@inproceedings{DalitzChrapary2018, author = {Dalitz, Wolfgang and Chrapary, Hagen}, title = {Software Products, Software Versions, Archiving of Software, and swMATH}, booktitle = {Mathematical Software - ICMS 2018}, doi = {10.1007/978-3-319-96418-8_15}, pages = {123 -- 127}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{DalitzChraparySperber2018, author = {Dalitz, Wolfgang and Chrapary, Hagen and Sperber, Wolfram}, title = {Software Knowledge Management and swMATH}, booktitle = {Fachgruppe Didaktik der Mathematik der Universit{\"a}t Paderborn}, doi = {10.17877/DE290R-19281}, pages = {401 -- 404}, year = {2018}, abstract = {Mathematische Software ist heute ein weitverbreitetes Werkzeug in der Forschung, aber auch in der mathematischen Bildung. Die Anzahl mathematischer Softwareprodukte w{\"a}chst, nicht zuletzt durch die Anforderungen der Anwender, stark. Anders als f{\"u}r mathematische Publikationen sind f{\"u}r das Management mathematischer Software viele Fragen offen und werden noch diskutiert, etwa die Standardisierung von Software Zitationen. Der Aufbau einer effizienten Infrastruktur f{\"u}r Software ist eine notwendige Voraussetzung f{\"u}r die {\"U}berpr{\"u}fung von Forschungsergebnissen, die mittels Software erzielt worden sind und wichtig f{\"u}r die Entscheidung, ob eine bestimmte Software zur L{\"o}sung eines Problems verwendet werden soll. Das swMATH [1] Portal gibt einen weitgehend vollst{\"a}ndigen {\"U}berblick {\"u}ber die existierende mathematische Software. Es ist ein Dienst entstanden, der automatisiert die im Web vorhandenen Informationen zu einer Software identifiziert, auswertet und verf{\"u}gbar macht. Der Dienst soll insbesondere durch die Verkn{\"u}pfung mit anderen Quellen, etwa dem Internet Archive, persistente Informationen {\"u}ber ein Software Produkt und dessen Versionen liefern.}, language = {en} } @article{ChraparyDalitzNeunetal.2017, author = {Chrapary, Hagen and Dalitz, Wolfgang and Neun, Winfried and Sperber, Wolfram}, title = {Design, Concepts, and State of the Art of the swMATH Service}, volume = {11}, journal = {Mathematics in Computer Science}, number = {3-4}, doi = {10.1007/s11786-017-0305-5}, pages = {469 -- 481}, year = {2017}, abstract = {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.}, language = {en} } @article{ChraparyDalitzSperber2017, author = {Chrapary, Hagen and Dalitz, Wolfgang and Sperber, Wolfram}, title = {swMATH - Challenges, Next Steps, and Outlook}, volume = {Vol-1785}, journal = {CICM-WS-WIP 2016, Workshop and Work in Progress Papers at CICM 2016}, url = {http://nbn-resolving.de/urn:nbn:de:0074-1785-8}, pages = {107 -- 116}, year = {2017}, abstract = {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.}, language = {en} } @misc{OPUS4-7579, title = {alsoMATH - A Database for Mathematical Algorithms and Software}, volume = {2019}, editor = {Dalitz, Wolfgang}, publisher = {Cezary Kaliszyk}, doi = {http://cl-informatik.uibk.ac.at/cek/cicm-wip-tentative/}, year = {2019}, abstract = {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.}, language = {en} } @article{EiflerGleixner2021, author = {Eifler, Leon and Gleixner, Ambros}, title = {A Computational Status Update for Exact Rational Mixed Integer Programming}, journal = {Integer Programming and Combinatorial Optimization: 22th International Conference, IPCO 2021}, doi = {10.1007/978-3-030-73879-2_12}, year = {2021}, abstract = {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.}, language = {en} } @misc{EiflerGleixner2021, author = {Eifler, Leon and Gleixner, Ambros}, title = {A Computational Status Update for Exact Rational Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81298}, year = {2021}, abstract = {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.}, language = {en} } @misc{BertholdWitzig2020, author = {Berthold, Timo and Witzig, Jakob}, title = {Conflict Analysis for MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78964}, year = {2020}, abstract = {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.}, language = {en} } @misc{WitzigBerthold2019, author = {Witzig, Jakob and Berthold, Timo}, title = {Conflict-Free Learning for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/978-3-030-58942-4_34}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75338}, year = {2019}, abstract = {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.}, language = {en} } @misc{Shinano2021, author = {Shinano, Yuji}, title = {UG - Ubiquity Generator Framework v1.0.0beta}, doi = {10.12752/8521}, year = {2021}, abstract = {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.}, language = {en} } @inproceedings{WitzigBerthold2020, author = {Witzig, Jakob and Berthold, Timo}, title = {Conflict-Free Learning for Mixed Integer Programming}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020}, number = {12296}, publisher = {Springer, Cham.