TY - GEN A1 - Wiebel, Alexander A1 - Preis, Philipp A1 - Vos, Frans M. A1 - Hege, Hans-Christian T1 - Computation and Application of 3D Strokes on Visible Structures in Direct Volume Rendering N2 - In this paper we describe VisiTrace, a novel technique to draw 3D lines in 3D volume rendered images. It allows to draw strokes in the 2D space of the screen to produce 3D lines that run on top or in the center of structures actually visible in the volume rendering. It can handle structures that only shortly occlude the structure that has been visible at the starting point of the stroke and is able to ignore such structures. For this purpose a shortest path algorithm finding the optimal curve in a specially designed graph data structure is employed. We demonstrate the usefulness of the technique by applying it to MRI data from medicine and engineering, and show how the method can be used to mark or analyze structures in the example data sets, and to automatically obtain good views toward the selected structures. T3 - ZIB-Report - 13-20 KW - DVR KW - interaction Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18070 SN - 1438-0064 ER - TY - GEN A1 - Raack, Christian A1 - Raymond, Annie A1 - Werner, Axel A1 - Schlechte, Thomas T1 - Integer Programming and Sports Rankings N2 - Sports rankings are obtained by applying a system of rules to evaluate the performance of the participants in a competition. We consider rankings that result from assigning an ordinal rank to each competitor according to their performance. We develop an integer programming model for rankings that allows us to calculate the number of points needed to guarantee a team the ith position, as well as the minimum number of points that could yield the ith place. The model is very general and can thus be applied to many types of sports. We discuss examples coming from football (soccer), ice hockey, and Formula~1. We answer various questions and debunk a few myths along the way. Are 40 points enough to avoid relegation in the Bundesliga? Do 95 points guarantee the participation of a team in the NHL playoffs? Moreover, in the season restructuration currently under consideration in the NHL, will it be easier or harder to access the playoffs? Is it possible to win the Formula~1 World Championship without winning at least one race or without even climbing once on the podium? Finally, we observe that the optimal solutions of the aforementioned model are associated to extreme situations which are unlikely to happen. Thus, to get closer to realistic scenarios, we enhance the model by adding some constraints inferred from the results of the previous years. T3 - ZIB-Report - 13-19 KW - sport ranking KW - integer programming Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18068 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover Branching N2 - In this paper, we present a new branching strategy for nonconvex MINLP that aims at driving the created subproblems towards linearity. It exploits the structure of a minimum cover of an MINLP, a smallest set of variables that, when fixed, render the remaining system linear: whenever possible, branching candidates in the cover are preferred. Unlike most branching strategies for MINLP, Undercover branching is not an extension of an existing MIP branching rule. It explicitly regards the nonlinearity of the problem while branching on integer variables with a fractional relaxation solution. Undercover branching can be naturally combined with any variable-based branching rule. We present computational results on a test set of general MINLPs from MINLPLib, using the new strategy in combination with reliability branching and pseudocost branching. The computational cost of Undercover branching itself proves negligible. While it turns out that it can influence the variable selection only on a smaller set of instances, for those that are affected, significant improvements in performance are achieved. T3 - ZIB-Report - 13-14 Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18030 SN - 1438-0064 ER - TY - GEN A1 - Harrod, Steven A1 - Schlechte, Thomas T1 - A Direct Comparison of Physical Block Occupancy Versus Timed Block Occupancy in Train Timetabling Formulations N2 - Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by constraining time intervals between trains, while the other formulation, HGF, monitors physical occupation of controlled track segments. The results demonstrate that both ACP and HGF return comparable solutions in the aggregate, with some significant differences in select instances, and a pattern of significant differences in performance and constraint enforcement overall. T3 - ZIB-Report - 13-18 KW - Railway Scheduling KW - Train Timetabling KW - Track Allocation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17946 SN - 1438-0064 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 - Hiller, Benjamin A1 - Klug, Torsten A1 - Witzig, Jakob T1 - Reoptimization in branch-and-bound algorithms with an application to elevator control N2 - We consider reoptimization (i.e. the solution of a problem based on information available from solving a similar problem) for branch-and-bound algorithms and propose a generic framework to construct a reoptimizing branch-and-bound algorithm. We apply this to an elevator scheduling algorithm solving similar subproblems to generate columns using branch-and-bound. Our results indicate that reoptimization techniques can substantially reduce the running times of the overall algorithm. T3 - ZIB-Report - 13-15 KW - reoptimization KW - branch-and-bound KW - column generation KW - elevator control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17876 SN - 1438-0064 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Gollmer, Ralf A1 - Hayn, Christine A1 - Henrion, Rene A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Mirkov, Radoslava A1 - Morsi, Antonio A1 - Römisch, Werner A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets N2 - The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined. T3 - ZIB-Report - 13-13 KW - Gas Market Liberalization KW - Entry-Exit Model KW - Gas Network Access Regulation KW - Mixed-Integer Nonlinear Nonconvex Stochastic Optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17821 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - Computing the Minimal Rebinding Effect Included in a Given Kinetics N2 - The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process. On the macro scale this process comprises the Markov property. This Makovian view is spoiled when switching to the atomistic scale of a binding process. We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states. This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem. The results form our examples show good agreement with data form laboratory. T3 - ZIB-Report - 13-12 KW - Rebinding KW - Molecular Kinetics KW - Conformation Dynamics Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17796 SN - 1438-0064 ER - TY - GEN A1 - Humpola, Jesco A1 - Fügenschuh, Armin T1 - A New Class of Valid Inequalities for Nonlinear Network Design Problems N2 - We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. Assume that there does not exist a feasible flow that fulfills all physical constraints and meets the desired entry and exit amounts. Then a natural question is where to extend the network by adding pipes in the most economic way such that this flow becomes feasible. Answering this question is computationally demanding because of the difficult problem structure. We use mixed-integer nonlinear programming techniques that rely on an outer approximation of the overall problem, and a branching on decision variables. We formulate a new class of valid inequalities (or cutting planes) which reduce the overall solution time when added to the formulation. We demonstrate the computational merits of our approach on test instances. T3 - ZIB-Report - 13-06 KW - Network Design KW - Mixed-Integer Nonlinear Programming KW - Cutting Planes Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17771 SN - 1438-0064 ER - TY - GEN A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Olany, Amiya A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - Modeling potassium balance in dairy cows N2 - Potassium is fundamental for cell functioning including signal transduction, acid-base- and water-metabolism. Since diet of dairy cows is generally rich in potassium, hypokalemia was not in the focus of research for long time. Furthermore, hypokalemia was not frequently diagnosed because blood potassium content is difficult to measure. In recent years, measurement methods have been improved. Nowadays hypokalemia is increasingly diagnosed in cows with disorders such as abomasal displacement, ketosis or down cow syndrome, calling for intensified research on this topic. In this report we describe the development of a basic mechanistic, dynamic model of potassium balance based on ordinary differential and algebraic equations. Parameter values are obtained from data of a clinical trial in which potassium balance and the influence of therapeutic intervention in glucose and electrolyte metabolism on potassium balance in non-lactating dairy cows were studied. The model is formulated at a high abstraction level and includes information and hypotheses from literature. This work represents a first step towards the understanding and design of effective prophylactic feed additives and treatment strategies. T3 - ZIB-Report - 13-09 KW - systems biology KW - differential equations KW - metabolism Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17749 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Analyzing the computational impact of MIQCP solver components 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. T3 - ZIB-Report - 13-08 KW - mixed-integer quadratically constrained programming KW - mixed-integer programming KW - branch-and-cut KW - nonconvex KW - global optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17754 SN - 1438-0064 ER - TY - GEN A1 - Klindt, Marco A1 - Baum, Daniel A1 - Prohaska, Steffen A1 - Hege, Hans-Christian T1 - iCon.text – a customizable iPad app for kiosk applications in museum exhibitions N2 - We present iCon.text, a kiosk platform for the iPad centered around artefacts, whose content and layout can be tailored without programming skills for specific museum exhibitions. The central metaphor to access information is a virtual postcard with one front and a customizable number of back sides that provide details about exhibits to museum visitors in textual and image form. Back sides can link to others cards. Access to these postcards is possible through one or more navigation views that can be navigated to from a navigation bar. The entry point to the application is designed as a multitouch interactive pile of cards in a playful manner that allows visitors of any age an easy approach to the presentation and interaction metaphor. To directly access a certain postcard, a mosaic view can be uitilized to provide an overview about all available exhibits. A category view groups postcards into themes. Locating artefacts on a zoomable map or exhibition floor plan allows for conveying information about spatial contexts between different objects and their location. Furthermore, contexts can be illustrated with a two stage view comprising an overview and corresponding detail views to provide further insights into the spatial, temporal, and thematic contexts of artefacts. The application scaffolding allows the design of bilingual presentations to support exhibitions with an international audience. The logo of the presenting institution or exhibition can be incorporated to display the the kiosk's corporate design branding and to access an imprint or further informations. Usage is logged into files to provide a basis for extracting statistical information about the usage. The details about the exhibits are presented as images and as such impose no limit to the design choices made by the content provider or exhibition designer. The application (enhanced with a panoramic view) has been integrated successfully into a large special exhibition about the ancient city of Pergamon 2011/2012 at the Pergamon Museum Berlin within the interdisciplinary project "Berlin Sculpture Network". T3 - ZIB-Report - 13-07 KW - HCI KW - Cultural Heritage KW - Kiosk application KW - iPad Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17731 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 - GEN A1 - Heinz, Stefan A1 - Ku, Wen-Yang A1 - Beck, J. Christopher T1 - Recent improvements using constraint integer programming for resource allocation and scheduling N2 - Recently, we compared the performance of mixed-integer programming (MIP), constraint programming (CP), and constraint integer programming (CIP) to a state-of-the-art logic-based Benders manual decomposition (LBBD) for a resource allocation/scheduling problem. For a simple linear relaxation, the LBBD and CIP models deliver comparable performance with MIP also performing well. Here we show that algorithmic developments in CIP plus the use of an existing tighter relaxation substantially improve one of the CIP approaches. Furthermore, the use of the same relaxation in LBBD and MIP models significantly improves their performance. While such a result is known for LBBD, to the best of our knowledge, the other results are novel. Our experiments show that both CIP and MIP approaches are competitive with LBBD in terms of the number of problems solved to proven optimality, though MIP is about three times slower on average. Further, unlike the LBBD and CIP approaches, the MIP model is able to obtain provably high-quality solutions for all problem instances. T3 - ZIB-Report - 13-05 KW - constraint integer programming KW - constraint programming KW - cumulative constraint KW - mixed integer programming KW - optional activities Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17676 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Weltge, Stefan T1 - Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming N2 - Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation. This paper shows how the dual solutions of the auxiliary linear programs can be used to learn what we call Lagrangian variable bound constraints. These are linear inequalities that explain OBBT's domain reductions in terms of the bounds on other variables and the objective value of the incumbent solution. Within a spatial branch-and-bound algorithm, they can be learnt a priori (during OBBT at the root node) and propagated within the search tree at very low computational cost. Experiments with an implementation inside the MINLP solver SCIP show that this reduces the number of branch-and-bound nodes and speeds up solution times. T3 - ZIB-Report - 13-04 KW - MINLP KW - optimization-based bound tightening KW - optimality-based bound tightening KW - OBBT KW - propagation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17631 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 - 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 - Sagnol, Guillaume T1 - On the semidefinite representations of real functions applied to symmetric matrices N2 - We present a new semidefinite representation for the trace of a real function f applied to symmetric matrices, when a semidefinite representation of the convex function f is known. Our construction is intuitive, and yields a representation that is more compact than the previously known one. We also show with the help of matrix geometric means and the Riemannian metric of the set of positive definite matrices that for a rational number p in the interval (0,1], the matrix X raised to the exponent p is the largest element of a set represented by linear matrix inequalities. We give numerical results for a problem inspired from the theory of experimental designs, which show that the new semidefinite programming formulation yields a speed-up factor in the order of 10. T3 - ZIB-Report - 12-50 KW - semidefinite representability KW - optimal experimental designs KW - SDP KW - matrix geometric mean Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17511 SN - 1438-0064 VL - 439 SP - 2829 EP - 2843 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Buwaya, Julia A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach N2 - We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented. T3 - ZIB-Report - 12-47 KW - Stackelberg Equilibrium KW - Game Theory KW - Mixed Integer Programming Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17401 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 - Salvagnin, Domenico T1 - Cloud branching N2 - Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the current LP relaxation. These strategies naturally extend state-of-the-art methods like strong branching, pseudocost branching, and their hybrids. We show that by exploiting dual degeneracy, and thus multiple alternative optimal solutions, it is possible to enhance traditional methods. We present preliminary computational results, applying the newly proposed strategy to full strong branching, which is known to be the MIP branching rule leading to the fewest number of search nodes. It turns out that cloud branching can reduce the mean running time by up to 30% on standard test sets. T3 - ZIB-Report - 13-01 KW - mixed integer programming KW - branching rule KW - search strategy KW - dual degeneracy Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17301 SN - 1438-0064 ER - TY - GEN A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - A Hybrid Branch-and-Bound Approach for Exact Rational Mixed-Integer Programming N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances. T3 - ZIB-Report - 12-49 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17171 SN - 1438-0064 ER - TY - GEN A1 - Betker, Andreas A1 - Kosiankowski, Dirk A1 - Lange, Christoph A1 - Pfeuffer, Frank A1 - Raack, Christian A1 - Werner, Axel T1 - Energy efficiency in extensive multilayer core and regional networks with protection N2 - Energy-efficient operation of large telecommunication networks is an important issue today and in the near future. Given that the energy consumption rises with the ever increasing demand for capacity and network speed, there is a growing interest in strategies for a sustainable network management. It is a well-known fact that traffic demands vary significantly over time, most notably in day/night- and in weekly cycles. This provides the main potential for energy-saving strategies. We study the question of how much power is necessary to operate a network with state-of-the-art hardware during peak or low-traffic times. The study respects realistic side constraints, such as protection requirements and routing schemes, and takes the special structure of an extensive nation-wide optical network, including backbone and regional sections, into account. We formulate mixed integer programming models for the corresponding optimization problems using predictions for traffic matrices, as well as state-of-the-art hardware and power models. We address questions as the following: How much energy is spent in the core and in metro regions of the network and how big are the savings in low-demand scenarios if we always assume the system power-minimum in these situations? What is the influence of different hardware on the overall energy consumption? How much do different routing schemes or protection scenarios restrict potential energy savings? T3 - ZIB-Report - 12-45 KW - telecommunications KW - network design KW - routing KW - energy efficiency Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17154 SN - 1438-0064 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Hayn, Christine A1 - Michaels, Dennis T1 - Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production N2 - The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt the production process. For the mechanical separation process of fibers from stickies a separator screen is used. This machine has one input feed and two output streams, called the accept and the reject. In the accept the fibers are concentrated, whereas the reject has a higher concentration of stickies. The machine can be controlled by setting its reject rate. But even when the reject rate is set properly, after just a single screening step, the accept still has too many stickies, or the reject too many fibers. To get a proper separation, several separators have to be assembled into a network. From a mathematical point of view this problem can be seen as a multi-commodity network flow design problem with a nonlinear, controllable distribution function at each node. We present a nonlinear mixed-integer programming model for the simultaneous selection of a subset of separators, the network's topology, and the optimal setting of each separator. Numerical results are obtained via different types of linearization of the nonlinearities and the use of mixed-integer linear solvers, and compared with state-of-the-art global optimization software. T3 - ZIB-Report - 12-44 KW - Mixed-Integer Linear Programming KW - Nonlinear Programming KW - Piecewise Linear Approximation KW - Topology Optimization KW - Network Design Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16862 SN - 1438-0064 ER - TY - GEN A1 - Ehlke, Moritz A1 - Ramm, Heiko A1 - Lamecker, Hans A1 - Zachow, Stefan T1 - Efficient projection and deformation of volumetric intensity models for accurate simulation of X-ray images N2 - We present an efficient GPU-based method to generate virtual X-ray images from tetrahedral meshes which are associated with attenuation values. In addition, a novel approach is proposed that performs the model deformation on the GPU. The tetrahedral grids are derived from volumetric statistical shape and intensity models (SSIMs) and describe anatomical structures. Our research targets at reconstructing 3D anatomical shapes by comparing virtual X-ray images generated using our novel approach with clinical data while varying the shape and density of the SSIM in an optimization process. We assume that a deformed SSIM adequately represents an anatomy of interest when the similarity between the virtual and the clinical X-ray image is maximized. The OpenGL implementation presented here generates accurate (virtual) X-ray images at interactive rates, thus qualifying it for its use in the reconstruction process. T3 - ZIB-Report - 12-40 KW - Digitally Reconstructed Radiograph (DRR), Anatomy Reconstruction, Statistical Shape and Intensity Model (SSIM), GPU acceleration Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16580 SN - 1438-0064 ER - TY - GEN A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously. T3 - ZIB-Report - 12-41 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16531 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Tuchscherer, Andreas T1 - An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups N2 - The task of an elevator control is to schedule the elevators of a group such that small waiting and travel times for the passengers are obtained. We present an exact reoptimization algorithm for this problem. A reoptimization algorithm computes a new schedule for the elevator group each time a new passenger arrives. Our algorithm uses column generation techniques and is, to the best of our knowledge, the first exact reoptimization algorithms for a group of passenger elevators. To solve the column generation problem, we propose a Branch & Bound method. T3 - ZIB-Report - 12-43 KW - elevator control, online optimization, reoptimization algorithms, column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16485 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Stochastic dominance analysis of Online Bin Coloring algorithms N2 - This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations. T3 - ZIB-Report - 12-42 KW - online algorithms, stochastic dominance, algorithm analysis, Markov chains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16502 SN - 1438-0064 ER - TY - GEN A1 - Reuther, Markus A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Integrated Optimization of Rolling Stock Rotations for Intercity Railways N2 - This paper provides a highly integrated solution approach for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a generic hypergraph based mixed integer programming model and an integrated algorithm for the considered rolling stock rotation planning problem. The new developed approach is able to handle a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects. By the integration of this large bundle of technical railway aspects, we show that our approach has the power to produce implementable rolling stock rotations for our industrial cooperation partner DB Fernverkehr. This is the first time that the rolling stock rotations at DB Fernverkehr could be optimized by an automated system utilizing advanced mathematical programming techniques. T3 - ZIB-Report - 12-39 KW - Mixed Integer Programming KW - Railway Optimization KW - Rolling Stock Rostering Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16424 SN - 1438-0064 ER - TY - GEN A1 - Schlechte, Thomas T1 - Railway Track Allocation N2 - This article gives an overview of the results of the author's PhD thesis. The thesis deals with the mathematical optimization for the efficient use of railway infrastructure. We address the optimal allocation of the available railway track capacity - the track allocation problem. This track allocation problem is a major challenge for a railway company, independent of whether a free market, a private monopoly, or a public monopoly is given. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense sizes of the problem instances. Mathematical models and optimization techniques can result in huge gains for both railway customers and operators, e.g., in terms of cost reductions or service quality improvements. We tackle this challenge by developing novel mathematical models and associated innovative algorithmic solution methods for large scale instances. We made considerable progress on solving track allocation problems by two main features - a novel modeling approach for the macroscopic track allocation problem and algorithmic improvements based on the utilization of the bundle method. This allows us to produce for the first time reliable solutions for a real world instance, i.e., the Simplon corridor in Switzerland. T3 - ZIB-Report - 12-38 KW - large-scale integer programming KW - network aggregation KW - configuration models KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16402 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros T1 - Factorization and update of a reduced basis matrix for the revised simplex method N2 - In this paper, we describe a method to enhance the FTRAN and BTRAN operations in the revised simplex algorithm by using a reduced basis matrix defined by basic columns and nonbasic rows. This submatrix of the standard basis matrix is potentially much smaller, but may change its dimension dynamically from iteration to iteration. For the classical product form update ("eta update"), the idea has been noted already by Zoutendijk, but only preliminarily tested by Powell in the early 1970s. We extend these ideas to Forrest-Tomlin type update formulas for an LU factorization of the reduced basis matrix, which are suited for efficient implementation within a state-of-the-art simplex solver. The computational advantages of the proposed method apply to pure LP solving as well as to LP-based branch-and-cut algorithms. It can easily be integrated into existing simplex codes. T3 - ZIB-Report - 12-36 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16349 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Schulz, Jens A1 - Beck, J. Christopher T1 - Using dual presolving reductions to reformulate cumulative constraints N2 - Dual presolving reductions are a class of reformulation techniques that remove feasible or even optimal solutions while guaranteeing that at least one optimal solution remains, as long as the original problem was feasible. Presolving and dual reductions are important components of state-of-the-art mixed-integer linear programming solvers. In this paper, we introduce them both as unified, practical concepts in constraint programming solvers. Building on the existing idea of variable locks, we formally define and justify the use of dual information for cumulative constraints during a presolving phase of a solver. In particular, variable locks are used to decompose cumulative constraints, detect irrelevant variables, and infer variable assignments and domain reductions. Since the computational complexity of propagation algorithms typically depends on the number of variables and/or domain size, such dual reductions are a source of potential computational speed-up. Through experimental evidence on resource constrained project scheduling problems, we demonstrate that the conditions for dual reductions are present in well-known benchmark instances and that a substantial proportion of them can be solved to optimality in presolving -- without search. While we consider this result very promising, we do not observe significant change in overall run-time from the use of our novel dual reductions. T3 - ZIB-Report - 12-37 KW - dual reductions KW - cumulative constraints KW - presolving KW - variable locks Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16321 SN - 1438-0064 ER - TY - GEN A1 - Anco, Stephen A1 - Mohiuddin, Mohammad A1 - Wolf, Thomas T1 - Travelling waves and conservation laws for complex mKdV-type equations N2 - Travelling waves and conservation laws are studied for a wide class of $U(1)$-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves include deriving new complex solitary waves and kinks that generalize the well-known