TY - GEN A1 - Orlowski, Sebastian A1 - Wessäly, Roland T1 - An Integer Programming Model for Multi-Layer Network Design N2 - We present an integer linear programming model for the design of multi-layer telecommunication networks. The formulation integrates hardware, capacity, routing, and grooming decisions in \emph{any} n umber of network layers. Practical hardware restrictions and cost can accurately be taken into account for technologies based on connection-oriented routing protocols. T3 - ZIB-Report - 04-49 KW - multi-layer networks KW - integer programming KW - network design KW - routing KW - grooming Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8248 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 - THES A1 - Martin, Alexander T1 - Integer Programs with Block Structure N2 - In this thesis we study and solve integer programs with block structure, i.\,e., problems that after the removal of certain rows (or columns) of the constraint matrix decompose into independent subproblems. The matrices associated with each subproblem are called blocks and the rows (columns) to be removed linking constraints (columns). Integer programs with block structure come up in a natural way in many real-world applications. The methods that are widely used to tackle integer programs with block structure are decomposition methods. The idea is to decouple the linking constraints (variables) from the problem and treat them at a superordinate level, often called master problem. The resulting residual subordinate problem then decomposes into independent subproblems that often can be solved more efficiently. Decomposition methods now work alternately on the master and subordinate problem and iteratively exchange information to solve the original problem to optimality. In Part I we follow a different approach. We treat the integer programming problem as a whole and keep the linking constraints in the formulation. We consider the associated polyhedra and investigate the polyhedral consequences of the involved linking constraints. The variety and complexity of the new inequalities that come into play is illustrated on three different types of real-world problems. The applications arise in the design of electronic circuits, in telecommunication and production planning. We develop a branch-and-cut algorithm for each of these problems, and our computational results show the benefits and limits of the polyhedral approach to solve these real-world models with block structure. Part II of the thesis deals with general mixed integer programming problems, that is integer programs with no apparent structure in the constraint matrix. We will discuss in Chapter 5 the main ingredients of an LP based branch-and-bound algorithm for the solution of general integer programs. Chapter 6 then asks the question whether general integer programs decompose into certain block structures and investigate whether it is possible to recognize such a structure. The remaining two chapters exploit information about the block structure of an integer program. In Chapter 7 we parallelize parts of the dual simplex algorithm, the method that is commonly used for the solution of the underlying linear programs within a branch-and-cut algorithm. In Chapter 8 we try to detect small blocks in the constraint matrix and to derive new cutting planes that strengthen the integer programming formulation. These inequalities may be associated with the intersection of several knapsack problems. We will see that they significantly improve the quality of the general integer programming solver introduced in Chapter 5. T3 - ZIB-Report - SC-99-03 KW - integer programming KW - cutting planes KW - block structure Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3911 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 - GEN A1 - Achterberg, Tobias A1 - Bixby, Robert E. A1 - Gu, Zonghao A1 - Rothberg, Edward A1 - Weninger, Dieter T1 - Presolve Reductions in Mixed Integer Programming N2 - Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature. T3 - ZIB-Report - 16-44 KW - integer programming KW - presolving KW - Gurobi Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60370 SN - 1438-0064 ER - TY - THES A1 - Achterberg, Tobias T1 - Constraint Integer Programming N2 - This thesis introduces the novel paradigm of constraint integer programming (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method. N2 - Diese Arbeit stellt einen integrierten Ansatz aus Constraint Programming (CP) und Gemischt-Ganzzahliger Programmierung (Mixed Integer Programming, MIP) vor, den wir Constraint Integer Programming (CIP) nennen. Sowohl Modellierungs- als auch Lösungstechniken beider Felder fließen in den neuen integrierten Ansatz ein, um die unterschiedlichen Stärken der beiden Gebiete zu kombinieren. Als weiteren Beitrag stellen wir der wissenschaftlichen Gemeinschaft die Software SCIP zur Verfügung, die ein Framework für Constraint Integer Programming darstellt und zusätzlich Techniken des SAT-Lösens beinhaltet. SCIP ist im Source Code für akademische und nicht-kommerzielle Zwecke frei erhältlich. Unser Ansatz des Constraint Integer Programming ist eine Verallgemeinerung von MIP, die zusätzlich die Verwendung beliebiger Constraints erlaubt, solange sich diese durch lineare Bedingungen ausdrücken lassen falls alle ganzzahligen Variablen auf feste Werte eingestellt sind. Die Constraints werden von einer beliebigen Kombination aus CP- und MIP-Techniken behandelt. Dies beinhaltet insbesondere die Domain Propagation, die Relaxierung der Constraints durch lineare Ungleichungen, sowie die Verstärkung der Relaxierung durch dynamisch generierte Schnittebenen. Die derzeitige Version von SCIP enthält alle Komponenten, die für das effiziente Lösen von Gemischt-Ganzzahligen Programmen benötigt werden. Die vorliegende Arbeit liefert eine ausführliche Beschreibung dieser Komponenten und bewertet verschiedene Varianten in Hinblick auf ihren Einfluß auf das Gesamt-Lösungsverhalten anhand von aufwendigen praktischen Experimenten. Dabei wird besonders auf die algorithmischen Aspekte eingegangen. Der zweite Hauptteil der Arbeit befasst sich mit der Chip-Design-Verifikation, die ein wichtiges Thema innerhalb des Fachgebiets der Electronic Design Automation darstellt. Chip-Hersteller müssen sicherstellen, dass der logische Entwurf einer Schaltung der gegebenen Spezifikation entspricht. Andernfalls würde der Chip fehlerhaftes Verhalten aufweisen, dass zu Fehlfunktionen innerhalb des Gerätes führen kann, in dem der Chip verwendet wird. Ein wichtiges Teilproblem in diesem Feld ist das Eigenschafts-Verifikations-Problem, bei dem geprüft wird, ob der gegebene Schaltkreisentwurf eine gewünschte Eigenschaft aufweist. Wir zeigen, wie dieses Problem als Constraint Integer Program modelliert werden kann und geben eine Reihe von problemspezifischen Algorithmen an, die die Struktur der einzelnen Constraints und der Gesamtschaltung ausnutzen. Testrechnungen auf Industrie-Beispielen vergleichen unseren Ansatz mit den bisher verwendeten SAT-Techniken und belegen den Erfolg unserer Methode. KW - Ganzzahlige Programmierung KW - Constraint Programmierung KW - SAT KW - Chip-Verifikation KW - integer programming KW - constraint programming KW - SAT KW - chip verification Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:83-opus-16117 ER -