@misc{MuellerSerranoGleixner2019, author = {M{\"u}ller, Benjamin and Serrano, Felipe and Gleixner, Ambros}, title = {Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72759}, year = {2019}, abstract = {One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.}, language = {en} } @misc{BertholdGamrathSalvagnin2019, author = {Berthold, Timo and Gamrath, Gerald and Salvagnin, Domenico}, title = {Exploiting Dual Degeneracy in Branching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73028}, year = {2019}, abstract = {Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper, we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud ) of the current LP relaxation. These strategies naturally extend common methods like most infeasible branching, strong branching, pseudocost branching, and their hybrids, but we also propose a novel branching rule called cloud diameter branching. We show that dual degeneracy, a requirement for alternative LP optima, is present for many instances from common MIP test sets. Computational experiments show significant improvements in the quality of branching decisions as well as reduced branching effort when using our modifications of existing branching rules. We discuss different ways to generate a cloud of solutions and present extensive computational results showing that through a careful implementation, cloud modifications can speed up full strong branching by more than 10 \% on standard test sets. Additionally, by exploiting degeneracy, we are also able to improve the state-of-the-art hybrid branching rule and reduce the solving time on affected instances by almost 20 \% on average.}, language = {en} } @misc{SerranoSchwarzGleixner2019, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73253}, year = {2019}, abstract = {Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (1967) and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by general, not necessarily convex, differentiable functions that satisfy a mild condition.}, language = {en} } @inproceedings{ShinanoRehfeldtKoch2019, author = {Shinano, Yuji and Rehfeldt, Daniel and Koch, Thorsten}, title = {Building Optimal Steiner Trees on Supercomputers by Using up to 43,000 Cores}, volume = {11494}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_35}, pages = {529 -- 539}, year = {2019}, abstract = {SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively parallel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best-known solutions to instances from the benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB.}, language = {en} } @article{BernalVigerskeTrespalaciosetal.2017, author = {Bernal, David E. and Vigerske, Stefan and Trespalacios, Francisco and Grossmann, Ignacio E.}, title = {Improving the performance of DICOPT in convex MINLP problems using a feasibility pump}, journal = {Optimization Methods and Software}, year = {2017}, abstract = {The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are diffcult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive that the nonlinear subproblems produced by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm for DICOPT. Computational comparisons with previous versions of DICOPT and other MINLP solvers on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solving time.}, language = {en} } @misc{WitzigBertholdHeinz2019, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Computational Aspects of Infeasibility Analysis in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74962}, year = {2019}, abstract = {The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. This method is called dual proof analysis. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide an intense computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first integrated approach to use both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set MIPLIB 2017; the presented algorithms have been implemented within the non-commercial MIP solver SCIP and the commercial MIP solver FICO Xpress.}, language = {en} } @inproceedings{ShinanoRehfeldtGally2019, author = {Shinano, Yuji and Rehfeldt, Daniel and Gally, Tristan}, title = {An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries}, booktitle = {Proceedings of the 9th IEEE Workshop Parallel / Distributed Combinatorics and Optimization}, publisher = {IEEE}, doi = {10.1109/IPDPSW.2019.00095}, pages = {530 -- 541}, year = {2019}, abstract = {Branch-and-bound (B\&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B\&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature.}, language = {en} } @inproceedings{RehfeldtShinanoKoch2021, author = {Rehfeldt, Daniel and Shinano, Yuji and Koch, Thorsten}, title = {SCIP-Jack: An exact high performance solver for Steiner tree problems in graphs and related problems}, booktitle = {Modeling, Simulation and Optimization of Complex Processes HPSC 2018}, publisher = {Springer}, doi = {10.1007/978-3-030-55240-4_10}, year = {2021}, abstract = {The Steiner tree problem in graphs is one of the classic combinatorial optimization problems. Furthermore, many related problems, such as the rectilinear Steiner tree problem or the maximum-weight connected subgraph problem, have been described in the literature—with a wide range of practical applications. To embrace this wealth of problem classes, the solver SCIP-JACK has been developed as an exact framework for classic Steiner tree and 11 related problems. Moreover, the solver comes with both shared- and distributed memory extensions by means of the UG framework. Besides its versatility, SCIP-JACK is highly competitive for most of the 12 problem classes it can solve, as for instance demonstrated by its top ranking in the recent PACE 2018 Challenge. This article describes the current state of SCIP-JACK and provides up-to-date computational results, including several instances that can now be solved for the first time to optimality.}, language = {en} } @misc{Scheizel2018, type = {Master Thesis}, author = {Scheizel, Jenia}, title = {A fast Flow based Heuristic for MIP modelled SCM Problems}, year = {2018}, language = {en} } @misc{AndersonHendelLeBodicetal.2019, author = {Anderson, Daniel and Hendel, Gregor and Le Bodic, Pierre and Viernickel, Jan Merlin}, title = {Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72653}, year = {2019}, abstract = {We propose a simple and general online method to measure the search progress within the Branch-and-Bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for Mixed-Integer Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases.}, language = {en} } @article{BertholdFarmerHeinzetal.2018, author = {Berthold, Timo and Farmer, James and Heinz, Stefan and Perregaard, Michael}, title = {Parallelization of the FICO Xpress Optimizer}, volume = {33}, journal = {Optimization Methods and Software}, number = {3}, doi = {10.1080/10556788.2017.1333612}, pages = {518 -- 529}, year = {2018}, abstract = {Computing hardware has mostly thrashed out the physical limits for speeding up individual computing cores. Consequently, the main line of progress for new hardware is growing the number of computing cores within a single CPU. This makes the study of efficient parallelization schemes for computation-intensive algorithms more and more important. A natural precondition to achieving reasonable speedups from parallelization is maintaining a high workload of the available computational resources. At the same time, reproducibility and reliability are key requirements for software that is used in industrial applications. In this paper, we present the new parallelization concept for the state-of-the-art MIP solver FICO Xpress-Optimizer. MIP solvers like Xpress are expected to be deterministic. This inevitably results in synchronization latencies which render the goal of a satisfying workload a challenge in itself. We address this challenge by following a partial information approach and separating the concepts of simultaneous tasks and independent threads from each other. Our computational results indicate that this leads to a much higher CPU workload and thereby to an improved, almost linear, scaling on modern high-performance CPUs. As an added value, the solution path that Xpress takes is not only deterministic in a fixed environment, but also, to a certain extent, thread-independent. This paper is an extended version of Berthold et al. [Parallelization of the FICO Xpress-Optimizer, in Mathematical Software - ICMS 2016: 5th International Conference, G.-M. Greuel, T. Koch, P. Paule, and A. Sommere, eds., Springer International Publishing, Berlin, 2016, pp. 251-258] containing more detailed technical descriptions, illustrative examples and updated computational results.}, language = {en} } @article{TawfikLimbourg2019, author = {Tawfik, Christine and Limbourg, Sabine}, title = {A Bilevel Model for Network Design and Pricing Based on a Level-of-Service Assessment}, volume = {53}, journal = {Transportation Science}, number = {6}, publisher = {Informs}, address = {Transportation Science}, doi = {10.1287/trsc.2019.0906}, pages = {1609 -- 1626}, year = {2019}, abstract = {Within a wide view to stimulate intermodal transport, this paper is devoted to the examination of the intrinsically related problems of designing freight carrying services and determining their associated prices as observed by the shipper firms. A path-based multicommodity formulation is developed for a medium-term planning horizon, from the perspective of an intermodal operator. In the quest of incorporating nonprice attributes, two approaches are proposed to depict a realistic assessment of the service quality. First, frequency delay constraints are added to the upper level problem. Second, based on a random utility model, behavioural concepts are integrated in the expression of the lower level as a logistics costs minimization problem. Exact tests are invoked on real-world instances, demonstrating the capability of the presented approaches of reaching reasonable results within acceptable computation times and optimality gaps. The broader level-of-service perspective imposes additional costs on the service providers, although to a lesser extent on long-distance freight corridors, as indicated by the computed market share and net profit. Further experiments are conducted to test the impact of certain transport management instruments (e.g. subsidies and service capacities) on the modal split, as well as to assess the intermodality's future based on a scenario analysis methodology.}, language = {en} } @article{MunguiaOxberryRajanetal.2019, author = {Munguia, Lluis-Miquel and Oxberry, Geoffrey and Rajan, Deepak and Shinano, Yuji}, title = {Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs}, journal = {Computational Optimization and Applications}, doi = {10.1007/s10589-019-00074-0}, year = {2019}, abstract = {PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch \& Bound (B\&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B\&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B\&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores.}, language = {en} } @article{AchterbergBixbyGuetal.2019, author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, journal = {INFORMS Journal on Computing}, year = {2019}, abstract = {Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.}, language = {en} } @inproceedings{BertholdPerregaardMeszaros2018, author = {Berthold, Timo and Perregaard, Michael and M{\´e}sz{\´a}ros, Csaba}, title = {Four Good Reasons to Use an Interior Point Solver Within a MIP Solver}, booktitle = {Kliewer N., Ehmke J., Bornd{\"o}rfer R. (eds) Operations Research Proceedings 2017}, doi = {10.1007/978-3-319-89920-6_22}, pages = {159 -- 164}, year = {2018}, abstract = {"Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex" This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation.}, language = {en} } @misc{GleixnerBertholdMuelleretal.2016, author = {Gleixner, Ambros and Berthold, Timo and M{\"u}ller, Benjamin and Weltge, Stefan}, title = {Three Enhancements for Optimization-Based Bound Tightening}, issn = {1438-0064}, doi = {10.1007/s10898-016-0450-4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57803}, year = {2016}, abstract = {Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17\% to 19\% on average. Most importantly, more instances can be solved when using OBBT.}, language = {en} } @misc{VigerskeGleixner2016, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1335312}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59377}, year = {2016}, abstract = {This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.