@misc{CheungGleixnerSteffy2016, author = {Cheung, Kevin K. H. and Gleixner, Ambros and Steffy, Daniel}, title = {Verifying Integer Programming Results}, issn = {1438-0064}, doi = {10.1007/978-3-319-59250-3_13}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61044}, year = {2016}, abstract = {Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certificate format is designed with simplicity in mind and is composed of a list of statements that can be sequentially verified using a limited number of simple yet powerful inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of mixed-integer linear programming instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.}, language = {en} } @misc{RehfeldtKochShinano2022, author = {Rehfeldt, Daniel and Koch, Thorsten and Shinano, Yuji}, title = {Faster exact solution of sparse MaxCut and QUBO problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85715}, year = {2022}, language = {en} } @misc{ItoShinano2018, author = {Ito, Satoshi and Shinano, Yuji}, title = {Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70591}, year = {2018}, abstract = {The clinch (elimination) number is a minimal number of future wins (losses) needed to clinch (to be eliminated from) a specified place in a sports league. Several optimization models and computational results are shown in this paper for calculating clinch and elimination numbers in the presence of predefined multiple tiebreaking criteria. The main subject of this paper is to provide a general algorithmic framework based on integer programming with utilizing possibly multilayered upper and lower bounds.}, language = {en} } @misc{GleixnerBastubbeEifleretal.2018, author = {Gleixner, Ambros and Bastubbe, Michael and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Schubert, Christoph and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Walter, Matthias and Wegscheider, Fabian and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 6.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69361}, year = {2018}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.}, language = {en} } @misc{WeberSagerGleixner2018, author = {Weber, Tobias and Sager, Sebastian and Gleixner, Ambros}, title = {Solving Quadratic Programs to High Precision using Scaled Iterative Refinement}, issn = {1438-0064}, doi = {10.1007/s12532-019-00154-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68152}, year = {2018}, abstract = {Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and M{\´e}sz{\´a}ros benchmark library.}, language = {en} } @misc{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}, issn = {1438-0064}, doi = {10.1007/s11786-017-0305-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62263}, 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} } @misc{Francobaldi2021, type = {Master Thesis}, author = {Francobaldi, Matteo}, title = {Learning to Use Local Cuts}, year = {2021}, abstract = {We propose a machine learning approach to address a specific algorithmic question that arises during the solving process of a mixed-integer linear programming problem, namely, whether to use cutting planes only at the root node or also at internal nodes of the branch-and-bound search tree, or equivalently, whether to run a cut-and-branch or rather a branch-and-cut algorithm. Within a supervised regression framework, we develop three machine learning models, Linear Model, Random Forest and Neural Network, for predicting the relative performance between the two methods, local-cut and no-local-cut. Hence, through an extensive computational study conducted with FICO Xpress over a large test bed of problems, we evaluate the produced strategies, and we show that they are able to provide, upon the existing policies, a significant improvement to the performance of the solver. In fact, a variant of the random forest suggested in the present work has already been implemented by the development team of Xpress, and released with version 8.13 of the software.}, language = {en} } @misc{EiflerGleixnerPulaj2021, author = {Eifler, Leon and Gleixner, Ambros and Pulaj, Jonad}, title = {A Safe Computational Framework for Integer Programming applied to Chv{\´a}tal's Conjecture}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-84444}, year = {2021}, abstract = {We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a rational branch-and-bound certificate produced by an exact integer programming solver, SCIP, in order to circumvent floating-point roundoff errors present in most state-of-the-art solvers for mixed-integer programs. The resulting certificates are self-contained and checker software exists that can verify their correctness independently of the integer programming solver used to produce the certificate. This acts as a safeguard against programming errors that may be present in complex solver software. The viability of this approach is tested by applying it to finite cases of Chv{\´a}tal's conjecture, a long-standing open question in extremal combinatorics. We take particular care to verify also the correctness of the input for this specific problem, using the Coq formal proof assistant. As a result we are able to provide a first machine-assisted proof that Chv{\´a}tal's conjecture holds for all downsets whose union of sets contains seven elements or less.