}, doi = {10.1007/978-3-030-58942-4_34}, pages = {521 -- 530}, year = {2020}, abstract = {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.}, language = {en} } @misc{GamrathAndersonBestuzhevaetal.2020, author = {Gamrath, Gerald and Anderson, Daniel and Bestuzheva, Ksenia and Chen, Wei-Kun and Eifler, Leon and Gasse, Maxime and Gemander, Patrick and Gleixner, Ambros and Gottwald, Leona and Halbig, Katrin and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Le Bodic, Pierre and Maher, Stephen J. and Matter, Frederic and Miltenberger, Matthias and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Tawfik, Christine and Vigerske, Stefan and Wegscheider, Fabian and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 7.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78023}, year = {2020}, abstract = {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.}, language = {en} } @misc{RehfeldtKoch2020, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {On the exact solution of prize-collecting Steiner tree problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78174}, year = {2020}, language = {en} } @misc{HendelAndersonLeBodicetal.2020, author = {Hendel, Gregor and Anderson, Daniel and Le Bodic, Pierre and Pfetsch, Marc}, title = {Estimating the Size of Branch-And-Bound Trees}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78144}, year = {2020}, abstract = {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.}, language = {en} } @article{GamrathGleixnerKochetal.2019, author = {Gamrath, Gerald and Gleixner, Ambros and Koch, Thorsten and Miltenberger, Matthias and Kniasew, Dimitri and Schl{\"o}gel, Dominik and Martin, Alexander and Weninger, Dieter}, title = {Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming}, volume = {37}, journal = {Journal of Computational Mathematics}, doi = {10.4208/jcm.1905-m2019-0055}, pages = {866 -- 888}, year = {2019}, abstract = {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.}, language = {en} } @phdthesis{Eifler2024, author = {Eifler, Leon}, title = {Algorithms and Certificates for Exact Mixed Integer Programming}, doi = {https://doi.org/10.14279/depositonce-23941}, year = {2024}, abstract = {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 Chv{\´a}tals 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.}, language = {en} } @inproceedings{SofranacGleixnerPokutta2021, author = {Sofranac, Boro and Gleixner, Ambros and Pokutta, Sebastian}, title = {An Algorithm-Independent Measure of Progress for Linear Constraint Propagation}, volume = {210}, booktitle = {27th International Conference on Principles and Practice of Constraint Programming (CP 2021)}, doi = {10.4230/LIPIcs.CP.2021.52}, pages = {52:1 -- 52:17}, year = {2021}, abstract = {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.}, language = {en} } @article{MathieuCardereraPokutta2022, author = {Mathieu, Besan{\c{c}}on and Carderera, Alejandro and Pokutta, Sebastian}, title = {FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients}, volume = {34}, journal = {INFORMS Journal on Computing}, number = {5}, doi = {10.1287/ijoc.2022.1191}, pages = {2383 -- 2865}, year = {2022}, abstract = {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.}, language = {en} } @article{RehfeldtKoch2023, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Implications, Conflicts, and Reductions for Steiner Trees}, volume = {197}, journal = {Mathematical Programming}, publisher = {Springer}, doi = {10.1007/s10107-021-01757-5}, pages = {903 -- 966}, year = {2023}, language = {en} } @misc{EiflerGleixnerPulaj2018, author = {Eifler, Leon and Gleixner, Ambros and Pulaj, Jonad}, title = {Chv{\´a}tal's Conjecture Holds for Ground Sets of Seven Elements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70240}, year = {2018}, abstract = {We establish a general computational framework for Chv{\´a}tal's conjecture based on exact rational integer programming. As a result we prove Chv{\´a}tal'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.