}, language = {en} } @misc{RehfeldtHobbieSchoenheitetal.2019, author = {Rehfeldt, Daniel and Hobbie, Hannes and Sch{\"o}nheit, David and Gleixner, Ambros and Koch, Thorsten and M{\"o}st, Dominik}, title = {A massively parallel interior-point solver for linear energy system models with block structure}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74321}, year = {2019}, abstract = {Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers|already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an interior-point solver that exploits common structures of linear energy system models to efficiently run in parallel on distributed memory systems. The solver is designed for linear programs with doubly bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. Special effort has been put into handling large numbers of linking constraints and variables as commonly observed in energy system models. In order to handle this strong linkage, a distributed preconditioning of the Schur complement is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the existing parallel interior-point solver PIPS-IPM. We evaluate the computational performance on energy system models with up to 700 million non-zero entries in the constraint matrix, and with more than 200 million columns and 250 million rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market clearing. It has been widely applied in the literature on energy system analyses during the recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models.}, language = {en} } @misc{D'AndreagiovanniGleixner2016, author = {D'Andreagiovanni, Fabio and Gleixner, Ambros}, title = {Towards an accurate solution of wireless network design problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59010}, year = {2016}, abstract = {The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.}, language = {en} } @misc{GleixnerKempkeKochetal.2019, author = {Gleixner, Ambros and Kempke, Nils-Christian and Koch, Thorsten and Rehfeldt, Daniel and Uslu, Svenja}, title = {First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method}, issn = {1438-0064}, doi = {10.1007/978-3-030-48439-2_13}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74084}, year = {2019}, abstract = {In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.}, language = {en} } @phdthesis{Gleixner2015, author = {Gleixner, Ambros}, title = {Exact and Fast Algorithms for Mixed-Integer Nonlinear Programming}, publisher = {Logos Verlag Berlin}, isbn = {978-3-8325-4190-3}, pages = {341}, year = {2015}, abstract = {Mixed-integer nonlinear programming (MINLP) comprises the broad class of finite-dimensional mathematical optimization problems from mixed-integer linear programming and global optimization. The combination of the two disciplines allows us to construct more accurate models of real-world systems, while at the same time it increases the algorithmic challenges that come with solving them. This thesis presents new methods that improve the numerical reliability and the computational performance of global MINLP solvers. Since state-of-the-art algorithms for nonconvex MINLP fundamentally rely on solving linear programming (LP) relaxations, we address numerical accuracy directly for LP by means of LP iterative refinement: a new algorithm to solve linear programs to arbitrarily high levels of precision. The thesis is supplemented by an exact extension of the LP solver SoPlex, which proves on average 1.85 to 3 times faster than current state-of-the-art software for solving general linear programs exactly over the rational numbers. These methods can be generalized to quadratic programming. We study their application to numerically difficult multiscale LP models for metabolic networks in systems biology. To improve the computational performance of LP-based MINLP solvers, we show how the expensive, but effective, bound-tightening technique called optimization-based bound tightening can be approximated more efficiently via feasibility-based bound tightening. The resulting implementation increases the number of instances that can be solved and reduces the average running time of the MINLP solver SCIP by 17-19\% on hard mixed-integer nonlinear programs. Last, we present branching rules that exploit the presence of nonlinear integer variables, i.e., variables both contained in nonlinear terms and required to be integral. The new branching rules prefer integer variables when performing spatial branching, and favor variables in nonlinear terms when resolving integer infeasibility. They reduce the average running time of SCIP by 17\% on affected instances. Most importantly, all of the new methods enable us to solve problems which could not be solved before, either due to their numerical complexity or because of limited computing resources.}, language = {en} } @misc{GleixnerEiflerGallyetal.2017, author = {Gleixner, Ambros and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gemander, Patrick and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Vigerske, Stefan and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 5.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66297}, year = {2017}, abstract = {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.}, language = {en} } @inproceedings{WitzigBertholdHeinz2019, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, volume = {11494}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_6}, pages = {84 -- 94}, year = {2019}, abstract = {Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part.}, language = {en} } @inproceedings{BertholdStuckeyWitzig2019, author = {Berthold, Timo and Stuckey, Peter and Witzig, Jakob}, title = {Local Rapid Learning for Integer Programs}, volume = {11494}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_5}, pages = {67 -- 83}, year = {2019}, abstract = {Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0, 1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local Rapid Learning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems.}, language = {en} } @article{BestuzhevaHijaziCoffrin2019, author = {Bestuzheva, Ksenia and Hijazi, Hassan and Coffrin, Carleton}, title = {Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching}, volume = {32}, journal = {INFORMS Journal on Computing}, number = {3}, publisher = {INFORMS Institute for Operations Research and the Management Sciences}, address = {5521 Research Park Drive, Suite 200, Catonsville, MD 21228 USA}, doi = {https://doi.org/10.1287/ijoc.2019.0900}, pages = {682 -- 696}, year = {2019}, abstract = {This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the Convex Quadratic relaxation of the Optimal Transmission Switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the Optimal Transmission Switching problem in Power Systems. Using the proposed improvements, along with bound propagation, on 23 medium-size test cases in the PGLib benchmark library with a relaxation gap of more than 1\%, we reduce the gap to less than 1\% on 5 instances. The tightened model has promising computational results when compared to state-of-the-art formulations.