}, language = {en} } @misc{Shinano2020, author = {Shinano, Yuji}, title = {UG - Ubiquity Generator Framework v0.9.1}, doi = {10.12752/8508}, year = {2020}, 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. For MIP solving, ParaSCIP and FiberSCIP are well debugged and should be stable. For MINLP solving, they are relatively stable, but not as thoroughly debugged. This release version should handle branch-and-cut approaches where subproblems are defined by variable bounds and also by constrains for ug[SCIP,*] ParaSCIP and FiberSCIP). Therefore, problem classes other than MIP or MINLP can be handled, but they have not been tested yet. v0.9.1: Update orbitope cip files.}, language = {en} } @misc{EiflerNicolasThouveninGleixner2023, author = {Eifler, Leon and Nicolas-Thouvenin, Jules and Gleixner, Ambros}, title = {Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-92573}, year = {2023}, abstract = {This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: the speed of LP iterative refinement, in particular in the majority of cases when a double-precision floating-point solver is able to compute approximate solutions with small errors, and the robustness of precision boosting whenever extended levels of precision become necessary. We compare the practical performance of the resulting algorithm with both puremethods on a large set of LPs and mixed-integer programs (MIPs). The results show that the combined algorithm solves more instances than a pure LP iterative refinement approach, while being faster than pure precision boosting. When embedded in an exact branch-and-cut framework for MIPs, the combined algorithm is able to reduce the number of failed calls to the exact LP solver to zero, while maintaining the speed of the pure LP iterative refinement approach.}, language = {en} } @misc{EiflerGleixner2023, author = {Eifler, Leon and Gleixner, Ambros}, title = {Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-90159}, year = {2023}, abstract = {This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5\% more instances and reduce solving times by 26.8\% on the MIPLIB 2017 benchmark test set.}, language = {en} } @misc{LenzSerrano2021, author = {Lenz, Ralf and Serrano, Felipe}, title = {Tight Convex Relaxations for the Expansion Planning Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81459}, year = {2021}, abstract = {Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58\%.}, language = {en} } @misc{BestuzhevaGleixnerVigerske2021, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Vigerske, Stefan}, title = {A Computational Study of Perspective Cuts}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81821}, year = {2021}, abstract = {The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time.}, language = {en} } @misc{ShinanoHeinzVigerskeetal.2013, author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, issn = {1438-0064}, doi = {10.1287/ijoc.2017.0762}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42595}, year = {2013}, abstract = {Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated.}, language = {en} } @misc{Hendel2014, type = {Master Thesis}, author = {Hendel, Gregor}, title = {Empirical Analysis of Solving Phases in Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54270}, pages = {159}, year = {2014}, abstract = {Modern solving software for mixed-integer programming (MIP) incorporates numerous algorithmic components whose behavior is controlled by user parameter choices, and whose usefulness dramatically varies depending on the progress of the solving process. In this thesis, our aim is to construct a phase-based solver that dynamically reacts on phase transitions with an appropriate change of its component behavior. Therefore, we decompose the branch-and-bound solving process into three distinct phases: The first phase objective is to find a feasible solution. During the second phase, a sequence of incumbent solutions gets constructed until the incumbent is eventually optimal. Proving optimality is the central objective of the remaining third phase. Based on the MIP-solver SCIP we construct a phase-based solver to make use of the phase concept in two steps: First, we identify promising components for every solving phase individually and show that their combination is beneficial on a test bed of practical MIP instances. We then present and evaluate three heuristic criteria to make use of the phase-based solver in practice, where it is infeasible to distinguish between the last two phases before the termination of the solving process.}, language = {en} } @misc{Witzig2014, type = {Master Thesis}, author = {Witzig, Jakob}, title = {Reoptimization Techniques in MIP Solvers}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54067}, pages = {176}, year = {2014}, abstract = {Many optimization problems can be modeled as Mixed Integer Programs (MIPs). In general, MIPs cannot be solved efficiently, since solving MIPs is NP-hard, see, e.g., Schrijver, 2003. Common methods for solving NP-hard problems are branch-and-bound and column generation. In the case of column generation, the original problem becomes decomposed or re-formulated into one ore more smaller subproblems, which are easier to solve. Each of these subproblems is solved separately and recurrently, which can be interpreted as solving a sequence of optimization problems. In this thesis, we consider a sequence of MIPs which only differ in the respective objective functions. Furthermore, we assume each of these MIPs get solved with a