TY - GEN A1 - Hendel, Gregor A1 - Miltenberger, Matthias A1 - Witzig, Jakob T1 - Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms N2 - State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics as well as Simplex pricing strategies. For each class we propose a selection strategy that is updated based on the observed runtime behavior, aiming to ultimately select only the best algorithms for a given instance. We review several common strategies for such a selection scenario under uncertainty, also known as Multi Armed Bandit Problem. In order to apply those bandit strategies, we carefully design reward functions to rank and compare each individual heuristic or pricing algorithm within its respective class. Finally, we discuss the computational benefits of using the proposed adaptive selection within the \scip Optimization Suite on publicly available MIP instances. T3 - ZIB-Report - 18-36 KW - mixed integer programming KW - primal heuristics KW - multi armed bandit Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69563 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in Presolving for Mixed Integer Programming N2 - 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. T3 - ZIB-Report - 13-48 KW - mixed-integer programming KW - presolving KW - preprocessing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42530 SN - 1438-0064 ER - TY - CHAP A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-Based Primal Heuristics for Mixed Integer Programming T2 - Optimization in the Real World N2 - 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. Y1 - 2015 SN - 978-4-431-55419-6 U6 - https://doi.org/10.1007/978-4-431-55420-2_3 VL - 13 SP - 37 EP - 53 PB - Springer Japan ER - TY - GEN A1 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - Experiments with Conflict Analysis in Mixed Integer Programming N2 - 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. T3 - ZIB-Report - 16-63 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61087 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Maher, Stephen J. A1 - Müller, Benjamin A1 - Pedroso, João Pedro T1 - Exact Methods for Recursive Circle Packing N2 - 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. T3 - ZIB-Report - 17-07 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62039 ER - TY - GEN A1 - Cheung, Kevin K. H. A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Verifying Integer Programming Results N2 - 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. T3 - ZIB-Report - 16-58 KW - correctness, verification, proof, certificate, optimality, infeasibility, mixed-integer linear programming Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61044 SN - 1438-0064 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem JF - SIAM Journal on Optimization N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1137/17M1145963 VL - 29 IS - 1 SP - 369 EP - 398 PB - Society for Industrial and Applied Mathematics ER - TY - GEN A1 - Fujisawa, Katsuki A1 - Shinano, Yuji A1 - Waki, Hayato T1 - Optimization in the Real World T2 - Mathematics for Industry (MFI) Y1 - 2015 SN - 978-4-431-55419-6 U6 - https://doi.org/10.1007/978-4-431-55420-2 VL - 13 PB - Springer Tokyo Heidelberg New York Dordrecht London ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten ED - Hamadi, Youssef T1 - Parallel Solvers for Mixed Integer Linear Optimization T2 - Handbook of Parallel Constraint Reasoning Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-63516-3_8 SP - 283 EP - 336 PB - Springer Nature ER - TY - JOUR A1 - Furini, Fabio A1 - Traversi, Emiliano A1 - Belotti, Pietro A1 - Frangioni, Antonio A1 - Gleixner, Ambros A1 - Gould, Nick A1 - Liberti, Leo A1 - Lodi, Andrea A1 - Misener, Ruth A1 - Mittelmann, Hans A1 - Sahinidis, Nikolaos V. A1 - Vigerske, Stefan A1 - Wiegele, Angelika T1 - QPLIB: A Library of Quadratic Programming Instances JF - Mathematical Programming Computation N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-018-0147-4 VL - 11 IS - 2 SP - 237 EP - 265 ER - TY - CHAP A1 - Cheung, Kevin K. H. A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Verifying Integer Programming Results T2 - F. Eisenbrand and J. Koenemann, eds., Integer Programming and Combinatorial Optimization: 19th International Conference, IPCO 2017 N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-59250-3_13 VL - 10328 SP - 148 EP - 160 ER - TY - CHAP A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - SCIP-Jack—a solver for STP and variants with parallelization extensions: An update T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 SP - 191 EP - 196 ER - TY - CHAP A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_95 SP - 715 EP - 721 PB - Springer International Publishing ER - TY - GEN A1 - Gleixner, Ambros A1 - Bastubbe, Michael A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Schubert, Christoph A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Walter, Matthias A1 - Wegscheider, Fabian A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 6.0 N2 - 