}, language = {en} } @inproceedings{AndersonHendelLeBodicetal.2018, author = {Anderson, Daniel and Hendel, Gregor and Le Bodic, Pierre and Viernickel, Jan Merlin}, title = {Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation}, booktitle = {AAAI-19: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence}, year = {2018}, abstract = {We propose a simple and general online method to measure the search progress within the branch-and-bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for Mixed-Integer Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases.}, language = {de} } @inproceedings{GleixnerSteffy2019, author = {Gleixner, Ambros and Steffy, Daniel}, title = {Linear Programming using Limited-Precision Oracles}, booktitle = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, doi = {10.1007/978-3-030-17953-3_30}, pages = {399 -- 412}, year = {2019}, abstract = {Linear programming is a foundational tool for many aspects of integer and combinatorial optimization. This work studies the complexity of solving linear programs exactly over the rational numbers through use of an oracle capable of returning limited-precision LP solutions. It is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. Previous work has often considered oracles that provide solutions of an arbitrary specified precision. While this leads to polynomial-time algorithms, the level of precision required is often unrealistic for practical computation. In contrast, our work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.}, language = {en} } @inproceedings{Serrano2019, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, volume = {11480}, booktitle = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, doi = {10.1007/978-3-030-17953-3_29}, pages = {385 -- 398}, year = {2019}, abstract = {Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.}, language = {en} } @misc{ShinanoAchterbergBertholdetal.2015, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores}, issn = {1438-0064}, doi = {10.1109/IPDPS.2016.56}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56404}, year = {2015}, abstract = {This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.}, language = {en} } @misc{MunguiaOxberryRajanetal.2017, author = {Munguia, Lluis-Miquel and Oxberry, Geoffrey and Rajan, Deepak and Shinano, Yuji}, title = {Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs}, number = {ZIB-Report 17-58}, issn = {1438-0064}, doi = {10.1007/s10589-019-00074-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65517}, year = {2017}, abstract = {PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch \& Bound (B\&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B\&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B\&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores.}, language = {en} } @article{GamrathBertholdHeinzetal.2019, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, volume = {11}, journal = {Mathematical Programming Computation}, number = {4}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {10.1007/s12532-019-00159-1}, pages = {675 -- 702}, year = {2019}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60 \% of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.}, language = {en} } @misc{BertholdStuckeyWitzig2018, author = {Berthold, Timo and Stuckey, Peter and Witzig, Jakob}, title = {Local Rapid Learning for Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71190}, year = {2018}, abstract = {Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0, 1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local Rapid Learning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems.}, language = {en} } @misc{Hendel2018, author = {Hendel, Gregor}, title = {Adaptive Large Neighborhood Search for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71167}, year = {2018}, abstract = {Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search domains, which we call neighborhoods. The decision which neighborhood should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available neighborhoods based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing priorization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some neighborhoods which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP.}, language = {en} } @misc{WitzigBertholdHeinz2018, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71170}, year = {2018}, abstract = {Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part.}, language = {en} } @misc{Serrano2018, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71105}, year = {2018}, abstract = {Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.}, language = {en} } @article{WitzigGleixner2020, author = {Witzig, Jakob and Gleixner, Ambros}, title = {Conflict-Driven Heuristics for Mixed Integer Programming}, volume = {33}, journal = {INFORMS Journal on Computing}, number = {2}, doi = {10.1287/ijoc.2020.0973}, pages = {706 -- 720}, year = {2020}, abstract = {Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.}, language = {en} } @article{GleixnerHendelGamrathetal.2021, author = {Gleixner, Ambros and Hendel, Gregor and Gamrath, Gerald and Achterberg, Tobias and Bastubbe, Michael and Berthold, Timo and Christophel, Philipp M. and Jarck, Kati and Koch, Thorsten and Linderoth, Jeff and L{\"u}bbecke, Marco and Mittelmann, Hans and Ozyurt, Derya and Ralphs, Ted and Salvagnin, Domenico and Shinano, Yuji}, title = {MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library}, volume = {13}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-020-00194-3}, pages = {443 -- 490}, year = {2021}, abstract = {We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data.}, language = {en} } @misc{GleixnerSteffy2019, author = {Gleixner, Ambros and Steffy, Daniel}, title = {Linear Programming using Limited-Precision Oracles}, issn = {1438-0064}, doi = {10.1007/s10107-019-01444-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75316}, year = {2019}, abstract = {Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.