branch-and-bound algorithm. This thesis aims to figure out whether the solving process of a given sequence of MIPs can be accelerated by reoptimization. As reoptimization we understand starting the solving process of a MIP of this sequence at a given frontier of a search tree corresponding to another MIP of this sequence. At the beginning we introduce an LP-based branch-and-bound algorithm. This algorithm is inspired by the reoptimizing algorithm of Hiller, Klug, and the author of this thesis, 2013. Since most of the state-of-the-art MIP solvers come to decisions based on dual information, which leads to the loss of feasible solutions after changing the objective function, we present a technique to guarantee optimality despite using these information. A decision is based on a dual information if this decision is valid for at least one feasible solution, whereas a decision is based on a primal information if this decision is valid for all feasible solutions. Afterwards, we consider representing the search frontier of the tree by a set of nodes of a given size. We call this the Tree Compression Problem. Moreover, we present a criterion characterizing the similarity of two objective functions. To evaluate our approach of reoptimization we extend the well-known and well-maintained MIP solver SCIP to an LP-based branch-and-bound framework, introduce two heuristics for solving the Tree Compression Problem, and a primal heuristic which is especially fitted to column generation. Finally, we present computational experiments on several problem classes, e.g., the Vertex Coloring and k-Constrained Shortest Path. Our experiments show, that a straightforward reoptimization, i.e., without additional heuristics, provides no benefit in general. However, in combination with the techniques and methods presented in this thesis, we can accelerate the solving of a given sequence up to the factor 14. For this purpose it is essential to take the differences of the objective functions into account and to restart the reoptimization, i.e., solve the subproblem from scratch, if the objective functions are not similar enough. Finally, we discuss the possibility to parallelize the solving process of the search frontier at the beginning of each solving process.}, language = {en} } @misc{GamrathMelchioriBertholdetal.2015, author = {Gamrath, Gerald and Melchiori, Anna and Berthold, Timo and Gleixner, Ambros and Salvagnin, Domenico}, title = {Branching on multi-aggregated variables}, issn = {1438-0064}, doi = {10.1007/978-3-319-18008-3_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53829}, year = {2015}, abstract = {In mixed-integer programming, the branching rule is a key component to a fast convergence of the branch-and-bound algorithm. The most common strategy is to branch on simple disjunctions that split the domain of a single integer variable into two disjoint intervals. Multi-aggregation is a presolving step that replaces variables by an affine linear sum of other variables, thereby reducing the problem size. While this simplification typically improves the performance of MIP solvers, it also restricts the degree of freedom in variable-based branching rules. We present a novel branching scheme that tries to overcome the above drawback by considering general disjunctions defined by multi-aggregated variables in addition to the standard disjunctions based on single variables. This natural idea results in a hybrid between variable- and constraint-based branching rules. Our implementation within the constraint integer programming framework SCIP incorporates this into a full strong branching rule and reduces the number of branch-and-bound nodes on a general test set of publicly available benchmark instances. For a specific class of problems, we show that the solving time decreases significantly.}, language = {en} } @misc{WitzigGamrathHiller2015, author = {Witzig, Jakob and Gamrath, Gerald and Hiller, Benjamin}, title = {Reoptimization Techniques in MIP Solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-20086-6_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54375}, year = {2015}, abstract = {Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to ``warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.}, language = {en} } @misc{MaherFischerGallyetal.2017, author = {Maher, Stephen J. and Fischer, Tobias and Gally, Tristan and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Robert Lion and Hendel, Gregor and Koch, Thorsten and L{\"u}bbecke, Marco and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 4.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62170}, year = {2017}, abstract = {The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.}, language = {en} } @misc{GamrathFischerGallyetal.2016, author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, year = {2016}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, language = {en} } @misc{BallersteinMichaelsVigerske2013, author = {Ballerstein, Martin and Michaels, Dennis and Vigerske, Stefan}, title = {Linear Underestimators for bivariate functions with a fixed convexity behavior}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17641}, year = {2013}, abstract = {This is a technical report for the SCIP constraint handler cons_bivariate. We describe a cut-generation algorithm for a class of bivariate twice continuously differentiable functions with fixed convexity behavior over a box. Computational results comparing our cut-generation algorithms with state-of-the-art global optimization software on a series of randomly generated test instances are reported and discussed.