TY - GEN A1 - Euler, Ricardo A1 - Borndörfer, Ralf A1 - Strunk, Timo A1 - Takkula, Tuomo T1 - ULD Build-Up Scheduling with Dynamic Batching in an Air Freight Hub N2 - Air freight is usually shipped in standardized unit load devices (ULDs). The planning process for the consolidation of transit cargo from inbound flights or locally emerging shipments into ULDs for outbound flights is called build-up scheduling. More specifically, outbound ULDs must be assigned a time and a workstation subject to both workstation capacity constraints and the availability of shipments which in turn depends on break-down decisions for incoming ULDs. ULDs scheduled for the same outbound flight should be built up in temporal and spatial proximity. This serves both to minimize overhead in transportation times and to allow workers to move freight between ULDs. We propose to address this requirement by processing ULDs for the same outbound flight in batches. For the above build-up scheduling problem, we introduce a multi-commodity network design model. Outbound flights are modeled as commodities; transit cargo is represented by cargo flow volume and unpack and batch decisions are represented as design variables. The model is solved with standard MIP solvers on a set of benchmark data. For instances with a limited number of resource conflicts, near-optimal solutions are found in under two hours for a whole week of operations. T3 - ZIB-Report - 21-31 KW - Logistics KW - Airline Applications Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83482 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Incremental Heuristics for Periodic Timetabling N2 - We present incremental heuristics for the Periodic Event Scheduling Problem (PESP), the standard mathematical tool to optimize periodic timetables in public transport. The core of our method is to solve successively larger subinstances making use of previously found solutions. Introducing the technical notion of free stratifications, we formulate a general scheme for incremental heuristics for PESP. More practically, we use line and station information to create heuristics that add lines or stations one by one, and we evaluate these heuristics on instances of the benchmarking library PESPlib. This approach is indeed viable, and leads to new incumbent solutions for six PESPlib instances. T3 - ZIB-Report - 23-22 KW - Timetabling KW - Mixed-Integer Programming KW - Public Transport Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92309 SN - 1438-0064 ER - TY - GEN A1 - Bortoletto, Enrico A1 - Lindner, Niels T1 - Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times N2 - The Periodic Event Scheduling Problem (PESP) is a notoriously hard combinatorial optimization problem, essential for the design of periodic timetables in public transportation. The coefficients of the integer variables in the standard mixed integer linear programming formulations of PESP are the period time, e.g., 60 for a horizon of one hour with a resolution of one minute. In many application scenarios, lines with different frequencies have to be scheduled, leading to period times with many divisors. It then seems natural to consider derived instances, where the period time is a divisor of the original one, thereby smaller, and bounds are scaled and rounded accordingly. To this end, we identify two rounding schemes: wide and tight. We then discuss the approximation performance of both strategies, in theory and practice. T3 - ZIB-Report - 23-23 KW - Timetabling KW - Mixed-Integer Programming KW - Public Transport Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92315 SN - 1438-0064 ER - TY - GEN A1 - Hendel, Gregor A1 - Miltenberger, Matthias A1 - Witzig, Jakob T1 - Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms N2 - State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics as well as Simplex pricing strategies. For each class we propose a selection strategy that is updated based on the observed runtime behavior, aiming to ultimately select only the best algorithms for a given instance. We review several common strategies for such a selection scenario under uncertainty, also known as Multi Armed Bandit Problem. In order to apply those bandit strategies, we carefully design reward functions to rank and compare each individual heuristic or pricing algorithm within its respective class. Finally, we discuss the computational benefits of using the proposed adaptive selection within the \scip Optimization Suite on publicly available MIP instances. T3 - ZIB-Report - 18-36 KW - mixed integer programming KW - primal heuristics KW - multi armed bandit Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69563 SN - 1438-0064 ER - TY - GEN A1 - Anderson, Lovis A1 - Turner, Mark A1 - Koch, Thorsten T1 - Generative deep learning for decision making in gas networks N2 - A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%. T3 - ZIB-Report - 20-38 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81103 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Masing, Berenike T1 - On the Split Closure of the Periodic Timetabling Polytope N2 - The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P $=$ NP, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances. T3 - ZIB-Report - 23-16 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Split Closure KW - Mixed-Integer Programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91156 SN - 1438-0064 ER - TY - THES A1 - Francobaldi, Matteo T1 - Learning to Use Local Cuts N2 - 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. KW - Mathematical Programming KW - Machine Learning KW - Artificial Intelligence Y1 - 2021 ER - TY - GEN A1 - Schiewe, Philine A1 - Goerigk, Marc A1 - Lindner, Niels T1 - Introducing TimPassLib - A library for integrated periodic timetabling and passenger routing N2 - Classic models to derive a timetable for public transport often face a chicken-and-egg situation: A good timetable should offer passengers routes with small travel times, but the route choice of