}, language = {en} } @misc{HosodaMaherShinanoetal.2021, author = {Hosoda, Junko and Maher, Stephen J. and Shinano, Yuji and Villumsen, Jonas Christoffer}, title = {Location, transshipment and routing: An adaptive transportation network integrating long-haul and local vehicle routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-83438}, year = {2021}, abstract = {The routing of commodities is a tactical problem in supply chain management that aims to synchronise transportation services connecting a network of warehouses and consolidation locations. This paper considers the routing of commodities in a transportation network that is flexible in response to demand through changes to regional warehouse clustering and the designation of consolidation locations. Traditionally, warehouse clustering and consolidation locations are determined as part of strategic planning that is performed months to years in advance of operations---limiting the flexibility in transportation networks to respond to changes in demand. A mathematical programming-based algorithmic framework is proposed to integrate the strategic decisions of location planning with tactical decisions of vehicle routing and synchronisation. A multi-armed bandit problem is developed to explore warehouse clustering decisions and exploit those that lead to small transportation costs. An extensive computational study will show that the proposed algorithmic framework effectively integrates strategic and tactical planning decisions to reduce the overall transportation costs.}, language = {en} } @article{RehfeldtHobbieSchoenheitetal.2022, author = {Rehfeldt, Daniel and Hobbie, Hannes and Sch{\"o}nheit, David and Koch, Thorsten and M{\"o}st, Dominik and Gleixner, Ambros}, title = {A massively parallel interior-point solver for LPs with generalized arrowhead structure, and applications to energy system models}, volume = {296}, journal = {European Journal of Operational Research}, number = {1}, doi = {10.1016/j.ejor.2021.06.063}, pages = {60 -- 71}, year = {2022}, abstract = {Linear energy system models are a crucial component of energy system design and operations, as well as energy policy consulting. If detailed enough, such models lead to large-scale linear programs, which can be intractable even for the best state-of-the-art solvers. This article introduces an interior-point solver that exploits common structures of energy system models to efficiently run in parallel on distributed-memory systems. The solver is designed for linear programs with doubly-bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. In order to handle the large number of linking constraints and variables commonly observed in energy system models, a distributed Schur complement preconditioner is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the solver PIPS-IPM. We evaluate the computational performance on energy system models with up to four billion nonzero entries in the constraint matrix—and up to one billion columns and one billion rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market-clearing. It has been widely applied in the literature on energy system analyses in recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models.}, language = {en} } @inproceedings{RehfeldtKoch2021, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Implications, conflicts, and reductions for Steiner trees}, booktitle = {Integer Programming and Combinatorial Optimization: 22th International Conference, IPCO 2021}, doi = {10.1007/978-3-030-73879-2_33}, pages = {473 -- 487}, year = {2021}, language = {en} } @article{RehfeldtKoch2021, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {On the exact solution of prize-collecting Steiner tree problems}, journal = {INFORMS Journal on Computing}, doi = {10.1287/ijoc.2021.1087}, year = {2021}, language = {en} } @misc{MaherRalphsShinano2019, author = {Maher, Stephen J. and Ralphs, Ted and Shinano, Yuji}, title = {Assessing the Effectiveness of (Parallel) Branch-and-bound Algorithms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74702}, year = {2019}, abstract = {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.}, language = {en} } @article{GleixnerSteffy2020, author = {Gleixner, Ambros and Steffy, Daniel}, title = {Linear Programming using Limited-Precision Oracles}, volume = {183}, journal = {Mathematical Programming}, number = {1-2}, doi = {10.1007/s10107-019-01444-6}, pages = {525 -- 554}, year = {2020}, abstract = {Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.}, language = {en} } @article{Pulaj2019, author = {Pulaj, Jonad}, title = {Cutting planes for families implying Frankl's conjecture}, journal = {Mathematics of Computation}, doi = {10.1090/mcom/3461}, year = {2019}, abstract = {We find previously unknown families of sets which ensure Frankl's conjecture holds for all families that contain them using an algorithmic framework. The conjecture states that for any nonempty finite union-closed (UC) family there exists an element of the ground set in at least half the sets of the considered UC family. Poonen's Theorem characterizes the existence of weights which determine whether a given UC family implies the conjecture for all UC families which contain it. We design a cutting-plane method that computes the explicit weights which satisfy the existence conditions of Poonen's Theorem. This method enables us to answer several open questions regarding structural properties of UC families, including the construction of a counterexample to a conjecture of Morris from 2006.