}, language = {en} } @misc{BertholdHendel2013, author = {Berthold, Timo and Hendel, Gregor}, title = {Shift-And-Propagate}, issn = {1438-0064}, doi = {10.1007/s10732-014-9271-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17596}, year = {2013}, abstract = {For mixed integer programming, recent years have seen a growing interest in the design of general purpose primal heuristics for use inside complete solvers. Many of these heuristics rely on an optimal LP solution. Finding this may itself take a significant amount of time. The presented paper addresses this issue by the introduction of the Shift-And-Propagate heuristic. Shift-And-Propagate is a pre-root primal heuristic that does not require a previously found LP solution. It applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement of existing rounding and propagation heuristics.}, language = {en} } @misc{Shinano2017, author = {Shinano, Yuji}, title = {The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_20}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65545}, year = {2017}, abstract = {Mixed integer linear programming (MIP) is a general form to model combinatorial optimization problems and has many industrial applications. The performance of MIP solvers has improved tremendously in the last two decades and these solvers have been used to solve many real-word problems. However, against the backdrop of modern computer technology, parallelization is of pivotal importance. In this way, ParaSCIP is the most successful parallel MIP solver in terms of solving previously unsolvable instances from the well-known benchmark instance set MIPLIB by using supercomputers. It solved two instances from MIPLIB2003 and 12 from MIPLIB2010 for the first time to optimality by using up to 80,000 cores on supercomputers. ParaSCIP has been developed by using the Ubiquity Generator (UG) framework, which is a general software package to parallelize any state-of-the-art branch-and-bound based solver. This paper discusses 7 years of progress in parallelizing branch-and-bound solvers with UG.}, language = {en} } @misc{GamrathGleixnerKochetal.2016, 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}, issn = {1438-0064}, doi = {10.4208/jcm.1905-m2019-0055}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61107}, year = {2016}, abstract = {SAP's decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this paper we describe our coordinated efforts to ensure that the performance of the underlying solution algorithms matches the complexity of the large supply chain problems and tight time limits encountered in practice.}, language = {en} } @misc{GottwaldMaherShinano2016, author = {Gottwald, Robert Lion and Maher, Stephen J. and Shinano, Yuji}, title = {Distributed domain propagation}, issn = {1438-0064}, doi = {10.4230/LIPIcs.SEA.2017.6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61380}, year = {2016}, abstract = {Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite it's simplicity portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after a variables domain has been reduced. This paper investigates the impact of distributed domain propagation in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers.}, language = {en} } @misc{SchenkerBorndoerferSkutella2016, author = {Schenker, Sebastian and Bornd{\"o}rfer, Ralf and Skutella, Martin}, title = {A novel partitioning of the set of non-dominated points}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61286}, year = {2016}, abstract = {We consider a novel partitioning of the set of non-dominated points for general multi-objective integer programs with \$k\$ objectives. The set of non-dominated points is partitioned into a set of non-dominated points whose efficient solutions are also efficient for some restricted subproblem with one less objective; the second partition comprises the non-dominated points whose efficient solutions are inefficient for any of the restricted subproblems. We show that the first partition has the nice property that it yields finite rectangular boxes in which the points of the second partition are located.}, language = {en} } @misc{GamrathKochMaheretal.2015, author = {Gamrath, Gerald and Koch, Thorsten and Maher, Stephen J. and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A solver for STP and variants with parallelization extensions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54648}, year = {2015}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem specific. In contrast, this paper introduces a general purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This is achieved by transforming various problem variants into a general form and solving them using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.