passengers depends on the timetable. While models that fix passenger routes were frequently considered in the literature, integrated models that simultaneously optimize timetables and passenger routes have seen increasing attention lately. This creates a growing need for a set of instances that allows to test and compare new algorithmic developments for the integrated problem. Our paper addresses this requirement by presenting TimPassLib, a new benchmark library of instances for integrated periodic timetabling and passenger routing. T3 - ZIB-Report - 23-06 KW - periodic timetabling KW - optimization in public transport KW - data sets KW - benchmarking Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89741 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Ebert, Patricia T1 - Forward and Line-Based Cycle Bases for Periodic Timetabling N2 - The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances. T3 - ZIB-Report - 23-05 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89731 SN - 1438-0064 ER - TY - THES A1 - Miltenberger, Matthias T1 - Linear Programming in MILP Solving - A Computational Perspective N2 - Mixed-integer linear programming (MILP) plays a crucial role in the field of mathematical optimization and is especially relevant for practical applications due to the broad range of problems that can be modeled in that fashion. The vast majority of MILP solvers employ the LP-based branch-and-cut approach. As the name suggests, the linear programming (LP) subproblems that need to be solved therein influence their behavior and performance significantly. This thesis explores the impact of various LP solvers as well as LP solving techniques on the constraint integer programming framework SCIP Optimization Suite. SCIP allows for comparisons between academic and open-source LP solvers like Clp and SoPlex, as well as commercially developed, high-end codes like CPLEX, Gurobi, and Xpress. We investigate how the overall performance and stability of an MILP solver can be improved by new algorithmic enhancements like LP solution polishing and persistent scaling that we have implemented in the LP solver SoPlex. The former decreases the fractionality of LP solutions by selecting another vertex on the optimal hyperplane of the LP relaxation, exploiting degeneracy. The latter provides better numerical properties for the LP solver throughout the MILP solving process by preserving and extending the initial scaling factors, effectively also improving the overall performance of SCIP. Both enhancement techniques are activated by default in the SCIP Optimization Suite. Additionally, we provide an analysis of numerical conditions in SCIP through the lens of the LP solver by comparing different measures and how these evolve during the different stages of the solving process. A side effect of our work on this topic was the development of TreeD: a new and convenient way of presenting the search tree interactively and animated in the three-dimensional space. This visualization technique facilitates a better understanding of the MILP solving process of SCIP. Furthermore, this thesis presents the various algorithmic techniques like the row representation and iterative refinement that are implemented in SoPlex and that distinguish the solver from other simplex-based codes. Although it is often not as performant as its competitors, SoPlex demonstrates the ongoing research efforts in the field of linear programming with the simplex method. Aside from that, we demonstrate the rapid prototyping of algorithmic ideas and modeling approaches via PySCIPOpt, the Python interface to the SCIP Optimization Suite. This tool allows for convenient access to SCIP's internal data structures from the user-friendly Python programming language to implement custom algorithms and extensions without any prior knowledge of SCIP's programming language C. TreeD is one such example, demonstrating the use of several Python libraries on top of SCIP. PySCIPOpt also provides an intuitive modeling layer to formulate problems directly in the code without having to utilize another modeling language or framework. All contributions presented in this thesis are readily accessible in source code in SCIP Optimization Suite or as separate projects on the public code-sharing platform GitHub. KW - linear programming KW - mixed-integer programming KW - optimization KW - simplex KW - SCIP Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91873 UR - https://www.dr.hut-verlag.de/9783843953238.html SN - 9783843953238 PB - Verlag Dr. Hut GmbH ER - TY - GEN A1 - Eifler, Leon A1 - Gleixner, Ambros T1 - A Computational Status Update for Exact Rational Mixed Integer Programming N2 - The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours. T3 - ZIB-Report - 21-04 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81298 SN - 1438-0064 ER - TY - GEN A1 - Petkovic, Milena A1 - Chen, Ying A1 - Gamrath, Inken A1 - Gotzes, Uwe A1 - Hadjidimitriou, Natalia Selini A1 - Zittel, Janina A1 - Xu, Xiaofei A1 - Koch, Thorsten T1 - A Hybrid Approach for High Precision Prediction of Gas Flows N2 - About 20% of the German energy demand is supplied by natural gas. Ad- ditionally, for about twice the amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by so-called transmissions system operators or TSOs. The number one priority of the TSOs is to ensure security of supply. However, the TSOs have no knowledge of the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany’s largest TSO, operates a high- pressure transport network of about 12.000 km length. Since flexibility and security of supply is of utmost importance to the German Energy Transition (“Energiewende”) especially with the introduction of peak-load gas power stations, being able to predict in- and out-flow of the network is of great importance. In this paper we introduce a new hybrid forecast method applied to gas flows at the boundary nodes of a transport network. The new method employs optimized feature minimization and selection. We