}, language = {en} } @misc{Serrano2019, author = {Serrano, Felipe}, title = {Visible points, the separation problem, and applications to MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74016}, year = {2019}, abstract = {In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require that every valid cut separating the infeasible point from the restricted feasible region is still valid for the original feasible region. We translate this requirement in terms of the separation problem and the reverse polar. In particular, if the reverse polar of the restricted feasible region is the same as the reverse polar of the feasible region, then any cut valid for the restricted feasible region that \emph{separates} the infeasible point, is valid for the feasible region. We show that the reverse polar of the \emph{visible points} of the feasible region from the infeasible point coincides with the reverse polar of the feasible region. In the special where the feasible region is described by a single non-convex constraint intersected with a convex set we provide a characterization of the visible points. Furthermore, when the non-convex constraint is quadratic the characterization is particularly simple. We also provide an extended formulation for a relaxation of the visible points when the non-convex constraint is a general polynomial. Finally, we give some conditions under which for a given set there is an inclusion-wise smallest set, in some predefined family of sets, whose reverse polars coincide.}, language = {en} } @inproceedings{GleixnerKempkeKochetal.2020, author = {Gleixner, Ambros and Kempke, Nils-Christian and Koch, Thorsten and Rehfeldt, Daniel and Uslu, Svenja}, title = {First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method}, booktitle = {Operations Research Proceedings 2019}, edition = {1}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-030-48439-2_13}, pages = {105 -- 111}, year = {2020}, abstract = {In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.}, language = {en} } @inproceedings{BertholdGrimmReutheretal.2019, author = {Berthold, Timo and Grimm, Boris and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {Strategic Planning of Rolling Stock Rotations for Public Tenders}, volume = {Link{\"o}ping Electronic Conference Proceedings}, booktitle = {Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019}, number = {069}, publisher = {Link{\"o}ping University Electronic Press, Link{\"o}pings universitet}, isbn = {978-91-7929-992-7}, issn = {1650-3686}, pages = {148 -- 159}, year = {2019}, abstract = {Since railway companies have to apply for long-term public contracts to operate railway lines in public tenders, the question how they can estimate the operating cost for long-term periods adequately arises naturally. We consider a rolling stock rotation problem for a time period of ten years, which is based on a real world instance provided by an industry partner. We use a two stage approach for the cost estimation of the required rolling stock. In the first stage, we determine a weekly rotation plan. In the second stage, we roll out this weekly rotation plan for a longer time period and incorporate scheduled maintenance treatments. We present a heuristic approach and a mixed integer programming model to implement the process of the second stage. Finally, we discuss computational results for a real world tendering scenario.}, language = {en} } @article{MuellerSerranoGleixner2020, author = {M{\"u}ller, Benjamin and Serrano, Felipe and Gleixner, Ambros}, title = {Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms}, volume = {30}, journal = {SIAM Journal on Optimization}, number = {2}, doi = {10.1137/19M1249825}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72767}, pages = {1339 -- 1365}, year = {2020}, abstract = {One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.}, language = {en} } @misc{MuellerSerranoGleixner2019, author = {M{\"u}ller, Benjamin and Serrano, Felipe and Gleixner, Ambros}, title = {Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72759}, year = {2019}, abstract = {One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.}, language = {en} } @misc{BertholdGamrathSalvagnin2019, author = {Berthold, Timo and Gamrath, Gerald and Salvagnin, Domenico}, title = {Exploiting Dual Degeneracy in Branching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73028}, year = {2019}, abstract = {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.