}, language = {en} } @misc{Hendel2015, author = {Hendel, Gregor}, title = {Enhancing MIP branching decisions by using the sample variance of pseudo-costs}, issn = {1438-0064}, doi = {10.1007/978-3-319-18008-3_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54591}, year = {2015}, abstract = {The selection of a good branching variable is crucial for small search trees in Mixed Integer Programming. Most modern solvers employ a strategy guided by history information, mainly the variable pseudo-costs, which are used to estimate the objective gain. At the beginning of the search, such information is usually collected via an expensive look-ahead strategy called strong-branching until variables are considered reliable. The reliability notion is thereby mostly based on fixed-number thresholds, which may lead to ineffective branching decisions on problems with highly varying objective gains. We suggest two new notions of reliability motivated by mathematical statistics that take into account the sample variance of the past observations on each variable individually. The first method prioritizes additional strong-branching look-aheads on variables whose pseudo-costs show a large variance by measuring the relative error of a pseudo-cost confidence interval. The second method performs a two-sample Student-t test for filtering branching candidates with a high probability to be better than the best history candidate. Both methods were implemented in the MIP-solver SCIP and computational results on standard MIP test sets are presented.}, language = {en} } @misc{GamrathSchubert2017, author = {Gamrath, Gerald and Schubert, Christoph}, title = {Measuring the impact of branching rules for mixed-integer programming}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_23}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64722}, year = {2017}, abstract = {Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching.}, language = {en} } @misc{RehfeldtKoch2017, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Generalized preprocessing techniques for Steiner tree and maximum-weight connected subgraph problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65439}, year = {2017}, abstract = {This article introduces new preprocessing techniques for the Steiner tree problem in graphs and one of its most popular relatives, the maximum-weight connected subgraph problem. Several of the techniques generalize previous results from the literature. The correctness of the new methods is shown, but also their NP-hardness is demonstrated. Despite this pessimistic worst-case complexity, several relaxations are discussed that are expected to allow for a strong practical efficiency of these techniques in strengthening both exact and heuristic solving approaches.}, language = {en} } @misc{BertholdPerregaardMeszaros2017, 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}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_22}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64599}, year = {2017}, 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} } @misc{MiltenbergerRalphsSteffy2017, author = {Miltenberger, Matthias and Ralphs, Ted and Steffy, Daniel}, title = {Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization}, journal = {Operations Research Proceedings 2017}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64645}, year = {2017}, abstract = {We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct.}, language = {en} } @misc{SchadeSchlechteWitzig2017, author = {Schade, Stanley and Schlechte, Thomas and Witzig, Jakob}, title = {Structure-based Decomposition for Pattern-Detection for Railway Timetables}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64525}, year = {2017}, abstract = {We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers.}, language = {en} } @misc{Humpola2015, author = {Humpola, Jesco}, title = {Sufficient Pruning Conditions for MINLP in Gas Network Design}, doi = {10.1007/s13675-016-0077-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53489}, year = {2015}, abstract = {One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology extension problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. In this article we offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex NLP can be certified by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speed-up for the necessary computations.}, language = {en} } @misc{Witzig2017, author = {Witzig, Jakob}, title = {Conflict Driven Diving for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66116}, year = {2017}, abstract = {The analysis of infeasibility plays an important role in solving satisfiability problems (SAT) and mixed integer programs (MIPs). In mixed integer programming, this procedure is called conflict analysis. So far, modern MIP solvers use conflict analysis only for propagation and improving the dual bound, i.e., fathoming nodes that cannot contain feasible solutions. In this short paper, we present a new approach which uses conflict information to improve the primal bound during a MIP solve. To derive new improving primal solutions we use a conflict driven diving heuristic called conflict diving that uses the information obtained by conflict analysis. Conflict diving pursues a twofold strategy. By using conflict information the new diving approach is guided into parts of the search space that are usually not explored by other diving heuristics. At the same time, conflict diving has a fail-fast-strategy to reduce the time spent if it cannot find a new primal solution. As a byproduct, additional valid conflict constraints can be derived, from which a MIP solver can gain benefit to improve the dual bound as well. To show the added-value of conflict diving within a MIP solver, conflict diving has been implemented within the non-commercial MIP solver SCIP. Experiments are carried out on general MIP instances from standard public test sets, like MIPLIB2010 or Cor@l.