}, language = {en} } @misc{GeorgesGleixnerGojicetal.2018, author = {Georges, Alexander and Gleixner, Ambros and Gojic, Gorana and Gottwald, Robert Lion and Haley, David and Hendel, Gregor and Matejczyk, Bartlomiej}, title = {Feature-Based Algorithm Selection for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68362}, year = {2018}, abstract = {Mixed integer programming is a versatile and valuable optimization tool. However, solving specific problem instances can be computationally demanding even for cutting-edge solvers. Such long running times are often significantly reduced by an appropriate change of the solver's parameters. In this paper we investigate "algorithm selection", the task of choosing among a set of algorithms the ones that are likely to perform best for a particular instance. In our case, we treat different parameter settings of the MIP solver SCIP as different algorithms to choose from. Two peculiarities of the MIP solving process have our special attention. We address the well-known problem of performance variability by using multiple random seeds. Besides solving time, primal dual integrals are recorded as a second performance measure in order to distinguish solvers that timed out. We collected feature and performance data for a large set of publicly available MIP instances. The algorithm selection problem is addressed by several popular, feature-based methods, which have been partly extended for our purpose. Finally, an analysis of the feature space and performance results of the selected algorithms are presented.}, language = {en} } @inproceedings{CaoGleixnerMiltenberger2016, author = {Cao, Karl-Ki{\^e}n and Gleixner, Ambros and Miltenberger, Matthias}, title = {Methoden zur Reduktion der Rechenzeit linearer Optimierungsmodelle in der Energiewirtschaft - Eine Performance-Analyse}, booktitle = {EnInnov 2016: 14. Symposium Energieinnovation 2016}, year = {2016}, abstract = {Dieser Beitrag stellt m{\"o}gliche Ans{\"a}tze zur Reduktion der Rechenzeit von linearen Optimierungsproblemen mit energiewirtschaftlichem Anwendungshintergrund vor. Diese Ans{\"a}tze bilden im Allgemeinen die Grundlage f{\"u}r konzeptionelle Strategien zur Beschleunigung von Energiesystemmodellen. Zu den einfachsten Beschleunigungsstrategien z{\"a}hlt die Verkleinerung der Modelldimensionen, was beispielsweise durch {\"A}ndern der zeitlichen, r{\"a}umlichen oder technologischen Aufl{\"o}sung eines Energiesystemmodells erreicht werden kann. Diese Strategien sind zwar h{\"a}ufig ein Teil der Methodik in der Energiesystemanalyse, systematische Benchmarks zur Bewertung ihrer Effektivit{\"a}t werden jedoch meist nicht durchgef{\"u}hrt. Die vorliegende Arbeit adressiert genau diesen Sachverhalt. Hierzu werden Modellinstanzen des Modells REMix in verschiedenen Gr{\"o}ßenordnungen mittels einer Performance-Benchmark-Analyse untersucht. Die Ergebnisse legen zum einen den Schluss nahe, dass verk{\"u}rzte Betrachtungszeitr{\"a}ume das gr{\"o}ßte Potential unter den hier analysierten Strategien zur Reduktion von Rechenzeit bieten. Zum anderen empfiehlt sich die Verwendung des Barrier-L{\"o}sungsverfahrens mit multiplen Threads unter Vernachl{\"a}ssigung des Cross-Over.}, language = {de} } @inproceedings{D'AndreagiovanniGleixner2016, author = {D'Andreagiovanni, Fabio and Gleixner, Ambros}, title = {Towards an accurate solution of wireless network design problems}, booktitle = {Cerulli R., Fujishige S., Mahjoub A. (eds) Combinatorial Optimization. ISCO 2016}, doi = {10.1007/978-3-319-45587-7_12}, pages = {135 -- 147}, year = {2016}, abstract = {The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.}, language = {en} } @inproceedings{DevriendtGleixnerNordstroem2020, author = {Devriendt, Jo and Gleixner, Ambros and Nordstr{\"o}m, Jakob}, title = {Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search}, volume = {12296}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020}, publisher = {Springer}, pages = {xxiv -- xxvi}, year = {2020}, abstract = {Conflict-driven Pseudo-Boolean (PB) solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though PB solvers have the potential to be exponentially more efficient than CDCL solvers in theory, in practice they can sometimes get hopelessly stuck even when the linear program (LP) relaxation is infeasible over the reals. Inspired by mixed integer programming (MIP), we address this problem by interleaving incremental LP solving with cut generation within the conflict-driven PB search. This hybrid approach, which for the first time combines MIP techniques with full-blown conflict analysis over linear inequalities using the cutting planes method, significantly improves performance on a wide range of benchmarks, approaching a "best of two worlds" scenario between SAT-style conflict-driven search and MIP-style branch-and-cut.}, language = {en} } @misc{MuellerKuhlmannVigerske2017, author = {M{\"u}ller, Benjamin and Kuhlmann, Renke and Vigerske, Stefan}, title = {On the performance of NLP solvers within global MINLP solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_84}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64504}, year = {2017}, abstract = {Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.}, language = {en} } @inproceedings{HendelMiltenbergerWitzig2018, author = {Hendel, Gregor and Miltenberger, Matthias and Witzig, Jakob}, title = {Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms}, booktitle = {OR 2018: International Conference on Operations Research}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{MuellerKuhlmannVigerske2018, author = {M{\"u}ller, Benjamin and Kuhlmann, Renke and Vigerske, Stefan}, title = {On the performance of NLP solvers within global MINLP solvers}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_84}, pages = {633 -- 639}, year = {2018}, abstract = {Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.}, language = {en} } @inproceedings{MuellerMuñozGasseetal.2020, author = {M{\"u}ller, Benjamin and Muñoz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming}, booktitle = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, doi = {10.1007/978-3-030-45771-6_25}, pages = {322 -- 337}, year = {2020}, abstract = {The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm's ability to generate strong dual bounds through extensive computational experiments.}, language = {en} } @misc{WitzigGleixner2019, author = {Witzig, Jakob and Gleixner, Ambros}, title = {Conflict-Driven Heuristics for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1287/ijoc.2020.0973}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72204}, year = {2019}, abstract = {Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.}, language = {en} } @misc{HendelMiltenbergerWitzig2018, author = {Hendel, Gregor and Miltenberger, Matthias and Witzig, Jakob}, title = {Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69563}, year = {2018}, abstract = {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.}, language = {en} } @misc{GamrathKochMartinetal.2013, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in Presolving for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/s12532-015-0083-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42530}, year = {2013}, abstract = {Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice.}, language = {en} } @incollection{GamrathBertholdHeinzetal.2015, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-Based Primal Heuristics for Mixed Integer Programming}, volume = {13}, booktitle = {Optimization in the Real World}, publisher = {Springer Japan}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_3}, pages = {37 -- 53}, 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{WitzigBertholdHeinz2016, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Experiments with Conflict Analysis in Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/978-3-319-59776-8_17}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61087}, year = {2016}, abstract = {The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The result of the analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. The dual LP solution provides a set of multipliers that can be used to generate a single new globally valid linear constraint. The main contribution of this short paper is an empirical evaluation of two ways to combine both approaches. Experiments are carried out on general MIP instances from standard public test sets such as Miplib2010; the presented algorithms have been implemented within the non-commercial MIP solver SCIP. Moreover, we present a pool-based approach to manage conflicts which addresses the way a MIP solver traverses the search tree better than aging strategies known from SAT solving.}, language = {en} } @misc{GleixnerMaherMuelleretal.2017, author = {Gleixner, Ambros and Maher, Stephen J. and M{\"u}ller, Benjamin and Pedroso, Jo{\~a}o Pedro}, title = {Exact Methods for Recursive Circle Packing}, doi = {10.1007/s10479-018-3115-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62039}, year = {2017}, abstract = {Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig-Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a "price-and-verify" algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.}, language = {en} } @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} } @article{RehfeldtKoch2019, 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}, volume = {29}, journal = {SIAM Journal on Optimization}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/17M1145963}, pages = {369 -- 398}, year = {2019}, 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{FujisawaShinanoWaki2015, author = {Fujisawa, Katsuki and Shinano, Yuji and Waki, Hayato}, title = {Optimization in the Real World}, volume = {13}, journal = {Mathematics for Industry (MFI)}, publisher = {Springer Tokyo Heidelberg New York Dordrecht London}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2}, year = {2015}, language = {en} } @inproceedings{BreuerBussieckCaoetal.2018, 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}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_85}, pages = {641 -- 647}, year = {2018}, 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} } @article{FuriniTraversiBelottietal.2019, author = {Furini, Fabio and Traversi, Emiliano and Belotti, Pietro and Frangioni, Antonio and Gleixner, Ambros and Gould, Nick and Liberti, Leo and Lodi, Andrea and Misener, Ruth and Mittelmann, Hans and Sahinidis, Nikolaos V. and Vigerske, Stefan and Wiegele, Angelika}, title = {QPLIB: A Library of Quadratic Programming Instances}, volume = {11}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-018-0147-4}, pages = {237 -- 265}, year = {2019}, abstract = {This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.}, language = {en} } @phdthesis{Pulaj2017, author = {Pulaj, Jonad}, title = {Cutting Planes for Union-Closed Families}, year = {2017}, abstract = {Frankl's (union-closed sets) conjecture states that for any nonempty finite union-closed (UC) family of distinct sets there exists an element in at least half of the sets. Poonen's Theorem characterizes the existence of weights which determine whether a given UC family ensures Frankl's conjecture holds for all UC families which contain it. The weight systems are nontrivial to identify for a given UC family, and methods to determine such weight systems have led to several other open questions and conjectures regarding structures in UC families. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen's Theorem using computational integer programming coupled with redundant verification routines that ensure correctness. We find over one hundred previously unknown families of sets which ensure Frankl's conjecture holds for all families that contain any of them. This improves significantly on all previous results of the kind. Our framework allows us to answer several open questions and conjectures regarding structural properties of UC families, including proving the 3-sets conjecture of Morris from 2006 which characterizes the minimum number of 3-sets that ensure Frankl's conjecture holds for all families that contain them. Furthermore, our method provides a general algorithmic road-map for improving other known results and uncovering structures in UC families.}, language = {en} } @inproceedings{CheungGleixnerSteffy2017, author = {Cheung, Kevin K. H. and Gleixner, Ambros and Steffy, Daniel}, title = {Verifying Integer Programming Results}, volume = {10328}, booktitle = {F. Eisenbrand and J. Koenemann, eds., Integer Programming and Combinatorial Optimization: 19th International Conference, IPCO 2017}, doi = {10.1007/978-3-319-59250-3_13}, pages = {148 -- 160}, year = {2017}, 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 MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of 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 MIP 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} } @inproceedings{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {SCIP-Jack—a solver for STP and variants with parallelization extensions: An update}, booktitle = {Operations Research Proceedings 2017}, pages = {191 -- 196}, 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} } @article{VierhausFuegenschuhGottwaldetal.2017, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin and Gottwald, Robert Lion and Gr{\"o}sser, Stefan}, title = {Using white-box nonlinear optimization methods in system dynamics policy improvement}, volume = {33}, journal = {System Dynamics Review}, number = {2}, doi = {10.1002/sdr.1583}, pages = {138 -- 168}, year = {2017}, abstract = {We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published "towards a global equilibrium" run with equal cost of intervention.