}, language = {en} } @misc{ShinanoRehfeldtGalley2019, author = {Shinano, Yuji and Rehfeldt, Daniel and Galley, Tristan}, title = {An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72804}, year = {2019}, abstract = {Branch-and-bound (B\&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B\&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature.}, language = {en} } @misc{SerranoSchwarzGleixner2019, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73253}, year = {2019}, abstract = {Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (1967) and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by general, not necessarily convex, differentiable functions that satisfy a mild condition.}, language = {en} } @inproceedings{ShinanoRehfeldtKoch2019, author = {Shinano, Yuji and Rehfeldt, Daniel and Koch, Thorsten}, title = {Building Optimal Steiner Trees on Supercomputers by Using up to 43,000 Cores}, volume = {11494}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_35}, pages = {529 -- 539}, year = {2019}, abstract = {SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively parallel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best-known solutions to instances from the benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB.}, language = {en} } @article{BernalVigerskeTrespalaciosetal.2017, author = {Bernal, David E. and Vigerske, Stefan and Trespalacios, Francisco and Grossmann, Ignacio E.}, title = {Improving the performance of DICOPT in convex MINLP problems using a feasibility pump}, journal = {Optimization Methods and Software}, year = {2017}, abstract = {The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are diffcult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive that the nonlinear subproblems produced by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm for DICOPT. Computational comparisons with previous versions of DICOPT and other MINLP solvers on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solving time.}, language = {en} } @misc{WitzigBertholdHeinz2019, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Computational Aspects of Infeasibility Analysis in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74962}, year = {2019}, abstract = {The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. This method is called dual proof analysis. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide an intense computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first integrated approach to use both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set MIPLIB 2017; the presented algorithms have been implemented within the non-commercial MIP solver SCIP and the commercial MIP solver FICO Xpress.}, language = {en} } @inproceedings{ShinanoRehfeldtGally2019, author = {Shinano, Yuji and Rehfeldt, Daniel and Gally, Tristan}, title = {An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries}, booktitle = {Proceedings of the 9th IEEE Workshop Parallel / Distributed Combinatorics and Optimization}, publisher = {IEEE}, doi = {10.1109/IPDPSW.2019.00095}, pages = {530 -- 541}, year = {2019}, abstract = {Branch-and-bound (B\&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B\&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature.}, language = {en} } @inproceedings{RehfeldtShinanoKoch2021, author = {Rehfeldt, Daniel and Shinano, Yuji and Koch, Thorsten}, title = {SCIP-Jack: An exact high performance solver for Steiner tree problems in graphs and related problems}, booktitle = {Modeling, Simulation and Optimization of Complex Processes HPSC 2018}, publisher = {Springer}, doi = {10.1007/978-3-030-55240-4_10}, year = {2021}, abstract = {The Steiner tree problem in graphs is one of the classic combinatorial optimization problems. Furthermore, many related problems, such as the rectilinear Steiner tree problem or the maximum-weight connected subgraph problem, have been described in the literature—with a wide range of practical applications. To embrace this wealth of problem classes, the solver SCIP-JACK has been developed as an exact framework for classic Steiner tree and 11 related problems. Moreover, the solver comes with both shared- and distributed memory extensions by means of the UG framework. Besides its versatility, SCIP-JACK is highly competitive for most of the 12 problem classes it can solve, as for instance demonstrated by its top ranking in the recent PACE 2018 Challenge. This article describes the current state of SCIP-JACK and provides up-to-date computational results, including several instances that can now be solved for the first time to optimality.