}, language = {en} } @misc{AchterbergBixbyGuetal.2016, author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60370}, year = {2016}, 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} } @misc{RehfeldtKochMaher2016, author = {Rehfeldt, Daniel and Koch, Thorsten and Maher, Stephen J.}, title = {Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem}, issn = {1438-0064}, doi = {10.1002/net.21857}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60420}, year = {2016}, abstract = {The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90 percent of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-Jack.}, language = {en} } @misc{Pulaj2016, author = {Pulaj, Jonad}, title = {Cutting Planes for Families Implying Frankl's Conjecture}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60626}, year = {2016}, abstract = {We find previously unknown families which imply Frankl's conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen's Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non-Frankl-Complete (Non-FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen's Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non-FC-families.}, language = {en} } @misc{WitzigBeckenbachEifleretal.2016, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, issn = {1438-0064}, doi = {10.1137/16M1091162}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60353}, year = {2016}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @misc{MaherMiltenbergerPedrosoetal.2016, author = {Maher, Stephen J. and Miltenberger, Matthias and Pedroso, Jo{\~a}o Pedro and Rehfeldt, Daniel and Schwarz, Robert and Serrano, Felipe}, title = {PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite}, issn = {1438-0064}, doi = {10.1007/978-3-319-42432-3_37}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61348}, year = {2016}, abstract = {SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.}, language = {en} } @misc{GamrathKochMaheretal.2016, author = {Gamrath, Gerald and Koch, Thorsten and Maher, Stephen J. and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A solver for STP and variants with parallelization extensions}, issn = {1438-0064}, doi = {10.1007/s12532-016-0114-x}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60170}, year = {2016}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.}, language = {en} } @misc{RehfeldtKoch2016, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP}, issn = {1438-0064}, doi = {10.4208/jcm.1709-m2017-0002}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59777}, year = {2016}, abstract = {Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem to the Steiner arborescence problem are introduced for the first time. Furthermore, we demonstrate the considerable implications for practical solving approaches, including the computation of strong upper and lower bounds.}, language = {en} } @misc{BreuerBussieckCaoetal.2017, author = {Breuer, Thomas and Bussieck, Michael and Cao, Karl-Kien and Cebulla, Felix and Fiand, Frederik and Gils, Hans Christian and Gleixner, Ambros and Khabi, Dmitry and Koch, Thorsten and Rehfeldt, Daniel and Wetzel, Manuel}, title = {Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_85}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66183}, year = {2017}, abstract = {Current linear energy system models (ESM) acquiring to provide sufficient detail and reliability frequently bring along problems of both high intricacy and increasing scale. Unfortunately, the size and complexity of these problems often prove to be intractable even for commercial state-of-the-art linear programming solvers. This article describes an interdisciplinary approach to exploit the intrinsic structure of these large-scale linear problems to be able to solve them on massively parallel high-performance computers. A key aspect are extensions to the parallel interior-point solver PIPS-IPM originally developed for stochastic optimization problems. Furthermore, a newly developed GAMS interface to the solver as well as some GAMS language extensions to model block-structured problems will be described.}, language = {en} } @misc{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {SCIP-Jack—a solver for STP and variants with parallelization extensions: An update}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66416}, year = {2018}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. Although the different Steiner tree problem variants are usually strongly related, solution approaches employed so far have been prevalently problem-specific. Against this backdrop, the solver SCIP-Jack was created as a general-purpose framework that can be used to solve the classical Steiner tree problem and 11 of its variants. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. Furthermore, SCIP-Jack includes various newly developed algorithmic components such as preprocessing routines and heuristics. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. After the introduction of SCIP-Jack at the 2014 DIMACS Challenge on Steiner problems, the overall performance of the solver has considerably improved. This article provides an overview on the current state.}, language = {en} } @misc{RehfeldtKoch2017, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem}, issn = {1438-0064}, doi = {10.1137/17M1145963}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64699}, year = {2017}, abstract = {Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced.}, language = {en} } @misc{Rehfeldt2015, type = {Master Thesis}, author = {Rehfeldt, Daniel}, title = {A Generic Approach to Solving the Steiner Tree Problem and Variants}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57817}, pages = {185}, year = {2015}, abstract = {Spawned by practical applications, numerous variations of the classical Steiner tree problem in graphs have been studied during the last decades. Despite the strong relationship between the different variants, solution approaches employed so far have been prevalently problem-specific. In contrast, we pursue a general-purpose strategy resulting in a solver able to solve both the classical Steiner tree problem and ten of its variants without modification. These variants include well-known problems such as the prize-collecting Steiner tree problem, the maximum-weight connected subgraph problem or the rectilinear minimum Steiner tree problem. Bolstered by a variety of new methods, most notably reduction techniques, our solver is not only of unprecedented versatility, but furthermore competitive or even superior to specialized state-of-the-art programs for several Steiner problem variants.}, language = {en} } @misc{GamrathKochRehfeldtetal.2014, author = {Gamrath, Gerald and Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A massively parallel STP solver}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52293}, year = {2014}, abstract = {In this article we describe the impact from embedding a 15 year old model for solving the Steiner tree problem in graphs in a state-of-the-art MIP-Framework, making the result run in a massively parallel environment and extending the model to solve as many variants as possible. We end up with a high-perfomance solver that is capable of solving previously unsolved instances and, in contrast to its predecessor, is freely available for academic research.}, language = {en} } @misc{RalphsShinanoBertholdetal.2016, author = {Ralphs, Ted and Shinano, Yuji and Berthold, Timo and Koch, Thorsten}, title = {Parallel Solvers for Mixed Integer Linear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62239}, year = {2016}, abstract = {In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.}, language = {en} } @misc{Hendel2015, author = {Hendel, Gregor}, title = {Exploiting Solving Phases for Mixed-Integer Programs}, issn = {1438-0064}, doi = {10.1007/978-3-319-42902-1_1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57098}, year = {2015}, abstract = {Modern MIP solving software incorporates dozens of auxiliary algorithmic components for supporting the branch-and-bound search in finding and improving solutions and in strengthening the relaxation. Intuitively, a dynamic solving strategy with an appropriate emphasis on different solving components and strategies is desirable during the search process. We propose an adaptive solver behavior that dynamically reacts on transitions between the three typical phases of a MIP solving process: The first phase objective is to find a feasible solution. During the second phase, a sequence of incumbent solutions gets constructed until the incumbent is eventually optimal. Proving optimality is the central objective of the remaining third phase. Based on the MIP-solver SCIP, we demonstrate the usefulness of the phase concept both with an exact recognition of the optimality of a solution, and provide heuristic alternatives to make use of the concept in practice.}, language = {en} } @misc{YokoyamaShinanoTaniguchietal.2014, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation}, issn = {1438-0064}, doi = {10.1016/j.enconman.2014.12.020}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49413}, year = {2014}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation variables is proposed to solve the optimal design problem of energy supply systems efficiently: At the upper level, the optimal values of design variables are searched by the branch and bound method; At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively during the search at the upper level; Lower bounds for the optimal value of the objective function are evaluated, and are utilized for the bounding operations at both the levels. This method is implemented into open and commercial MILP solvers. Illustrative and practical case studies on the optimal design of cogeneration systems are conducted, and the validity and effectiveness of the proposed method are clarified.}, language = {en} } @misc{GleixnerSteffyWolter2015, author = {Gleixner, Ambros and Steffy, Daniel and Wolter, Kati}, title = {Iterative Refinement for Linear Programming}, issn = {1438-0064}, doi = {10.1287/ijoc.2016.0692}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55118}, year = {2015}, abstract = {We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We show that this algorithm is effective in practice for computing extended precision solutions and that it leads to a direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SoPlex.}, language = {en} } @misc{GamrathBertholdHeinzetal.2015, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-based primal heuristics for mixed integer programming}, issn = {1438-0064}, doi = {http://dx.doi.org/10.1007/978-4-431-55420-2_3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55518}, year = {2015}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.