mKdV $\sech$ and $\tanh$ solutions. The main results on conservation laws consist of explicitly finding all 1st order conserved densities that yield phase-invariant counterparts of the well-known mKdV conserved densities for momentum, energy, and Galilean energy, and a new conserved density describing the angular twist of complex kink solutions. T3 - ZIB-Report - 12-34 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16124 SN - 1438-0064 ER - TY - GEN A1 - Anco, Stephen A1 - MacNaughton, Steven A. A1 - Wolf, Thomas T1 - Conservation laws and symmetries of quasilinear radial wave equations in multi-dimensions N2 - Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of point type and all conservation laws of a general energy-momentum type are explicitly determined, including those such as dilations, inversions, similarity energies and conformal energies that exist only for special powers or dimensions. In particular, all variational cases (when a Lagrangian formulation exists) and non-variational cases (when no Lagrangian exists) for these wave equations are considered. As main results, the classification yields generalized energies and radial momenta in certain non-variational cases, which are shown to arise from a new type of Morawetz dilation identity that produces conservation laws for each of the two classes of wave equations in a different way than Noether's theorem. T3 - ZIB-Report - 12-33 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16111 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas A1 - Schrüfer, Eberhard A1 - Webster, Kenneth T1 - Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs N2 - The paper reports on a computer algebra program {\sc LSSS} (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution in which many variables take the value zero. The program is applied to the symmetry investigation of a non-abelian Laurent ODE introduced recently by M.\ Kontsevich. The computed symmetries confirmed that a Lax pair found for this system earlier generates all first integrals of degree at least up to 14. T3 - ZIB-Report - 12-32 KW - linear algebraic systems, integrability, Lax pairs, noncommutative ODE, Laurent ODE Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16102 SN - 1438-0064 ER - TY - GEN A1 - Odesskii, Alexander A1 - Wolf, Thomas T1 - Compatible quadratic Poisson brackets related to a family of elliptic curves N2 - We construct nine pairwise compatible quadratic Poisson structures such that a generic linear combination of them is associated with an elliptic algebra in $n$ generators. Explicit formulas for Casimir elements of this elliptic Poisson structure are obtained. T3 - ZIB-Report - 12-31 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16097 SN - 1438-0064 ER - TY - GEN A1 - Euler, Marianna A1 - Euler, Norbert A1 - Wolf, Thomas T1 - The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws N2 - Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, {\it J. Phys A: Math. Theor} {\bf 43}, 492001 (20pp), 2010]. We consider two of those systems, denoted by Holm and Ivanov by CH(2,1) and CH(2,2), and report a class of integrating factors and its corresponding conservation laws for these two systems. In particular, we obtain the complete sent of first-order integrating factors for the systems in Cauchy-Kovalevskaya form and evaluate the corresponding sets of conservation laws for CH(2,1) and CH(2,2). T3 - ZIB-Report - 12-30 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16087 SN - 1438-0064 ER - TY - GEN A1 - Tunga, Burcu A1 - Weber, Marcus T1 - Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration N2 - This work aims to develop a new algorithm to calculate the free energy of water molecules by using a deterministic way. For this purpose, we assume a closed system confined to a physical volume, having water molecules in gas phase. To calculate the free energy of this sytem we utilized Mayer cluster expansion and the fluctuation free integration method. T3 - ZIB-Report - 12-35 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16031 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika ED - Delling, Daniel ED - Liberti, Leo T1 - A Direct Connection Approach to Integrated Line Planning and Passenger Routing T2 - ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems N2 - The treatment of transfers is a major challenge in line planning. Existing models either route passengers and lines sequentially, and hence disregard essential degrees of freedom, or they are of extremely large scale, and seem to be computationally intractable. We propose a novel direct connection approach that allows an integrated optimization of line and passenger routing, including accurate estimates of the number of direct travelers, for large-scale real-world instances. T3 - ZIB-Report - 12-29 KW - combinatorial optimization KW - integer programming KW - line planning KW - transfers Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15812 SN - 1438-0064 VL - 25 SP - 47 EP - 57 PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik ER - TY - GEN A1 - Scheumann, Rene A1 - Fügenschuh, Armin A1 - Schenker, Sebastian A1 - Vierhaus, Ingmar A1 - Borndörfer, Ralf A1 - Finkbeiner, Matthias T1 - Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation N2 - It is clear that a transformation to sustainable value creation is needed, because business as usual is not an option for preserving competitive advantages of leading industries. What does that mean? This contribution proposes possible approaches for a shift in existing manufacturing paradigms. In a first step, sustainability aspects from the German Sustainability Strategy and from the tools of life cycle sustainability assessment are chosen to match areas of a value creation process. Within these aspects are indicators, which can be measured within a manufacturing process. Once these data are obtained they can be used to set up a mathematical linear pulse model of manufacturing in order to analyse the evolution of the system over time, that is the transition process, by using a system dynamics approach. An increase of technology development by a factor of 2 leads to an increase of manufacturing but also to an increase of climate change. Compensation measures need to be taken. This can be done by e.g. taking money from the GDP (as an indicator of the aspect ``macroeconomic performance''). The value of the arc from that building block towards climate change must then be increased by a factor of 10. The choice of independent and representative indicators or aspects shall be validated and double-checked for their significance with the help of multi-criteria mixed-integer programming optimisation methods. T3 - ZIB-Report - 12-28 KW - Multi-Criteria Optimisation KW - Sustainability Indicator KW - System Dynamics KW - Value Creation Process Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15703 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 - Bondouy, Manon A1 - Röblitz, Susanna T1 - Mathematical modeling of follicular development in bovine estrous cycles N2 - Normal follicular growth is a prerequisite for successful fertilization of dairy cows. However, submission rates have been decreasing during the last decades because animals are not ovulating at the planned time of mating or insemination. In this study we use a mathematical model to investigate mechanisms that lead to anestrus. This model is derived by coupling two previously published models: a small model for the development of multiple follicles (Smith et al., 2004), and a large estrous cycle model (St\"otzel et al., 2012). We first investigate the influence of synchronization protocols on the time-shift of ovulation. In a second scenario we simulate an extended period of anestrus as it typically occurs after calving. T3 - ZIB-Report - 12-26 KW - ordinary differential equations KW - systems biology KW - reproduction KW - dairy cows Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15585 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Held, Harald A1 - Huang, Wei A1 - Vigerske, Stefan T1 - Towards globally optimal operation of water supply networks 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. T3 - ZIB-Report - 12-25 KW - MINLP, global optimization, operative planning, water supply networks Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15603 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 - Dreßler, Sebastian A1 - Steinke, Thomas T1 - A Novel Hybrid Approach to Automatically Determine Kernel Interface Data Volumes N2 - Scheduling algorithms for heterogeneous platforms make scheduling decisions based on several metrics. One of these metrics is the amount of data to be transferred from and to the accelerator. However, the automated determination of this metric is not a simple task. A few schedulers and runtime systems solve this problem by using regression models, which are imprecise though. Our novel approach for the determination of data volumes removes this limitation and thus provides a solution to obtain exact information. T3 - ZIB-Report - 12-23 KW - function parameter analysis KW - function parameter sizes KW - heterogeneous systems KW - scheduling metrics KW - tool flow Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15569 SN - 1438-0064 ER - TY - GEN A1 - Golas, Ulrike T1 - A General Attribution Concept for Models in M- adhesive Transformation Systems: Long Version N2 - Attributes are an important concept for modeling data in practical applications. Up to now there is no adequate way to define attributes for different kinds of models used in M-adhesive transformation systems, which are a special kind of graph transformation systems based on M-adhesive categories. Especially a proper representation and definition of attributes and their values as well as a suitable handling of the data does not fit well with other graph transformation formalisms. In this paper, we propose a new method to define attributes