}, language = {en} } @misc{Scheizel2018, type = {Master Thesis}, author = {Scheizel, Jenia}, title = {A fast Flow based Heuristic for MIP modelled SCM Problems}, year = {2018}, language = {en} } @misc{AndersonHendelLeBodicetal.2019, author = {Anderson, Daniel and Hendel, Gregor and Le Bodic, Pierre and Viernickel, Jan Merlin}, title = {Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72653}, year = {2019}, abstract = {We propose a simple and general online method to measure the search progress within the Branch-and-Bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for Mixed-Integer Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases.}, language = {en} } @article{BertholdFarmerHeinzetal.2018, author = {Berthold, Timo and Farmer, James and Heinz, Stefan and Perregaard, Michael}, title = {Parallelization of the FICO Xpress Optimizer}, volume = {33}, journal = {Optimization Methods and Software}, number = {3}, doi = {10.1080/10556788.2017.1333612}, pages = {518 -- 529}, year = {2018}, abstract = {Computing hardware has mostly thrashed out the physical limits for speeding up individual computing cores. Consequently, the main line of progress for new hardware is growing the number of computing cores within a single CPU. This makes the study of efficient parallelization schemes for computation-intensive algorithms more and more important. A natural precondition to achieving reasonable speedups from parallelization is maintaining a high workload of the available computational resources. At the same time, reproducibility and reliability are key requirements for software that is used in industrial applications. In this paper, we present the new parallelization concept for the state-of-the-art MIP solver FICO Xpress-Optimizer. MIP solvers like Xpress are expected to be deterministic. This inevitably results in synchronization latencies which render the goal of a satisfying workload a challenge in itself. We address this challenge by following a partial information approach and separating the concepts of simultaneous tasks and independent threads from each other. Our computational results indicate that this leads to a much higher CPU workload and thereby to an improved, almost linear, scaling on modern high-performance CPUs. As an added value, the solution path that Xpress takes is not only deterministic in a fixed environment, but also, to a certain extent, thread-independent. This paper is an extended version of Berthold et al. [Parallelization of the FICO Xpress-Optimizer, in Mathematical Software - ICMS 2016: 5th International Conference, G.-M. Greuel, T. Koch, P. Paule, and A. Sommere, eds., Springer International Publishing, Berlin, 2016, pp. 251-258] containing more detailed technical descriptions, illustrative examples and updated computational results.}, language = {en} } @article{TawfikLimbourg2019, author = {Tawfik, Christine and Limbourg, Sabine}, title = {A Bilevel Model for Network Design and Pricing Based on a Level-of-Service Assessment}, volume = {53}, journal = {Transportation Science}, number = {6}, publisher = {Informs}, address = {Transportation Science}, doi = {10.1287/trsc.2019.0906}, pages = {1609 -- 1626}, year = {2019}, abstract = {Within a wide view to stimulate intermodal transport, this paper is devoted to the examination of the intrinsically related problems of designing freight carrying services and determining their associated prices as observed by the shipper firms. A path-based multicommodity formulation is developed for a medium-term planning horizon, from the perspective of an intermodal operator. In the quest of incorporating nonprice attributes, two approaches are proposed to depict a realistic assessment of the service quality. First, frequency delay constraints are added to the upper level problem. Second, based on a random utility model, behavioural concepts are integrated in the expression of the lower level as a logistics costs minimization problem. Exact tests are invoked on real-world instances, demonstrating the capability of the presented approaches of reaching reasonable results within acceptable computation times and optimality gaps. The broader level-of-service perspective imposes additional costs on the service providers, although to a lesser extent on long-distance freight corridors, as indicated by the computed market share and net profit. Further experiments are conducted to test the impact of certain transport management instruments (e.g. subsidies and service capacities) on the modal split, as well as to assess the intermodality's future based on a scenario analysis methodology.}, language = {en} } @article{MunguiaOxberryRajanetal.2019, author = {Munguia, Lluis-Miquel and Oxberry, Geoffrey and Rajan, Deepak and Shinano, Yuji}, title = {Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs}, journal = {Computational Optimization and Applications}, doi = {10.1007/s10589-019-00074-0}, year = {2019}, abstract = {PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch \& Bound (B\&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B\&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B\&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores.}, language = {en} } @article{AchterbergBixbyGuetal.2019, author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, journal = {INFORMS Journal on Computing}, year = {2019}, abstract = {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.}, language = {en} } @inproceedings{BertholdPerregaardMeszaros2018, author = {Berthold, Timo and Perregaard, Michael and M{\´e}sz{\´a}ros, Csaba}, title = {Four Good Reasons to Use an Interior Point Solver Within a MIP Solver}, booktitle = {Kliewer N., Ehmke J., Bornd{\"o}rfer R. (eds) Operations Research Proceedings 2017}, doi = {10.1007/978-3-319-89920-6_22}, pages = {159 -- 164}, year = {2018}, abstract = {"Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex" This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation.}, language = {en} } @inproceedings{KochRehfeldtShinano2025, author = {Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {On the state of QUBO solving}, booktitle = {Operations Research Proceedings 2023. OR 2023}, publisher = {Springer}, doi = {10.1007/978-3-031-58405-3_46}, pages = {357 -- 365}, year = {2025}, abstract = {It is regularly claimed that quantum computers will bring breakthrough progress in solving challenging combinatorial optimization problems relevant in practice. In particular, Quadratic Unconstrained Binary Optimization (QUBO) problems are said to be the model of choice for use in (adiabatic) quantum systems during the noisy intermediate- scale quantum (NISQ) era. Even the first commercial quantum-based systems are advertised to solve such problems. Theoretically, any Integer Program can be converted into a QUBO. In practice, however, there are some caveats, as even for problems that can be nicely modeled as a QUBO, this might not be the most effective way to solve them. We review the state of QUBO solving on digital and quantum computers and provide insights regarding current benchmark instances and modeling.}, language = {en} } @misc{GleixnerBertholdMuelleretal.2016, author = {Gleixner, Ambros and Berthold, Timo and M{\"u}ller, Benjamin and Weltge, Stefan}, title = {Three Enhancements for Optimization-Based Bound Tightening}, issn = {1438-0064}, doi = {10.1007/s10898-016-0450-4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57803}, year = {2016}, abstract = {Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17\% to 19\% on average. Most importantly, more instances can be solved when using OBBT.}, language = {en} } @misc{VigerskeGleixner2016, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1335312}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59377}, year = {2016}, abstract = {This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.}, language = {en} } @misc{RehfeldtHobbieSchoenheitetal.2019, author = {Rehfeldt, Daniel and Hobbie, Hannes and Sch{\"o}nheit, David and Gleixner, Ambros and Koch, Thorsten and M{\"o}st, Dominik}, title = {A massively parallel interior-point solver for linear energy system models with block structure}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74321}, year = {2019}, abstract = {Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers|already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an interior-point solver that exploits common structures of linear energy system models to efficiently run in parallel on distributed memory systems. The solver is designed for linear programs with doubly bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. Special effort has been put into handling large numbers of linking constraints and variables as commonly observed in energy system models. In order to handle this strong linkage, a distributed preconditioning of the Schur complement is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the existing parallel interior-point solver PIPS-IPM. We evaluate the computational performance on energy system models with up to 700 million non-zero entries in the constraint matrix, and with more than 200 million columns and 250 million rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market clearing. It has been widely applied in the literature on energy system analyses during the recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models.}, language = {en} } @misc{D'AndreagiovanniGleixner2016, author = {D'Andreagiovanni, Fabio and Gleixner, Ambros}, title = {Towards an accurate solution of wireless network design problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59010}, year = {2016}, abstract = {The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.}, language = {en} }