}, language = {en} } @inproceedings{SchadeSchlechteWitzig2018, author = {Schade, Stanley and Schlechte, Thomas and Witzig, Jakob}, title = {Structure-based Decomposition for Pattern-Detection for Railway Timetables}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_95}, pages = {715 -- 721}, year = {2018}, 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} } @masterthesis{Wischlinsky2017, type = {Bachelor Thesis}, author = {Wischlinsky, William}, title = {Feasibility-based bound tightening via linear programming}, year = {2017}, 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} } @article{WeberSagerGleixner2019, author = {Weber, Tobias and Sager, Sebastian and Gleixner, Ambros}, title = {Solving Quadratic Programs to High Precision using Scaled Iterative Refinement}, volume = {11}, journal = {Mathematical Programming Computation}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/s12532-019-00154-6}, pages = {421 -- 455}, year = {2019}, 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} } @article{Gamrath2014, author = {Gamrath, Gerald}, title = {Improving strong branching by domain propagation}, volume = {2}, journal = {EURO Journal on Computational Optimization}, number = {3}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {10.1007/s13675-014-0021-8}, pages = {99 -- 122}, year = {2014}, abstract = {One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique MIP solvers usually apply at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, the state-of-the-art hybrid branching rule can be improved this way as well. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013.}, 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{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} } @article{YokoyamaShinanoTaniguchietal.2015, 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}, volume = {92}, journal = {Energy Conversion and Management}, doi = {10.1016/j.enconman.2014.12.020}, pages = {92 -- 104}, year = {2015}, 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 to be minimized 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} } @incollection{YokoyamaShinano2015, author = {Yokoyama, Ryohei and Shinano, Yuji}, title = {MILP Approaches to Optimal Design and Operation of Distributed Energy Systems}, volume = {Volume 13}, booktitle = {Optimization in the Real World}, publisher = {Springer}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_9}, pages = {157 -- 176}, year = {2015}, abstract = {Energy field is one of the practical areas to which optimization can contribute significantly. In this chapter, the application of mixed-integer linear programming (MILP) approaches to optimal design and operation of distributed energy systems is described. First, the optimal design and operation problems are defined, and relevant previous work is reviewed. Then, an MILP method utilizing the hierarchical relationship between design and operation variables is presented. In the optimal design problem, integer variables are used to express the types, capacities, numbers, operation modes, and on/off states 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. The presented method can change the enumeration tree for the branching and bounding procedures, and can search the optimal solution very efficiently. Finally, future work in relation to this method is described.}, 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} } @article{GamrathKochMaheretal.2017, 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}, volume = {9}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-016-0114-x}, pages = {231 -- 296}, year = {2017}, 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} } @inproceedings{ShinanoBertholdHeinz2016, author = {Shinano, Yuji and Berthold, Timo and Heinz, Stefan}, title = {A First Implementation of ParaXpress: Combining Internal and External Parallelization to Solve MIPs on Supercomputers}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, doi = {10.1007/978-3-319-42432-3_38}, pages = {308 -- 316}, year = {2016}, language = {en} } @book{GreuelKochPauleetal.2016, author = {Greuel, Martin and Koch, Thorsten and Paule, Peter and Sommese, Andrew}, title = {Mathematical Software - ICMS 2016, 5th Int. Conf. Berlin, Germany, July 11-14, 2016, Proceedings}, volume = {9725}, journal = {Lecture Notes in Computer Science (LNCS)}, publisher = {Springer}, isbn = {978-3-319-42431-6}, doi = {10.1007/978-3-319-42432-3}, pages = {XXIV, 532}, year = {2016}, language = {en} } @inproceedings{BertholdFarmerHeinzetal.2016, author = {Berthold, Timo and Farmer, James and Heinz, Stefan and Perregaard, Michael}, title = {Parallelization of the FICO Xpress-Optimizer}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, doi = {10.1007/978-3-319-42432-3_31}, pages = {251 -- 258}, year = {2016}, language = {en} } @inproceedings{ChraparyRen2016, author = {Chrapary, Hagen and Ren, Yue}, title = {The Software Portal swMATH: A State of the Art Report and Next Steps}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings}, doi = {10.1007/978-3-319-42432-3_49}, pages = {397 -- 402}, year = {2016}, language = {en} } @incollection{WuMaher2017, author = {Wu, Cheng-Lung and Maher, Stephen J.}, title = {Airline scheduling and disruption management}, booktitle = {L. Budd, S. Ison, eds., Air transportation management: an international perspective}, publisher = {Routledge}, address = {New York}, isbn = {9781472451064}, pages = {151 -- 167}, year = {2017}, language = {en} } @article{GleixnerBertholdMuelleretal.2017, author = {Gleixner, Ambros and Berthold, Timo and M{\"u}ller, Benjamin and Weltge, Stefan}, title = {Three Enhancements for Optimization-Based Bound Tightening}, volume = {67}, journal = {Journal of Global Optimization}, number = {4}, doi = {10.1007/s10898-016-0450-4}, pages = {731 -- 757}, year = {2017}, abstract = {Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17\% to 19\% on average. Most importantly, more instances can be solved when using OBBT.