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. T3 - ZIB-Report - 18-26 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69361 SN - 1438-0064 ER - TY - GEN A1 - Weber, Tobias A1 - Sager, Sebastian A1 - Gleixner, Ambros T1 - Solving Quadratic Programs to High Precision using Scaled Iterative Refinement N2 - 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 Mészáros benchmark library. T3 - ZIB-Report - 18-04 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68152 SN - 1438-0064 ER - TY - JOUR A1 - Weber, Tobias A1 - Sager, Sebastian A1 - Gleixner, Ambros T1 - Solving Quadratic Programs to High Precision using Scaled Iterative Refinement JF - Mathematical Programming Computation N2 - 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 Mészáros benchmark library. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-019-00154-6 VL - 11 SP - 421 EP - 455 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Hendel, Gregor A1 - Anderson, Daniel A1 - Le Bodic, Pierre A1 - Pfetsch, Marc T1 - Estimating the Size of Branch-And-Bound Trees JF - INFORMS Journal on Computing N2 - This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP. Y1 - 2021 U6 - https://doi.org/10.1287/ijoc.2021.1103 ER - TY - JOUR A1 - Csizmadia, Zsolt A1 - Berthold, Timo T1 - The confined primal integral: a measure to benchmark heuristic MINLP solvers against global MINLP solvers JF - Mathematical Programming N2 - It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and solution quality. It emphasizes the early part of the solution process by using an exponential decay. Thereby, it avoids that the order of solvers can be inverted by choosing an arbitrarily large time limit. We provide a closed analytic formula to compute the confined primal integral a posteriori and an incremental update formula to compute it during the run of an algorithm. For the latter, we show that we can drop one of the main assumptions of the primal integral, namely the knowledge of a fixed reference solution to compare against. Furthermore, we prove that the confined primal integral is a transitive measure when comparing local solves with different final solution values. Finally, we present a computational experiment where we compare a local MINLP solver that uses certain classes of cutting planes against a solver that does not. Both versions show very different tendencies w.r.t. average running time and solution quality, and we use the confined primal integral to argue which of the two is the preferred setting. Y1 - 2020 U6 - https://doi.org/10.1007/s10107-020-01547-5 ER - TY - JOUR A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 JF - Mathematical Programming Computation Y1 - 2011 UR - http://mpc.zib.de/index.php/MPC/article/view/56 U6 - https://doi.org/10.1007/s12532-011-0025-9 VL - 3 IS - 2 SP - 103 EP - 163 ER - TY - JOUR A1 - Gamrath, Gerald ED - Gomes, Carla ED - Sellmann, Meinolf T1 - Improving strong branching by propagation JF - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems N2 - Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers. It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time. Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38171-3_25 VL - 7874 SP - 347 EP - 354 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Gamrath, Gerald A1 - Lübbecke, Marco ED - Festa, P. T1 - Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs JF - Experimental Algorithms Y1 - 2010 U6 - https://doi.org/10.1007/978-3-642-13193-6_21 VL - 6049 SP - 239 EP - 252 PB - Springer-Verlag CY - Berlin ER - TY - JOUR A1 - Gamrath, Gerald T1 - Improving strong branching by domain propagation JF - EURO Journal on Computational Optimization N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1007/s13675-014-0021-8 VL - 2 IS - 3 SP - 99 EP - 122 PB - Springer CY - Berlin Heidelberg ER - TY - JOUR A1 - Gleixner, Ambros A1 - Held, Harald A1 - Huang, Wei A1 - Vigerske, Stefan T1 - Towards globally optimal operation of water supply networks JF - Numerical Algebra, Control and Optimization N2 - This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem. Y1 - 2012 U6 - https://doi.org/10.3934/naco.2012.2.695 VL - 2 IS - 4 SP - 695 EP - 711 ER - TY - CHAP A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - SCIP Optimization Suite を利用した 混合整数(線形/非線形) 計画問題の解法 T2 - Proceedings of the 24th RAMP symposium. The Operations Society of Japan, RAMP: Research Association of Mathematical Programming N2 - この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる. N2 - This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how in concert these can be used to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview over available interfaces, and outline plans for future development. Y1 - 2012 SP - 165 EP - 192 ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Analyzing the computational impact of MIQCP solver components JF - Numerical Algebra, Control and Optimization N2 - We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances. Y1 - 2012 U6 - https://doi.org/10.3934/naco.2012.2.739 