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 - THES A1 - Berthold, Timo T1 - Heuristic algorithms in global MINLP solvers N2 - In the literature for mixed integer programming, heuristic algorithms (particularly primal heuristics) are often considered as stand-alone procedures; in that context, heuristics are treated as an alternative to solving a problem to proven optimality. This conceals the fact that heuristic algorithms are a fundamental component of state-of-the-art global solvers for mixed integer linear programming (MIP) and mixed integer nonlinear programming (MINLP). In the present thesis, we focus on this latter aspect; we study heuristic algorithms that are tightly integrated within global MINLP solvers and analyze their impact on the overall solution process. Our contributions comprise generalizations of primal heuristics for MIP towards MINLP as well as novel ideas for MINLP primal heuristics and for heuristic algorithms to take branching decisions and to collect global information in MIP. These are: - Shift-and-Propagate, a novel propagation heuristic for MIP that does not require the solution to an LP relaxation, - a generic way to generalize large neighborhood search (LNS) heuristics from MIP to MINLP, - an Objective Feasibility Pump heuristic for nonconvex MINLP that uses second-order information and a dynamic selection of rounding procedures, - RENS, an LNS start heuristic for MINLP that optimizes over the set of feasible roundings of an LP solution, - Undercover, an LNS start heuristic for MINLP that solves a largest sub-MIP of a given MINLP, - Rapid Learning, a heuristic algorithm to generate globally valid conflict constraints for MIPs, - Cloud Branching, a heuristic algorithm that exploits dual degeneracy to reduce the number of candidates for branching variable selection. Additionally, we propose a new performance measure, the primal integral, that captures the benefits of primal heuristics better than traditional methods. In our computational study, we compare the performance of the MIP and MINLP solver SCIP with and without primal heuristics on six test sets with altogether 983 instances from academic and industrial sources, including our project partners ForNe, SAP, and Siemens. We observe that heuristics improve the solver performance regarding all measures that we used - by different orders of magnitude. We further see that the harder a problem is to solve to global optimality, the more important the deployment of primal heuristics becomes. The algorithms presented in this thesis are available in source code as part of the solver SCIP, of which the author has been a main developer for the last years. Methods described in this thesis have also been re-implemented within several commercial and noncommercial MIP and MINLP software packages, including Bonmin, CBC, Cplex, Gams, Sulum, and Xpress. KW - mixed integer nonlinear programming KW - primal heuristic KW - mixed integer programming KW - branching rule KW - large neighborhood search KW - solver software Y1 - 2014 UR - http://www.zib.de/berthold/Berthold2014.pdf SN - 978-3-8439-1931-9 PB - Dr. Hut Verlag ER - TY - GEN A1 - Berthold, Timo T1 - RENS – the optimal rounding N2 - This article introduces RENS, the relaxation enforced neighborhood search, a large neighborhood search algorithm for mixed integer nonlinear programming (MINLP) that uses a sub-MINLP to explore the set of feasible roundings of an optimal solution x' of a linear or nonlinear relaxation. The sub-MINLP is constructed by fixing integer variables x_j with x'_j in Z and bounding the remaining integer variables to x_j in {floor(x'_j), ceil(x'_j)}. We describe two different applications of RENS: as a standalone algorithm to compute an optimal rounding of the given starting solution and as a primal heuristic inside a complete MINLP solver. We use the former to compare different kinds of relaxations and the impact of cutting planes on the roundability of the corresponding optimal solutions. We further utilize RENS to analyze the performance of three rounding heuristics implemented in the branch-cut-and-price framework SCIP. Finally, we study the impact of RENS when it is applied as a primal heuristic inside SCIP. All experiments were performed on three publically available test sets of mixed integer linear programs (MIPs), mixed integer quadratically constrained programs (MIQCPs), and MINLPs, using solely software which is available in source code. It turns out that for these problem classes 60% to 70% of the instances have roundable relaxation optima and that the success rate of RENS does not depend on the percentage of fractional variables. Last but not least, RENS applied as primal heuristic complements nicely with existing root node heuristics in SCIP and improves the overall performance. T3 - ZIB-Report - 12-17 KW - Primal Heuristic KW - Mixed-Integer Nonlinear Programming KW - Large Neighborhood Search KW - Mixed-Integer Quadratically Constrained Programming KW - Mixed-Intger Programming Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15203 SN - 1438-0064 ER - TY - GEN 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 T1 - Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite 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. T3 - ZIB-Report - 12-24 KW - SCIP, MIP, MINLP, CIP, LP, modeling, optimization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15598 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Pfetsch, Marc T1 - Detecting Orbitopal Symmetries N2 - Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known. T3 - ZIB-Report - 08-33 KW - Symmetrie-Erkennung KW - Orbitope KW - Ganzzahlige Programmierung KW - Symmetrie-Brechung KW - Graphenisomorphie KW - symmetry