}, language = {en} } @inproceedings{YokoyamaNakamuraWakuietal.2016, author = {Yokoyama, Ryohei and Nakamura, Ryo and Wakui, Tetsuya and Shinano, Yuji}, title = {Evaluation of Performance Robustness of a Gas Turbine Cogeneration Plant Based on a Mixed-Integer Linear Model}, volume = {3}, booktitle = {ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition}, doi = {doi:10.1115/GT2016-56217}, pages = {1 -- 9}, year = {2016}, abstract = {In designing energy supply systems, designers are requested to rationally determine equipment types, capacities, and numbers in consideration of equipment operational strategies corresponding to seasonal and hourly variations in energy demands. However, energy demands have some uncertainty at the design stage, and the energy demands which become certain at the operation stage may differ from those estimated at the design stage. Therefore, designers should consider that energy demands have some uncertainty, evaluate the performance robustness against the uncertainty, and design the systems to heighten the robustness. Especially, this issue is important for cogeneration plants, because their performances depend significantly on both heat and power demands. Although robust optimal design methods of energy supply systems under uncertain energy demands were developed, all of them are based on linear models for energy supply systems. However, it is still a hard challenge to develop a robust optimal design method even based on a mixed-integer linear model. At the first step for this challenge, in this paper, a method of evaluating the performance robustness of energy supply systems under uncertain energy demands is proposed based on a mixed-integer linear model. This problem is formulated as a bilevel mixed-integer linear programming one, and a sequential solution method is applied to solve it approximately by discretizing uncertain energy demands within their intervals. In addition, a hierarchical optimization method in consideration of the hierarchical relationship between design and operation variables is applied to solve large scale problems efficiently. Through a case study on a gas turbine cogeneration plant for district energy supply, the validity and effectiveness of the proposed method and features of the performance robustness of the plant are clarified.}, language = {en} } @article{MaherDesaulniersSoumis2018, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints}, volume = {264}, journal = {European Journal of Operational Research}, number = {2}, doi = {10.1016/j.ejor.2017.06.041}, pages = {534 -- 547}, year = {2018}, 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 satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.}, language = {en} } @article{ShinanoHeinzVigerskeetal.2018, author = {Shinano, Yuji and Heinz, Stefan and Vigerske, Stefan and Winkler, Michael}, title = {FiberSCIP - A shared memory parallelization of SCIP}, volume = {30}, journal = {INFORMS Journal on Computing}, number = {1}, doi = {10.1287/ijoc.2017.0762}, pages = {11 -- 30}, year = {2018}, 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 mixed-integer linear programming 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, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaetal.2017, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Multiobjective Optimal Design of a Gas Turbine Cogeneration Plant by a Revised Hierarchical Optimization Method}, volume = {3}, booktitle = {ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition}, doi = {doi:10.1115/GT2017-64296}, pages = {1 -- 14}, year = {2017}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine design specifications in consideration of operational strategies corresponding to energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. A MILP method utilizing the hierarchical relationship between design and operation variables have been proposed to solve them efficiently. However, it cannot necessarily be effective to multi-objective optimal design problems because of the existence of a large number of competing design candidates. In this paper, the hierarchical MILP method is revised from the viewpoint of computation efficiency so that it can be applied practically to multi-objective optimal design problems. At the lower level, the order of the optimal operation problems to be solved is changed based on incumbents obtained previously to increase a lower bound for the optimal value of the combined objective function and reduce the number of the optimal operation problems to be solved. At the upper level, a lower bound for the optimal value of the combined objective function is incorporated into the solution method to reduce the number of the design candidates to be generated. This revised hierarchical MILP method is applied to a multiobjective optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.}, language = {en} } @inproceedings{Shinano2018, author = {Shinano, Yuji}, title = {The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_20}, pages = {143 -- 149}, year = {2018}, 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} } @inproceedings{GamrathSchubert2018, author = {Gamrath, Gerald and Schubert, Christoph}, title = {Measuring the impact of branching rules for mixed-integer programming}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_23}, pages = {165 -- 170}, year = {2018}, 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} } @article{ShinanoBertholdHeinz2018, author = {Shinano, Yuji and Berthold, Timo and Heinz, Stefan}, title = {ParaXpress: An Experimental Extension of the FICO Xpress-Optimizer to Solve Hard MIPs on Supercomputers}, volume = {33}, journal = {Optimization Methods \& Software}, number = {3}, doi = {10.1080/10556788.2018.1428602}, pages = {530 -- 539}, year = {2018}, abstract = {The Ubiquity Generator (UG) is a general framework for the external parallelization of mixed integer programming (MIP) solvers. In this paper, we present ParaXpress, a distributed memory parallelization of the powerful commercial MIP solver FICO Xpress. Besides sheer performance, an important feature of Xpress is that it provides an internal parallelization for shared memory systems. When aiming for a best possible performance of ParaXpress on a supercomputer, the question arises how to balance the internal Xpress parallelization and the external parallelization by UG against each other. We provide computational experiments to address this question and we show computational results for running ParaXpress on a Top500 supercomputer, using up to 43,344 cores in parallel.}, language = {en} } @misc{Schubert2017, type = {Master Thesis}, author = {Schubert, Christoph}, title = {Multi-Level Lookahead Branching}, year = {2017}, 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{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} } @inproceedings{Hendel2015, author = {Hendel, Gregor}, title = {Enhancing MIP Branching Decisions by Using the Sample Variance of Pseudo Costs}, volume = {9075}, booktitle = {Integration of AI and OR Techniques in Constraint Programming}, doi = {10.1007/978-3-319-18008-3_14}, pages = {199 -- 214}, 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 specialized version of a two-sample Student's 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} }