VL - 2 IS - 4 SP - 739 EP - 748 ER - TY - CHAP A1 - Hendel, Gregor A1 - Berthold, Timo A1 - Achterberg, Tobias T1 - Rounding and Propagation Heuristics for Mixed Integer Programming T2 - Operations Research Proceedings 2011 N2 - Primal heuristics are an important component of state-of-the-art codes for mixed integer programming. In this paper, we focus on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation). We give an overview of eight different approaches. To assess the impact of these primal heuristics on the ability to find feasible solutions, in particular early during search, we introduce a new performance measure, the primal integral. Computational experiments evaluate this and other measures on MIPLIB~2010 benchmark instances. Y1 - 2011 SP - 71 EP - 76 ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP JF - Mathematical Programming N2 - We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers. Y1 - 2014 U6 - https://doi.org/10.1007/s10107-013-0635-2 VL - 144 IS - 1-2 SP - 315 EP - 346 ER - TY - GEN A1 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP N2 - 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. T3 - ZIB-Report - 13-55 KW - parallel KW - branch-and-bound KW - deterministic parallelism KW - constraint integer programming KW - mixed integer programming KW - mixed integer nonlinear programming KW - SCIP KW - MIP KW - MINLP Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42595 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald T1 - Improving strong branching by domain propagation N2 - 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 usually used 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, also the state-of-the-art hybrid branching rule can be improved this way. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013. T3 - ZIB-Report - 13-47 KW - mixed-integer programming KW - branch-and-bound KW - branching rule KW - variable selection KW - strong branching KW - domain propagation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42546 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Melchiori, Anna A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Salvagnin, Domenico T1 - Branching on multi-aggregated variables N2 - 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. T3 - ZIB-Report - 15-10 KW - mixed-integer programming, branch-and-bound, branching rule, strong branching Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53829 SN - 1438-0064 ER - TY - GEN A1 - Witzig, Jakob A1 - Gamrath, Gerald A1 - Hiller, Benjamin T1 - Reoptimization Techniques in MIP Solvers N2 - 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. T3 - ZIB-Report - 15-24 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54375 SN - 1438-0064 ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - 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. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Winkler, Michael A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 3.2 N2 - 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. T3 - ZIB-Report - 15-60 KW - mixed-integer linear and nonlinear programming KW - MIP solver KW - MINLP solver KW - linear programming KW - LP solver KW - simplex method KW - modeling KW - parallel branch-and-bound KW - branch-cut-and-price framework KW - generic column generation KW - Steiner tree solver KW - multi-criteria optimization KW - mixed-integer semidefinite programming Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57675 SN - 1438-0064 ER - TY - GEN A1 - Ballerstein, Martin A1 - Michaels, Dennis A1 - Vigerske, Stefan T1 - Linear Underestimators for bivariate functions with a fixed convexity behavior N2 - 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. T3 - ZIB-Report - 13-02 KW - bivariate functions KW - convex envelope KW - global optimization KW - linear underestimator Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17641 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume T1 - Picos Documentation. Release 0.1.1. N2 - PICOS is a user friendly interface to several conic and integer programming solvers, very much like YALMIP under MATLAB. The main motivation for PICOS is to have the possibility to enter an optimization problem as a high level model, and to be able to solve it with several different solvers. Multidimensional and matrix variables are handled in a natural fashion, which makes it painless to formulate a SDP or a SOCP. This is very useful for educational purposes, and to quickly implement some models and test their validity on simple examples. Furthermore, with PICOS you can take advantage of the python programming language to read and write data, construct a list of constraints by using python list comprehensions, take slices of multidimensional variables, etc. T3 - ZIB-Report - 12-48 KW - mathematical programming KW - SDP KW - SOCP KW - python Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17396 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Shift-And-Propagate N2 - 