use a combination of an FAR, LSTM DNN and mathematical programming to achieve robust high quality forecasts on real world data for different types of network nodes. Keywords: Gas Forecast, Time series, Hybrid Method, FAR, LSTM, Mathematical Optimisation T3 - ZIB-Report - 19-26 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73525 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs N2 - 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. T3 - ZIB-Report - 23-28 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93095 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu T1 - A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming N2 - The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set. T3 - ZIB-Report - 23-21 KW - cutting plane selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91691 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. T3 - ZIB-Report - 23-19 KW - shortest path KW - flight planning KW - free flight KW - optimal control KW - global optimization KW - Newton's method Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91309 SN - 1438-0064 ER - TY - THES A1 - Turner, Mark T1 - Cutting Plane Selection for Mixed-Integer Linear Programming N2 - Mixed-Integer Linear Programming (MILP) is a ubiquitous and practical modelling paradigm that is essential for optimising a broad range of real-world systems. The backbone of all modern MILP solvers is the branch-and-cut algorithm, which is a hybrid of the branch-and-bound and cutting planes algorithms. Cutting planes (cuts) are linear inequalities that tighten the relaxation of a MILP. While a lot of research has gone into deriving valid cuts for MILPs, less emphasis has been put on determining which cuts to select. Cuts in general are generated in rounds, and a subset of the generated cuts must be added to the relaxation. The decision on which subset of cuts to add is called cut selection. This is a crucial task since adding too many cuts makes the relaxation large and slow to optimise over. Conversely, adding too few cuts results in an insufficiently tightened relaxation, and more relaxations need to be enumerated. To further emphasise the difficulty, the effectiveness of an applied cut is both dependent on the other applied cuts, and the state of the MILP solver. In this thesis, we present theoretical results on the importance and difficulty of cut selection, as well as practical results that use cut selection to improve general MILP solver performance. Improving general MILP solver performance is of great importance for practitioners and has many runoff effects. Reducing the solve time of currently solved systems can directly improve efficiency within the application area. In addition, improved performance enables larger systems to be modelled and optimised, and MILP to be used in areas where it was previously impractical due to time restrictions. Each chapter of this thesis corresponds to a publication on cut selection, where the contributions of this thesis can naturally be divided into four components. The first two components are motivated by instance-dependent performance. In practice, for each subroutine, including cut selection, MILP solvers have adjustable parameters with hard-coded default values. It is ultimately unrealistic to expect these default values to perform well for every instance. Rather, it would be ideal if the parameters were dependent on the given instance. To show this motivation is well founded, we first introduce a family of parametric MILP instances and cuts to showcase worst-case performance of cut selection for any fixed parameter value. We then introduce a graph neural network architecture and reinforcement learning framework for learning instance-dependent cut scoring parameters. In the following component, we formalise language for determining if a cut has theoretical usefulness from a polyhedral point of view in relation to other cuts. In addition, to overcome issues of infeasible projections and dual degeneracy, we introduce analytic center based distance measures. We then construct a lightweight multi-output regression model that predicts relative solver performance of an instance for a set of distance measures. The final two components are motivated by general MILP solver improvement via cut selection. Such improvement was shown to be possible, albeit difficult to achieve, by the first half of this thesis. We relate branch-and-bound and cuts through their underlying disjunctions. Using a history of previously computed Gomory mixed-integer cuts, we reduce the solve time of SCIP over the 67% of affected MIPLIB 2017 instances by 4%. In the final component, we introduce new cut scoring measures and filtering methods based on information from other MILP solving processes. The new cut selection techniques reduce the solve time of SCIP over the 97% of affected MIPLIB 2017 instances by 5%. KW - Mixed-Integer Programming KW - Cutting Planes KW - Cut Selection KW - Machine Learning Y1 - 2024 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. T3 - ZIB-Report - 22-28 KW - cut selection KW - anlalytic center KW - mixed-integer programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89065 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Anderson, Daniel A1 - Bestuzheva, Ksenia A1 - Chen, Wei-Kun A1 - Eifler, Leon A1 - Gasse, Maxime A1 - Gemander, Patrick A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Halbig, Katrin A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Le Bodic, Pierre A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Miltenberger, Matthias A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Tawfik, Christine A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 7.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders’ decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders’ decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 20-10 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78023 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 SN - 1438-0064 ER -