detection KW - orbitopes KW - integer programming KW - symmetry breaking KW - graph ismorphism Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10842 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Solving Pseudo-Boolean Problems with SCIP N2 - Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method. T3 - ZIB-Report - 08-12 KW - Pseudo-Boolean KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Pseudo-Boolean KW - constraint integer programming KW - integer programming KW - branch-and-cut KW - optimization software Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10671 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: a New Approach to Integrate CP and MIP N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-01 KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Chipverifikation KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10520 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo T1 - RENS - Relaxation Enforced Neighborhood Search N2 - In the recent years, a couple of quite successful large neighborhood search heuristics for mixed integer programs has been published. Up to our knowledge, all of them are improvement heuristics. We present a new start heuristic for general MIPs working in the spirit of large neighborhood search. It constructs a sub-MIP which represents the space of all feasible roundings of some fractional point - normally the optimum of the LP-relaxation of the original MIP. Thereby, one is able to determine whether a point can be rounded to a feasible solution and which is the best possible rounding. Furthermore, a slightly modified version of RENS proves to be a well-performing heuristic inside the branch-cut-and-price-framework SCIP. T3 - ZIB-Report - 07-28 KW - Primalheuristiken KW - Gemischt-Ganzzahlige Programmierung KW - Nachbarschaftssuche KW - mixed integer programming KW - primal heuristics KW - large neighborhood search Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4264 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo T1 - Heuristics of the Branch-Cut-and-Price-Framework SCIP N2 - In this paper we give an overview of the heuristics which are integrated into the open source branch-cut-and-price-framework SCIP. We briefly describe the fundamental ideas of different categories of heuristics and present some computational results which demonstrate the impact of heuristics on the overall solving process of SCIP. T3 - ZIB-Report - 07-30 KW - Primalheuristiken KW - Gemischt-Ganzzahlige Programmierung KW - Branch and Cut KW - SCIP KW - mixed integer programming KW - primal heuristics KW - branch and cut KW - SCIP Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10280 SN - 1438-0064 ER - TY - THES A1 - Berthold, Timo T1 - Primal Heuristics for Mixed Integer Programs N2 - A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics. Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10293 ER - TY - GEN A1 - Berthold, Timo A1 - Perregaard, Michael A1 - Mészáros, Csaba T1 - Four good reasons to use an Interior Point solver within a MIP solver N2 - "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. T3 - ZIB-Report - 17-42 KW - mixed integer programming KW - interior point algorithm KW - Newton barrier method KW - analytic center Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64599 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores T2 - Proc. of 30th IEEE International Parallel & Distributed Processing Symposium N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1109/IPDPS.2016.56 ER - TY - GEN 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 N2 - This paper reports on the fifth version of the Mixed Integer Programming Library. The MIPLIB 2010 is the first MIPLIB release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today's codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic. T3 - ZIB-Report - 10-31 KW - Mixed Integer Programming KW - Problem Instances KW - IP KW - MIP KW - MIPLIB Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12953 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Rounding and Propagation Heuristics for Mixed Integer Programming 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. T3 - ZIB-Report - 11-29 KW - primal heuristic KW - mixed integer programming KW - domain propagation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13255 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vigerske, Stefan T1 - Large Neighborhood Search beyond MIP N2 - Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics. T3 - ZIB-Report - 11-21 KW - Large Neighborhood Search KW - Primal Heuristic KW - MIP KW - MIQCP KW - Pseudo-Boolean Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12989 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Schulz, Jens T1 - An approximative Criterion for the Potential of Energetic Reasoning N2 - Energetic reasoning is one of the most powerful propagation algorithms in cumulative scheduling. In practice, however, it is not commonly used because it has a high running time and its success highly depends on the tightness of the variable bounds. In order to speed up energetic reasoning, we provide an easy-to-check necessary condition for energetic reasoning to detect infeasibilities. We present an implementation of energetic reasoning that employs this condition and that can be parametrically adjusted to handle the trade-off between solving time and propagation overhead. Computational results on instances from the PSPLIB are provided. These results show that using this condition decreases the running time by more than a half, although more search nodes need to be explored. T3 - ZIB-Report - 11-12 KW - conflict analysis KW - constraint integer programming KW - cumulative constraint KW - resource-constrained