in a natural, but still formally precise and widely applicable way. We define a new kind of adhesive category, called W-adhesive, that can be used for transformations of attributes, while the underlying models are still M-adhesive ones. As a result, attributed models can be used as they are intended to be, but with a formal background and proven well-behavior. T3 - ZIB-Report - 12-22 KW - graph transformation KW - attribution KW - adhesive categories Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15547 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Case Study on Optimizing Toll Enforcements on Motorways N2 - In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach. T3 - ZIB-Report - 12-21 KW - Vehicle Routing Problem KW - Duty Rostering KW - Integer Programming KW - Operations Research Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15498 SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Maierhofer, Christiane A1 - Richter, Regina T1 - Data Enhancement for Active Thermography N2 - Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise. T3 - ZIB-Report - 12-20 KW - data enhancement KW - active thermography KW - quantitative reconstruction KW - Green's functions Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15243 UR - http://qirt.gel.ulaval.ca/archives/qirt2012/papers/QIRT-2012-167.pdf SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Steffy, Daniel A1 - Wolter, Kati T1 - Improving the Accuracy of Linear Programming Solvers with Iterative Refinement N2 - We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We demonstrate that this algorithm is effective in practice for computing extended precision solutions and that this leads to direct improvement of the best known methods for solving LPs exactly over the rational numbers. T3 - ZIB-Report - 12-19 KW - Linear programming KW - Iterative refinement KW - Exact linear programming Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15451 SN - 1438-0064 ER - TY - GEN A1 - Klapproth, Corinna T1 - The Contact-Stabilized Newmark Method - Consistency Error of a Spatiotemporal Discretization N2 - The paper considers an improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatiotemporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up no now, the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the assumption of bounded total variation of the solution. Here, interest focusses on the consistency error of the Newmark scheme in physical energy norm after discretization both in time and in space. The resulting estimate for the local discretization error allows to prove global convergence of the Newmark scheme under an additional assumption on the active contact boundaries. T3 - ZIB-Report - 12-18 KW - dynamical contact problems, contact-stabilized Newmark method, consistency error Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15198 SN - 1438-0064 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 - Schiela, Anton T1 - A cubic regularization algorithm for nonconvex optimization in function space (in preparation) N2 - We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework. Moreover, several variants of step computations are compared. In the context of nonlinear elasticity it turns out the a cg method applied to an augmented Hessian is more robust than truncated cg. T3 - ZIB-Report - 12-16 KW - nonconvex optimization KW - optimization in function space KW - nonlinear elasticity Y1 - 2012 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Omont, Bertrand A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Stackelberg game to optimize the distribution of controls in transportation networks N2 - We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways. T3 - ZIB-Report - 12-15 KW - Stackelberg game KW - Polymatrix game KW - Controls in transportation networks Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14995 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Heismann, Olga T1 - The Hypergraph Assignment Problem N2 - The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP is NP-hard and APX-hard. Further, we present an extended integer linear programming formulation which implies, e. g., all clique inequalities. T3 - ZIB-Report - 12-14 KW - directed hypergraphs KW - hyperassignment KW - assignment Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14822 SN - 1438-0064 ER - TY - GEN A1 - Grötschel, Martin A1 - Neumann, Gerald T1 - 10 Jahre TELOTA N2 - Das TELOTA-Projekt - zunächst nur für zwei Jahre gestartet - feierte am 15. Juni 2011 sein 10-jähriges Bestehen im Rahmen eines Workshops mit einem abschließenden Festvortrag von Richard Stallmann zum Thema „Copyright versus community in the age of computer networks“. Diese Veranstaltung zeigte, wie aktuell die TELOTA-Themen weiterhin sind und dass diese eine große Resonanz in der allgemeinen Öffentlichkeit finden. Die TELOTA-Aktivitäten haben sich als wichtiger Bestandteil der IT-Infrastruktur der BBAW erwiesen, gehen aber weit über reinen Service hinaus. Sie beeinflussen die Forschung selbst und führen zu neuen interessanten wissenschaftlichen Fragestellungen. Der Rückblick auf die ersten zehn Jahre der TELOTA-Initiative in diesem Artikel soll einen kleinen Eindruck von dem geben, was bisher geleistet wurde. T3 - ZIB-Report - 12-13 KW - BBAW KW - Telota Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14799 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus T1 - The funnel trap paradox N2 - In this article, an illustrative example is given for the coarse-graining of a Markov process which leads to a shift in the statistical weights of a two-states-system. The example is based on a 2D-funnel trap. The funnel trap is constructed in such a way, that the area inside and outside of the trap is identical. However, observing the flight of the insect as a Markov process, the probability for being “in the trap” is higher. This example can be transferred to several kinds of processes (like receptor-ligandbinding processes in chemistry) and describes the influence of “re-entering events”. T3 - ZIB-Report - 12-12 KW - Markov process KW - Robust Perron Cluster Analysis KW - Conformation Dynamics Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14765 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Vehicle Rotation Planning for Intercity Railways N2 - This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers. T3 - ZIB-Report - 12-11 KW - rolling-stock-planning KW - mixed-integer-programming KW - hypergraphs KW - column generation KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14731 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Rapid Branching N2 - We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning. T3 - ZIB-Report - 12-10 KW - large scale optimization KW - rapid branching KW - column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14728 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Langenhan, Andreas A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen T1 - Duty Scheduling Templates N2 - We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice. T3 - ZIB-Report - 12-09 KW - duty scheduling KW - duty templates Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14699 SN - 1438-0064 ER - TY - GEN A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An optimal control problem in polyconvex hyperelasticity N2 - We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented. T3 - ZIB-Report - 12-08 KW - polyconvex elasticity KW - implant design KW - optimal control Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14745 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP 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. T3 - ZIB-Report - 12-07 KW - Primal Heuristic KW - Mixed-Integer Nonlinear Programming KW - Large Neighborhood Search KW - Mixed-Integer Quadratically Constrained Programming KW - Nonconvex Optimization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14631 SN - 1438-0064 ER - TY - GEN A1 - Sander, Oliver A1 - Klapproth, Corinna A1 - Youett, Jonathan A1 - Kornhuber, Ralf A1 - Deuflhard, Peter T1 - Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion N2 - We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity. Its efficient numerical simulation requires advanced numerical algorithms that have been developed just recently. Up to now, the model comprises bones, cartilage, and the major ligaments (patella and menisci are still missing). Bones (femur, tibia, and fibula) are modelled by linear elastic materials, cartilage by viscoelastic materials, ligaments by one-dimensional so-called Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity in the presence of strict contact inequalities. For the total spatio-temporal discretization we apply a method of layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts, we apply a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet-Neumann method, and the arising large algebraic systems are solved by a recent fast multigrid solver, the truncated non-smooth Newton multigrid method. T3 - ZIB-Report - 12-06 KW - contact problem KW - contact-stabilized Newmark method KW - domain decomposition KW - energy-momentum method KW - geodesic finite elements KW - knee model Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14512 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Beck, J. Christopher T1 - Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling N2 - Despite the success of constraint programming (CP) for scheduling, the much wider penetration of mixed integer programming (MIP) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems. T3 - ZIB-Report - 12-05 KW - constraint integer programming KW - constraint programming KW - cumulative constraint KW - mixed integer programming KW - optional activities Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14660 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Friedow, Isabel A1 - Karbstein, Marika T1 - Optimierung des Linienplans 2010 in Potsdam N2 - Im Zuge der