}, language = {en} } @misc{GamrathBertholdHeinzetal.2017, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, issn = {1438-0064}, doi = {10.1007/s12532-019-00159-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65387}, year = {2017}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early in the solving process and help to solve instances to optimality faster. In this paper, we present a scheme for primal start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved as an LP and the solution is rounded. If the rounded solution did not provide a feasible solution already, a sub-MIP is solved for the neighborhood defined by the variable fixings performed in the first phase. The global structures help to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about three out of five instances and therewith help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.}, language = {en} } @misc{BertholdHendelKoch2016, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {The Three Phases of MIP Solving}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1392519}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61607}, year = {2016}, abstract = {Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points.}, language = {en} } @misc{MaherDesaulniersSoumis2015, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {The tail assignment problem with look-ahead maintenance constraints}, issn = {1438-0064}, doi = {10.1016/j.ejor.2017.06.041}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56717}, year = {2015}, abstract = {The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to be operated the next day. The aim of this paper is to develop an operationally flexible tail assignment that satisfies short-range---within the next three days---aircraft maintenance requirements and performs the aircraft/flight gate assignment for each input line-of-flight. While maintenance plans commonly span multiple days, the related tail assignment problems can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by extending the one-day routes aircraft maintenance routing approach to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A mathematical model is presented that integrates the gate assignment and maintenance planning problems. To increase the satisfaction of maintenance requirements, an iterative algorithm is developed that modifies the fixed lines-of-flight provided as input to the tail assignment problem. The tail assignment problem and iterative algorithm are demonstrated to effectively satisfy maintenance requirements within appropriate run times using input data collected from three different airlines.}, language = {en} } @misc{BestuzhevaBesanconChenetal.2021, author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc E. and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85309}, year = {2021}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.}, language = {en} } @misc{BolusaniBesanconBestuzhevaetal.2024, author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Bestuzheva, Ksenia and Chmiela, Antonia and Dion{\´i}sio, Jo{\~a}o and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Ghannam, Mohammed and Gleixner, Ambros and Graczyk, Christoph and Halbig, Katrin and Hedtke, Ivo and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Kamp, Dominik and Koch, Thorsten and Kofler, Kevin and Lentz, Jurgen and Manns, Julian and Mexi, Gioni and M{\"u}hmer, Erik and E. Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Turner, Mark and Vigerske, Stefan and Weninger, Dieter and Xu, Liding}, title = {The SCIP Optimization Suite 9.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-95528}, year = {2024}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.}, language = {en} } @misc{TurnerChmielaKochetal.2023, author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93095}, year = {2023}, abstract = {A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.}, language = {en} } @misc{ChmielaMunozSerrano2021, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, doi = {10.1007/978-3-030-73879-2_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79994}, year = {2021}, abstract = {The generation of strong linear inequalities for QCQPs has been recently tackled by a number of authors using the intersection cut paradigm - a highly studied tool in integer programming whose flexibility has triggered these renewed efforts in non-linear settings. In this work, we consider intersection cuts using the recently proposed construction of maximal quadratic-free sets. Using these sets, we derive closed-form formulas to compute intersection cuts which allow for quick cut-computations by simply plugging-in parameters associated to an arbitrary quadratic inequality being violated by a vertex of an LP relaxation. Additionally, we implement a cut-strengthening procedure that dates back to Glover and evaluate these techniques with extensive computational experiments.}, language = {en} } @misc{BestuzhevaChmielaMuelleretal.2023, author = {Bestuzheva, Ksenia and Chmiela, Antonia and M{\"u}ller, Benjamin and Serrano, Felipe and Vigerske, Stefan and Wegscheider, Fabian}, title = {Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89348}, year = {2023}, abstract = {For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version~8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.}, language = {en} }