to terminate with an exact solution. Y1 - 2024 U6 - https://doi.org/https://doi.org/10.14279/depositonce-23941 ER - TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - An Algorithm-Independent Measure of Progress for Linear Constraint Propagation T2 - 27th International Conference on Principles and Practice of Constraint Programming (CP 2021) N2 - Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure -- independently of the algorithmic design -- the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported. Y1 - 2021 U6 - https://doi.org/10.4230/LIPIcs.CP.2021.52 VL - 210 SP - 52:1 EP - 52:17 ER - TY - JOUR A1 - Mathieu, Besançon A1 - Carderera, Alejandro A1 - Pokutta, Sebastian T1 - FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients JF - INFORMS Journal on Computing N2 - We present FrankWolfe.jl, an open-source implementation of several popular Frank–Wolfe and conditional gradients variants for first-order constrained optimization. The package is designed with flexibility and high performance in mind, allowing for easy extension and relying on few assumptions regarding the user-provided functions. It supports Julia’s unique multiple dispatch feature, and it interfaces smoothly with generic linear optimization formulations using MathOptInterface.jl. Y1 - 2022 U6 - https://doi.org/10.1287/ijoc.2022.1191 VL - 34 IS - 5 SP - 2383 EP - 2865 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Implications, Conflicts, and Reductions for Steiner Trees JF - Mathematical Programming Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01757-5 VL - 197 SP - 903 EP - 966 PB - Springer ER - TY - GEN A1 - Eifler, Leon A1 - Gleixner, Ambros A1 - Pulaj, Jonad T1 - Chvátal’s Conjecture Holds for Ground Sets of Seven Elements N2 - We establish a general computational framework for Chvátal’s conjecture based on exact rational integer programming. As a result we prove Chvátal’s conjecture holds for all downsets whose union of sets contains seven elements or less. The computational proof relies on an exact branch-and-bound certificate that allows for elementary verification and is independent of the integer programming solver used. T3 - ZIB-Report - 18-49 KW - extremal combinatorics KW - exact rational integer programming Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70240 SN - 1438-0064 ER -