Übernahme von 6 Linien der Havelbus Verkehrsgesellschaft mbH durch die ViP Verkehr in Potsdam GmbH ergab sich 2009 die Notwendigkeit der Entwicklung eines neuen Linien- und Taktplans für das Jahr 2010. Das Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) entwickelt in einem Projekt des DFG-Forschungszentrums Matheon ein Verfahren zur mathematischen Linienoptimierung. Dieses Tool wurde bei der Optimierung des ViP Linienplans 2010 in einer projektbegleitenden Studie eingesetzt, um Alternativen bei verschiedenen Planungs- und Zielvorgaben auszuloten. In dem Artikel wird eine Auswertung der Ergebnisse mit dem Verkehrsanalysesystem Visum der PTV AG beschrieben. Die Auswertungen bestätigen, dass mit Hilfe von mathematischer Optimierung eine weitere Verkürzung der Reisezeit um 1%, eine als um 6% verkürzt empfundene Reisezeit, 10% weniger Fahrzeit im Fahrzeug und eine gleichzeitige Kostenreduktion um 5% möglich sind. T3 - ZIB-Report - 12-04 KW - Fallstudie KW - Linienplan KW - Optimierung Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14486 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - A Note on Menger's Theorem for Hypergraphs N2 - We prove the companion Theorem to Menger's Theorem for hypergraphs. This result gives rise to a new class of blocking pairs of ideal matrices, that generalize the incidence matrices of cuts and paths. T3 - ZIB-Report - 12-03 KW - ideal matrices Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14471 SN - 1438-0064 ER - TY - GEN A1 - Hoang, Nam-Dung A1 - Koch, Thorsten T1 - Steiner Tree Packing Revisited N2 - The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even finding feasible solutions is already NP-hard. What makes this problem special is that in order to reach the overall optimal solution non-optimal solutions to the underlying NP-hard Steiner tree problems must be used. Any non-global approach to the STPP is likely to fail. Integer programming is currently the best approach for computing optimal solutions. In this paper we review some “classical” STPP instances which model the underlying real world application only in a reduced form. Through improved modelling, including some new cutting planes, and by emplyoing recent advances in solver technology we are for the first time able to solve those instances in the original 3D grid graphs to optimimality. T3 - ZIB-Report - 12-02 KW - Steiner tree packing KW - Integer Programming KW - grid graphs Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14625 SN - 1438-0064 ER - TY - GEN A1 - Grötschel, Martin T1 - Einblicke in die Diskrete Mathematik N2 - „Diskrete Mathematik, was ist das?“, ist eine typische Frage von Lehrern mit traditioneller Mathematikausbildung, denn dort kam und kommt diskrete Mathematik kaum vor. Die etwas Aufgeschlosseneren fragen: „Wenn (schon wieder) etwas Neues unterrichtet werden soll, was soll denn dann im Lehrplan gestrichen werden?“ Auf die zweite Frage wird hier nicht eingegangen. Das Ziel dieses Aufsatzes ist es, in diskrete Mathematik einzuführen, Interesse an diesem Fachgebiet zu wecken und dazu anzuregen, dieses auch im Schulunterricht (ein wenig) zu berücksichtigen. Die Schüler und Schülerinnen werden dafür dankbar sein – eine Erfahrung, die in vielen Unterrichtsreihen gemacht wurde. T3 - ZIB-Report - 12-01 KW - diskrete Mathematik Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14399 SN - 1438-0064 ER - TY - GEN A1 - Martin, Alexander A1 - Geißler, Björn A1 - Hayn, Christine A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Optimierung Technischer Kapazitäten in Gasnetzen N2 - Die mittel- und längerfristige Planung für den Gastransport hat sich durch Änderungen in den regulatorischen Rahmenbedingungen stark verkompliziert. Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel diskutiert die hieraus resultierenden mathematischen Planungsprobleme, welche als Validierung von Nominierungen und Buchungen, Bestimmung der technischen Kapazität und Topologieplanung bezeichnet werden. Diese mathematischen Optimierungsprobleme werden vorgestellt und Lösungsansätze skizziert. T3 - ZIB-Report - 11-56 KW - Gasnetzplanung KW - Technische Kapazitäten KW - Nominierungsvalidierung KW - Buchungsvalidierung KW - Topologieplanung Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15121 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Probabilistic alternatives for competitive analysis N2 - In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis. T3 - ZIB-Report - 11-55 KW - online algorithms KW - probabilistic analysis KW - competitive analysis KW - survey Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15131 SN - 1438-0064 ER - TY - GEN A1 - Grötschel, Martin A1 - Stephan, Rüdiger T1 - Characterization of Facets of the Hop Constrained Chain Polytope via Dynamic Programming N2 - In this paper, we study the hop constrained chain polytope, that is, the convex hull of the incidence vectors of (s,t)-chains using at most k arcs of a given digraph, and its dominant. We use extended formulations (implied by the inherent structure of the Moore-Bellman-Ford algorithm) to derive facet defining inequalities for these polyhedra via projection. Our findings result into characterizations of all facet defining {0,+1,-1}-inequalities for the hop constrained chain polytope and all facet defining {0,1}-inequalities for its dominant. Although the derived inequalities are already known, such classifications were not previously given to the best of our knowledge. Moreover, we use this approach to generalize so called jump inequalities, which have been introduced in a paper of Dahl and Gouveia in 2004. T3 - ZIB-Report - 11-54 KW - hop constraints KW - chains KW - dynamic programming KW - facets Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14914 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume T1 - Approximation of a Maximum-Submodular-Coverage problem involving spectral functions, with application to Experimental Design N2 - We study a family of combinatorial optimization problems defined by a parameter $p\in[0,1]$, which involves spectral functions applied to positive semidefinite matrices, and has some application in the theory of optimal experimental design. This family of problems tends to a generalization of the classical maximum coverage problem as $p$ goes to $0$, and to a trivial instance of the knapsack problem as $p$ goes to $1$. In this article, we establish a matrix inequality which shows that the objective function is submodular for all $p\in[0,1]$, from which it follows that the greedy approach, which has often been used for this problem, always gives a design within $1-1/e$ of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors. We prove an inequality which generalizes a classical result from the theory of optimal designs, and allows us to give a rounding procedure with an approximation factor which tends to $1$ as $p$ goes to $1$. T3 - ZIB-Report - 11-53 KW - Maximum Coverage KW - Optimal Experimental Design KW - Polynomial Time Approximability KW - Kiefer's p-criterion Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14956 SN - 1438-0064 VL - 151 IS - 1--2 SP - 258 EP - 276 ER - TY - GEN A1 - Sagnol, Guillaume T1 - Network-related problems in Optimal Experimental Design and Second Order Cone Programming N2 - In the past few years several applications of optimal experimental designs have emerged to optimize the measurements in communication networks. The optimal design problems arising from this kind of applications share three interesting properties: (i) measurements are only available at a small number of locations of the network; (ii) each monitor can simultaneously measure several quantities, which can be modeled by ``multiresponse experiments"; (iii) the observation matrices depend on the topology of the network. In this paper, we give an overview of these experimental design problems and recall recent results for the computation of optimal designs by Second Order Cone Programming (SOCP). New results for the network-monitoring of a discrete time process are presented. In particular, we show that the optimal design problem for the monitoring of an AR1 process can be reduced to the standard form and we give experimental results. T3 - ZIB-Report - 11-52 KW - Optimal Experimental Design KW - Second Order Cone Programming KW - Network measurements Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14942 SN - 1438-0064 VL - 51 IS - 51 SP - 161 EP - 171 ER - TY - GEN A1 - Sagnol, Guillaume T1 - A Class of Semidefinite Programs with rank-one solutions N2 - We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite matrix of rank at most $r$, where $r$ is the rank of the matrix involved in the objective function of the SDP. The optimization problems of this class are semidefinite packing problems, which are the SDP analogs to vector packing problems. Of particular interest is the case in which our result guarantees the existence of a solution of rank one: we show that the computation of this solution actually reduces to a Second Order Cone Program (SOCP). We point out an application in statistics, in the optimal design of experiments. T3 - ZIB-Report - 11-51 KW - SDP KW - Semidefinite Packing Problem KW - rank 1-solution KW - Low-rank solutions KW - SOCP KW - Optimal Experimental Design KW - Multiresponse experiments Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14933 SN - 1438-0064 ER - TY - GEN A1 - Menne, Ulrich A1 - Raack, Christian A1 - Wessäly, Roland A1 - Kharitonov, Daniel T1 - Optimal Degree of Optical Circuit Switching in IP-over-WDM Networks N2 - In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node, we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical (packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in traffic volume, demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints, we assess the relative roles of the two distinct equipment groups, IP routers and optical cross-connects, with respect