project scheduling KW - energetic reasoning Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12655 ER - TY - CHAP A1 - Berthold, Timo A1 - Feydy, Thibaut A1 - Stuckey, Peter ED - Lodi, Andrea ED - Milano, Michela ED - Toth, Paolo T1 - Rapid Learning for Binary Programs T2 - Proc. of CPAIOR 2010 Y1 - 2010 VL - 6140 SP - 51 EP - 55 PB - Springer ER - TY - CHAP A1 - Berthold, Timo ED - Kalcsics, Jörg ED - Nickel, Stefan T1 - Heuristics of the Branch-Cut-and-Price-Framework SCIP T2 - Operations Research Proceedings 2007 Y1 - 2008 SP - 31 EP - 36 PB - Springer-Verlag ER - TY - THES A1 - Berthold, Timo T1 - Primal Heuristics for Mixed Integer Programs Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2007/1054/ ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Lübbecke, Marco A1 - Möhring, Rolf A1 - Schulz, Jens ED - Lodi, Andrea ED - Milano, Michela ED - Toth, Paolo T1 - A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling T2 - Proc. of CPAIOR 2010 Y1 - 2010 VL - 6140 SP - 313 EP - 317 PB - Springer ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc ED - Kullmann, Oliver T1 - Nonlinear pseudo-Boolean optimization T2 - Theory and Applications of Satisfiability Testing – SAT 2009 Y1 - 2009 VL - 5584 SP - 441 EP - 446 PB - Springer ER - TY - CHAP A1 - Achterberg, Tobias A1 - Berthold, Timo ED - van Hoeve, Willem ED - Hooker, John T1 - Hybrid Branching T2 - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 6th International Conference, CPAIOR 2009 Y1 - 2009 VL - 5547 SP - 309 EP - 311 PB - Springer ER - TY - CHAP A1 - Berthold, Timo A1 - Pfetsch, Marc ED - Fleischmann, Bernhard ED - Borgwardt, Karl ED - Klein, Robert ED - Tuma, Axel T1 - Detecting Orbitopal Symmetries T2 - Operations Research Proceedings 2008 Y1 - 2009 SP - 433 EP - 438 PB - Springer-Verlag ER - TY - GEN A1 - Berthold, Timo T1 - Measuring the impact of primal heuristics N2 - In modern MIP solvers, primal heuristics play a major role in finding and improving feasible solutions early in the solution process. However, classical performance measures such as time to optimality or number of branch-and-bound nodes reflect the impact of primal heuristics on the overall solving process badly. This article discusses the question of how to evaluate the effect of primal heuristics. Therefore, we introduce a new performance measure, the "primal integral" which depends on the quality of solutions found during the solving process as well as on the points in time when they are found. Our computational results reveal that heuristics improve the performance of MIP solvers in terms of the primal bound by around 80%. Further, we compare five state-of-the-art MIP solvers w.r.t. the newly proposed measure. T3 - ZIB-Report - 13-17 KW - mixed integer programming KW - primal heuristic KW - performance measure Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17887 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite 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 these can be used in concert 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 of available interfaces, and outline plans for future development. T3 - ZIB-Report - 12-27 KW - LP, MIP, CIP, MINLP, modeling, optimization, SCIP, SoPlex, Zimpl Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15654 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Lübbecke, Marco A1 - Möhring, Rolf A1 - Schulz, Jens T1 - A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling N2 - We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well. T3 - ZIB-Report - 10-03 KW - constraint integer programming KW - cumulative constraint KW - scheduling KW - conflict analysis KW - resource-constrained project Scheduling Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11180 SN - 1438-0064 ER - TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor A1 - Koch, Thorsten T1 - From feasibility to improvement to proof: three phases of solving mixed-integer programs JF - Optimization Methods and Software N2 - Modern mixed-integer programming (MIP) solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three distinct phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behaviour of the non-commercial MIP solver Scip at the predicted phase transition points. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2017.1392519 VL - 33 IS - 3 SP - 499 EP - 517 PB - Taylor & Francis ER - TY - CHAP A1 - Gamrath, Gerald A1 - Melchiori, Anna A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Salvagnin, Domenico T1 - Branching on Multi-aggregated Variables T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015 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. Y1 - 2015 U6 - https://doi.org/10.1007/978-3-319-18008-3_10 VL - 9075 SP - 141 EP - 156 ER - TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Shift-and-Propagate JF - Journal of Heuristics N2 - In recent years, there has been a growing interest in the design of general purpose primal heuristics for use inside complete mixed integer programming solvers. Many of these heuristics rely on an optimal LP solution, which may take a significant amount of time to find. In this paper, we address this issue by introducing a pre-root primal heuristic that does not require a previously found LP solution. This heuristic, named Shift-and-Propagate , applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement to existing rounding and propagation heuristics. Y1 - 2014 U6 - https://doi.org/10.1007/s10732-014-9271-0 VL - 21 IS - 1 SP - 73 EP - 106 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Extending a CIP framework to solve MIQCPs N2 - This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach. T3 - ZIB-Report - 09-23 KW - mixed integer quadratically constrained programming KW - constraint integer programming KW - convex relaxation KW - nonconvex Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11371 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Nonlinear pseudo-Boolean optimization: relaxation or propagation? N2 - Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver. T3 - ZIB-Report - 09-11 KW - Pseudo-Boolean KW - constraint integer programming KW - linear relaxation KW - separation algorithm KW - domain propagation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11232 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Feydy, Thibaut A1 - Stuckey, Peter T1 - Rapid Learning for Binary Programs N2 - Learning during search allows solvers for discrete optimization problems to remember parts of the search that they have already performed and avoid revisiting redundant parts. Learning approaches pioneered by the SAT and CP communities have been successfully incorporated into the SCIP constraint integer programming platform. In this paper we show that performing a heuristic constraint programming search during root node processing of a binary program can rapidly learn useful nogoods, bound changes, primal solutions, and branching statistics that improve the remaining IP search. T3 - ZIB-Report - 10-04 KW - Ganzzahlige Programmierung KW - Constraintprogrammierung KW - Primalheuristik KW - Konfliktanalyse KW - constraint programming KW - integer programming KW - primal heuristic KW - conflict learning Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11663 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: Techniques and Applications N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-43 KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10950 SN - 1438-0064 ER - TY - GEN A1 - Arnold, Thomas A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Henrion, René A1 - Grötschel, Martin A1 - Koch, Thorsten A1 - Tischendorf, Caren A1 - Römisch, Werner T1 - A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs N2 - Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de T3 - ZIB-Report - 14-14 KW - gas transport optimization KW - mixed integer nonlinear programming Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49947 SN - 1438-0064 ER - TY - GEN A1 - Arnold, Thomas A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Henrion, René A1 - Grötschel, Martin A1 - Koch, Thorsten A1 - Tischendorf, Caren A1 - Römisch, Werner ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs T2 - MATHEON - Mathematics for Key Technologies N2 - Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de Y1 - 2014 U6 - https://doi.org/10.4171/137 VL - 1 SP - 135 EP - 146 PB - European Mathematical Society ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten T1 - Parallel Solvers for Mixed Integer Linear Programming N2 - In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures. T3 - ZIB-Report - 16-74 KW - parallel computing KW - integer programming KW - branch-and-bound KW - supercomputing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62239 SN - 1438-0064 ER - TY - CHAP A1 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - Experiments with Conflict Analysis in Mixed Integer Programming T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017 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. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-59776-8_17 VL - 10335 SP - 211 EP - 222 PB - Springer ER - TY - CHAP A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael ED - IEEE, T1 - Solving Hard MIPLIP2003 Problems with ParaSCIP on Supercomputers: An Update T2 - IPDPSW'14 Proceedings of the 2014 IEEE, International Parallel & Distributed Processing Symposium Workshops Y1 - 2014 SN - 978-1-4799-4117-9 U6 - https://doi.org/10.1109/IPDPSW.2014.174 SP - 1552 EP - 1561 PB - IEEE Computer Society CY - Washington, DC, USA ER - TY - GEN A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-based primal heuristics for mixed integer programming 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. T3 - ZIB-Report - 15-26 KW - mixed-integer programming, large neighborhood search, primal heuristics, domain propagation Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55518 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-driven fix-and-propagate heuristics for mixed integer programming N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early in the solving process and help to solve instances to optimality faster. In this paper, we present a scheme for primal start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved as an LP and the solution is rounded. If the rounded solution did not provide a feasible solution already, a sub-MIP is solved for the neighborhood defined by the variable fixings performed in the first phase. The global structures help to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about three out of five instances and therewith help to improve several performance measures for MIP solvers, including the primal integral and the average solving time. T3 - ZIB-Report - 17-56 KW - mixed-integer programming KW - primal heuristics KW - fix-and-propagate KW - large neighborhood search KW - domain propagation Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65387 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Hendel, Gregor A1 - Koch, Thorsten T1 - The Three Phases of MIP Solving N2 - Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points. T3 - ZIB-Report - 16-78 KW - optimization software KW - mixed-integer programming KW - branch-and-bound KW - adaptive search behavior KW - optimality prediction Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61607 SN - 1438-0064 ER - TY - JOUR A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017. Y1 - 2023 PB - Springer ER -