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. T3 - ZIB-Report - 13-03 KW - primal heuristic KW - mixed integer programming KW - domain propagation KW - rounding Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17596 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald T1 - Improving strong branching by propagation N2 - Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers. It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time. T3 - ZIB-Report - 12-46 KW - mixed-integer programming KW - branch-and-bound KW - branching rule KW - strong branching KW - domain propagation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17701 SN - 1438-0064 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack – A solver for STP and variants with parallelization extensions JF - Mathematical Programming Computation N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/s12532-016-0114-x VL - 9 IS - 2 SP - 231 EP - 296 ER - TY - CHAP A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Heinz, Stefan T1 - A First Implementation of ParaXpress: Combining Internal and External Parallelization to Solve MIPs on Supercomputers T2 - Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-42432-3_38 SP - 308 EP - 316 ER - TY - CHAP A1 - Berthold, Timo A1 - Farmer, James A1 - Heinz, Stefan A1 - Perregaard, Michael T1 - Parallelization of the FICO Xpress-Optimizer T2 - Mathematical Software - ICMS 2016, 5th International Conference Berlin, Germany, July 11-14, 2016 Proceedings Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-42432-3_31 SP - 251 EP - 258 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Berthold, Timo A1 - Müller, Benjamin A1 - Weltge, Stefan T1 - Three Enhancements for Optimization-Based Bound Tightening JF - Journal of Global Optimization N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/s10898-016-0450-4 VL - 67 IS - 4 SP - 731 EP - 757 ER - TY - JOUR A1 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP JF - INFORMS Journal on Computing N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1287/ijoc.2017.0762 VL - 30 IS - 1 SP - 11 EP - 30 ER - TY - CHAP A1 - Gottwald, Robert Lion A1 - Maher, Stephen J. A1 - Shinano, Yuji T1 - Distributed Domain Propagation T2 - 16th International Symposium on Experimental Algorithms (SEA 2017) N2 - Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite its 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 the domain of a variable has been reduced. In this paper we introduce distributed domain propagation, a technique that shares bound tightenings across solvers to trigger further domain propagations. We investigate its impact 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. Y1 - 2017 U6 - https://doi.org/10.4230/LIPIcs.SEA.2017.6 VL - 75 SP - 6:1 EP - 6:11 ER - TY - GEN A1 - Shinano, Yuji T1 - The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound N2 - 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. T3 - ZIB-Report - 17-60 KW - Parallelization, Branch-and-bound, Mixed Integer Programming, UG, ParaSCIP, FiberSCIP, ParaXpress, FiberXpress, SCIP-Jack Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65545 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji T1 - The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_20 SP - 143 EP - 149 PB - Springer International Publishing ER - TY - CHAP A1 - Gamrath, Gerald A1 - Schubert, Christoph T1 - Measuring the impact of branching rules for mixed-integer programming T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_23 SP - 165 EP - 170 PB - Springer International Publishing ER - TY - JOUR A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Heinz, Stefan T1 - ParaXpress: An Experimental Extension of the FICO Xpress-Optimizer to Solve Hard MIPs on Supercomputers JF - Optimization Methods & Software N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1080/10556788.2018.1428602 VL - 33 IS - 3 SP - 530 EP - 539 ER - TY - GEN A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming N2 - 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. T3 - ZIB-Report - 16-45 KW - supply chain management, supply network optimization, mixed-integer linear programming, primal heuristics, numerical stability, large-scale optimization Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61107 SN - 1438-0064 ER - TY - GEN A1 - Gottwald, Robert Lion A1 - Maher, Stephen J. A1 - Shinano, Yuji T1 - Distributed domain propagation N2 - 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. T3 - ZIB-Report - 16-71 KW - mixed integer programming KW - parallelization KW - domain propagation KW - portfolio solvers Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61380 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack - A solver for STP and variants with parallelization extensions N2 - 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. T3 - ZIB-Report - 15-27 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54648 SN - 1438-0064 N1 - A revised version is provided here: http://nbn-resolving.de/urn:nbn:de:0297-zib-60170. ER -