to resulting changes in cost-sensitive network architectures. T3 - ZIB-Report - 11-50 KW - IP-over-WDM KW - Circuit Switching KW - Opacity Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14843 SN - 1438-0064 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Werner, Axel A1 - Wessäly, Roland T1 - Estimating trenching costs in FTTx network planning N2 - In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ". T3 - ZIB-Report - 11-49 KW - Optical access networks KW - Optimization KW - Steiner trees Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14884 SN - 1438-0064 ER - TY - GEN A1 - Werner, Axel T1 - Kombinatorische Optimierung und die 40-Punkte-Regel N2 - Wieviele Punkte braucht eine Mannschaft in der Fußball-Bundesliga mindestens, um sicher dem Abstieg zu entgehen? Wir benutzen kombinatorische Optimierung, um diese und ähnliche Fragen zu beantworten. T3 - ZIB-Report - 11-48 KW - Kombinatorische Optimierung KW - Sport KW - Bundesliga Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14871 SN - 1438-0064 ER - TY - GEN A1 - Wessäly, Roland A1 - Werner, Axel A1 - Eckel, Klaus A1 - Seibel, Julia A1 - Orlowski, Sebastian A1 - Louchet, Hadrien A1 - Patzak, Erwin A1 - Bentz, Winfried T1 - Schätze heben bei der Planung von FTTx-Netzen: optimierte Nutzung von existierenden Leerrohren - eine Praxisstudie N2 - Das vom BMBF geförderte Projekt FTTX-PLAN entwickelt mathematische Modelle und Optimierungsverfahren, um automatisiert kostenoptimierte FTTx-Netze berechnen zu können. Wir zeigen anhand einer Praxisstudie in Zusammenarbeit mit der Regensburger R-KOM, wie ein Planer von diesen Verfahren profitieren kann, um die Auswirkungen bestimmter Entscheidungen auf die Netzstruktur und -kosten zu untersuchen. Wir illustrieren dies am Beispiel eines FTTB/FTTH-Vergleichs, der Variation von Kundenanbindungsraten und der gezielten Ausnutzung existierender Leerrohre, um Tiefbau zu vermeiden. T3 - ZIB-Report - 11-47 KW - Praxisstudie KW - Optische Zugangsnetze KW - Optimierung Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14861 UR - http://www.vde-verlag.de/buecher/453339/breitbandversorgung-in-deutschland-itg-fb-227.html SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Heismann, Olga T1 - Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning N2 - Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially. T3 - ZIB-Report - 11-46 KW - hyperassignments KW - vehicle rotation planning Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14564 UR - http://link.springer.com/chapter/10.1007%2F978-3-642-29210-1_10 SN - 1438-0064 ER - TY - GEN A1 - Wiebel, Alexander A1 - Vos, Frans M. A1 - Hege, Hans-Christian T1 - Perception-Oriented Picking of Structures in Direct Volumetric Renderings N2 - Radiologists from all application areas are trained to read slice-based visualizations of 3D medical image data. Despite the numerous examples of sophisticated three-dimensional renderings, especially all variants of direct volume rendering, such methods are often considered not very useful by radiologists who prefer slice-based visualization. Just recently there have been attempts to bridge this gap between 2D and 3D renderings. These attempts include specialized techniques for volume picking that result in repositioning slices. In this paper, we present a new volume picking technique that, in contrast to previous work, does not require pre-segmented data or metadata. The positions picked by our method are solely based on the data itself, the transfer function and, most importantly, on the way the volumetric rendering is perceived by viewers. To demonstrate the usefulness of the proposed method we apply it for automatically repositioning slices in an abdominal MRI scan, a data set from a flow simulation and a number of other volumetric scalar fields. Furthermore we discuss how the method can be implemented in combination with various different volumetric rendering techniques. T3 - ZIB-Report - 11-45 KW - DVR KW - picking KW - pointing KW - direct volume rendering Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14343 SN - 1438-0064 ER - TY - GEN A1 - Szabó, Jácint T1 - The set of solutions to nomination validation in passive gas transportation networks with a generalized flow formula N2 - In this paper we give an analytical description on the structure of solutions to the gas nomination validation problem in gas transportation networks. These networks are assumed to contain no active devices, only certain hypothetical pipelines, where the flow of gas is modeled by a generalized version of the quadratic Weymouth's equation. The purpose of considering generalized flow formulas is to be able to adapt our results to various gas network optimization problems involving gas flow formulas beyond Weymouth's equation. Such formulas can appear in leaves of branch and bound trees, or they can stem from discretization and linearization carried out at active devices. We call a balanced supply-demand vector a nomination, and the passive nomination validation problem is to decide whether there exist pressures at the nodes generating a given nomination. We prove that in our setup the pressure square vectors generating a given nomination form a one-dimensional connected and continuous curve in the pressure square space, and this curve is a line for the classical Weymouth's equation. We also present a visual approach for the easy comprehension of how this solution curve arises; we give a short investigation of the set of feasible nominations; and finally we give a proof that the nomination validation problem in gas networks with active devices is NP-complete. T3 - ZIB-Report - 11-44 KW - pressure drop equation KW - gas networks KW - generalized flow formula Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15151 SN - 1438-0064 ER - TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Workload and busy period for M/GI/1 with a general impatience mechanism N2 - The paper deals with the workload and busy period for the M/GI/1 system under FCFS discipline, where the customers may become impatient during their waiting for service with generally distributed maximal waiting times and also during their service with generally distributed maximal service times depending on the time waited for service. This general impatience mechanism, originally introduced by Kovalenko (1961) and considered by Daley (1965), too, covers the special cases of impatience on waiting times as well as impatience on sojourn times, for which Boxma et al. (2010), (2011) gave new results and outlined special cases recently. Our unified approach bases on the vector process of workload and busy time. Explicit representations for the LSTs of workload and busy period are given in case of phase-type distributed impatience. T3 - ZIB-Report - 11-43 KW - impatient customers KW - workload KW - busy period KW - waiting time dependent service Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14304 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - An IP Approach to Toll Enforcement Optimization on German Motorways N2 - This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany. T3 - ZIB-Report - 11-42 KW - Toll Enforcement KW - Vehicle Routing Problem KW - Duty Roster Planning KW - Integer Programming Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14299 SN - 1438-0064 ER - TY - GEN A1 - Clasen, Malte A1 - Paar, Philip A1 - Prohaska, Steffen T1 - Level of Detail for Trees Using Clustered Ellipsoids N2 - We present a level of detail method for trees based on ellipsoids and lines. We leverage the Expectation Maximization algorithm with a Gaussian Mixture Model to create a hierarchy of high-quality leaf clusterings, while the branches are simplified using agglomerative bottom-up clustering to preserve the connectivity. The simplification runs in a preprocessing step and requires no human interaction. For a fly by over and through a scene of 10k trees, our method renders on average at 40 ms/frame, up to 6 times faster than billboard clouds with comparable artifacts. T3 - ZIB-Report - 11-41 KW - level of detail KW - rendering KW - natural scene KW - Gaussian mixture model Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14251 SN - 1438-0064 ER - TY - GEN A1 - Koch, Thorsten A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - What could a million CPUs do to solve Integer Programs? N2 - Given the steady increase in cores per CPU, it is only a matter of time until supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments. T3 - ZIB-Report - 11-40 Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14222 SN - 1438-0064 ER - TY - GEN A1 - Deuflhard, Peter A1 - Schiela, Anton A1 - Weiser, Martin T1 - Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia N2 - This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator. T3 - ZIB-Report - 11-39 KW - hyperthermia therapy planning KW - mathematical modelling KW - Maxwell equations KW - state constraints KW - parameter identification Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14204 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Schlechte, Thomas A1 - Stephan, Rüdiger A1 - Winkler, Michael T1 - Solving steel mill slab design problems N2 - The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results. Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality. T3 - ZIB-Report - 11-38 KW - steel mill slab design problem KW - multiple knapsack problem with color constraints KW - integer programming KW - set partitioning KW - binpacking with side constraints Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14089 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton A1 - Hintermüller, Michael T1 - On the Length of the Primal-Dual Path in Moreau-Yosida-based Path-following for State Constrained Optimal Control: Analysis and Numerics N2 - We derive a-priori estimates on the length of the primal-dual path that results from a Moreau-Yosida approximation of the feasible set for state constrained optimal control problems. These bounds depend on the regularity of the state and the dimension of the problem. Comparison with numerical results indicates that these bounds are sharp and are attained for the case of a single active point. T3 - ZIB-Report - 11-37 KW - state constraints KW - PDE constrained optimization KW - path-following Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14071 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning N2 - We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved. T3 - ZIB-Report - 11-36 KW - Rolling Stock Planning, Hypergraph Modeling, Integer Programming, Column Generation, Rapid Branching Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-32746 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Railway Track Allocation - Simulation, Aggregation, and Optimization N2 - Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data. T3 - ZIB-Report - 11-35 KW - railway models, railway capacity, track allocation framework Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14031 SN - 1438-0064 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Kutschka, Manuel A1 - Raack, Christian T1 - Robust Network Design: Formulations, Valid Inequalities, and Computations N2 - Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim [2004]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness. To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge. For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods. T3 - ZIB-Report - 11-34 KW - robust network design KW - cutset inequalities Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13890 SN - 1438-0064 ER - TY - GEN A1 - Grötschel, Martin T1 - Mathematik, Politik und Recht N2 - Politiker müssten doch in der Lage sein, faire Wahlverfahren, rationale gesellschaftliche Entscheidungsprozesse und schlupflochfreie Marktregulierungen zu finden. Und wenn sie sich nicht einigen können, so denkt fast jeder, dann sollen das eben unsere Gerichte regeln. Dies ist im Allgemeinen unerfüllbares Wunschdenken. Die Gründe dafür sind oft mathematischer Natur. Man kann z. B. mathematisch beweisen, dass es (in einem präzisierbaren Sinn) gar keine „fairen“ Wahlverfahren und nur in seltenen Fällen „rationale“ Entscheidungsprozesse gibt. Ein anderer Sachverhalt liegt z. B. bei Regulierungs- oder Deregulierungsmaßnahmen vor. Die dabei zu berücksichtigenden technischen Restriktionen sind häufig so kompliziert (man denke u. a. an die technischen Vorschriften im Schienen- oder Luftverkehr oder zum Betrieb von Pipelines), dass sie einfach nicht in juristischer Sprache formuliert werden können. Gut gemeinte Verordnungen sind nicht selten mathematisch widersprüchlich, führen auf praktisch unlösbare Probleme oder überfordern das Verständnis aller Beteiligten. Diese Beispiele legen nahe, dass bei einigen Gesetzgebungsprozessen und Verordnungen mathematischer Sachverstand erforderlich ist. Dieser wird derzeit aber nur sehr selten genutzt. T3 - ZIB-Report - 11-33 KW - Mathematik als Entscheidungshilfe KW - Spieltheorie KW - Kostenaufteilungsprobleme KW - Wahlverfahren und Mathematik Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13845 SN - 1438-0064 ER - TY - GEN A1 - Schlechte, Thomas T1 - Railway Track Allocation - Simulation and Optimization N2 - Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway infrastructure provider. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market. This leads to an increase of slot requests and then it is natural that conflicts occur among them. Furthermore, railway infrastructure networks consist of very expensive assets, even more they are rigid due to the long-term upgrade process. In order to make best use of these valuable infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithmic methodology can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and a general framework to support the integration of simulation and optimization for railway capacity allocation. T3 - ZIB-Report - 11-32 KW - railway models KW - railway capacity KW - track allocation framework Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13632 SN - 1438-0064 ER - TY - GEN A1 - Giovanidis, Anastasios A1 - Pulaj, Jonad T1 - The Multiperiod Network Design Problem: Lagrangian-based Solution Approaches N2 - We present and prove a theorem which gives the optimal dual vector for which a Lagrangian dual problem in the Single Period Design Problem (SPDP) is maximized. Furthermore we give a straightforward generalization to the Multi-Period Design Problem (MPDP). Based on the optimal dual values derived we compute the solution of the Lagrangian relaxation and compare it with the linear relaxation and optimal IP values. T3 - ZIB-Report - 11-31 KW - Network Design KW - Lagrangian Relaxation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13367 ER - TY - GEN A1 - Gottwald, Susanne T1 - Recommender Systeme für den Einsatz in Bibliotheken N2 - In diesem Report wird ein Überblick über Recommender Systeme (RS) im Bibliotheksbereich gegeben, welche Eigenschaften RS haben und welche Bedeutung sie damit für Bibliotheken besitzen. Es existieren semantische und nicht-semantische Lösungen, die dem Benutzer aus einer Menge von Publikationen die für ihn relevantesten empfehlen. Diese Arbeiten sowie eine Einleitung in das Thema werden präsentiert und mit den gewonnenen Kenntnissen ein Ausblick auf mögliche Entwicklungen gegeben. T3 - ZIB-Report - 11-30 KW - Semantic Web KW - Recommender Systems Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13261 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 - Manfred, Brandt A1 - Andreas, Brandt T1 - On sojourn times for an infinite-server system in random environment and its application to processor sharing systems N2 - We deal with an infinite-server system where the service speed is governed by a stationary and ergodic process with countably many states. Applying a random time transformation such that the service speed becomes one, the sojourn time of a class of virtual requests with given required service time is equal in distribution to an additive functional defined via a stationary version of the time-changed process. Thus bounds for the expectation of functions of additive functionals yield bounds for the expectation of functions of virtual sojourn times, in particular bounds for fractional moments and the distribution function. Interpreting the $GI(n)/GI(n)/\infty$ system or equivalently the $GI(n)/GI$ system under state-dependent processor sharing as an infinite-server system with random states given by the number $n$ of requests in the system provides results for sojourn times of virtual requests. In case of $M(n)/GI(n)/\infty$, the sojourn times of arriving and added requests are equal in distribution to sojourn times of virtual requests in modified systems, which yields many results for the sojourn times of arriving and added requests. In case of integer moments, the bounds generalize earlier results for $M/GI(n)/\infty$. In particular, the mean sojourn times of arriving and added requests in $M(n)/GI(n)/\infty$ are proportional to the required service time, generalizing Cohen's famous result for $M/GI(n)/\infty$. T3 - ZIB-Report - 11-28 KW - infinite-server KW - random environment KW - time transformation KW - sojourn times KW - state-dependent processor sharing Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13190 ER - TY - GEN A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Weber, Marcus T1 - Soft Versus Hard Metastable Conformations in Molecular Simulations N2 - Particle methods have become indispensible in conformation dynamics to compute transition rates in protein folding, binding processes and molecular design, to mention a few. Conformation dynamics requires at a decomposition of a molecule's position space into metastable conformations. In this paper, we show how this decomposition can be obtained via the design of either ``soft'' or ``hard'' molecular conformations. We show, that the soft approach results in a larger metastabilitiy of the decomposition and is thus more advantegous. This is illustrated by a simulation of Alanine Dipeptide. T3 - ZIB-Report - 11-27 KW - Proteins, Conformation Space, Meshfree Methods Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13189 ER - TY - GEN A1 - Anco, Stephen A1 - Ali, Sajid A1 - Wolf, Thomas T1 - Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions N2 - A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of similarity variables given by group foliations of this heat equation, using its admitted group of scaling symmetries. This technique yields explicit similarity solutions as well as other explicit solutions of a more general (non-similarity) form having interesting analytical behavior connected with blow up and dispersion. In contrast, standard similarity reduction of this heat equation gives a semilinear ODE that cannot be explicitly solved by familiar integration techniques such as point symmetry reduction or integrating factors. T3 - ZIB-Report - 11-26 KW - semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13213 ER - TY - GEN A1 - Anco, Stephen A1 - Ali, Sajid A1 - Wolf, Thomas T1 - Exact solutions of nonlinear partial differential equations by the method of group foliation reduction N2 - A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method is based on group foliation reduction and employs a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation. T3 - ZIB-Report - 11-25 KW - semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13171 ER - TY - GEN A1 - Wolf, Thomas A1 - Efimovskaya, Olga T1 - On integrability of the Kontsevich non-abelian ODE system N2 - We consider systems of ODEs with the right hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich. We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries. T3 - ZIB-Report - 11-24 KW - integrability, Lax pairs, noncommutative ODE, Laurent ODE Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13113 ER -