TY - GEN A1 - Anderson, Lovis A1 - Hiller, Benjamin T1 - A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes N2 - Optimization models often feature disjunctions of polytopes as submodels. Such a disjunctive set is initially (at best) relaxed to its convex hull, which is then refined by branching. To measure the error of the convex relaxation, the (relative) difference between the volume of the convex hull and the volume of the disjunctive set may be used. This requires a method to compute the volume of the disjunctive set. Naively, this can be done via inclusion/exclusion and leveraging the existing code for the volume of polytopes. However, this is often inefficient. We propose a revised variant of an old algorithm by Bieri and Nef (1983) for this purpose. The algorithm uses a sweep-plane to incrementally calculate the volume of the disjunctive set as a function of the offset parameter of the sweep-plane. T3 - ZIB-Report - 18-37 KW - Disjunctive Programming KW - Volume Algorithm KW - Union of Polytopes Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69489 SN - 1438-0064 ER - TY - GEN A1 - Wende, Florian T1 - SIMD Enabled Functions on Intel Xeon CPU and Intel Xeon Phi Coprocessor N2 - To achieve high floating point compute performance, modern processors draw on short vector SIMD units, as found e.g. in Intel CPUs (SSE, AVX1, AVX2 as well as AVX-512 on the roadmap) and the Intel Xeon Phi coprocessor, to operate an increasingly larger number of operands simultaneously. Making use of SIMD vector operations therefore is essential to get close to the processor’s floating point peak performance. Two approaches are typically used by programmers to utilize the vector units: compiler driven vectorization via directives and code annotations, and manual vectorization by means of SIMD intrinsic operations or assembly. In this paper, we investigate the capabilities of the current Intel compiler (version 15 and later) to generate vector code for non-trivial coding patterns within loops. Beside the more or less uniform data-parallel standard loops or loop nests, which are typical candidates for SIMDfication, the occurrence of e.g. (conditional) function calls including branching, and early returns from functions may pose difficulties regarding the effective use of vector operations. Recent improvements of the compiler's capabilities involve the generation of SIMD-enabled functions. We will study the effectiveness of the vector code generated by the compiler by comparing it against hand-coded intrinsics versions of different kinds of functions that are invoked within innermost loops. T3 - ZIB-Report - 15-17 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54163 SN - 1438-0064 ER - TY - GEN A1 - Wende, Florian A1 - Steinke, Thomas A1 - Reinefeld, Alexander T1 - The Impact of Process Placement and Oversubscription on Application Performance: A Case Study for Exascale Computing N2 - With the growing number of hardware components and the increasing software complexity in the upcoming exascale computers, system failures will become the norm rather than an exception for long-running applications. Fault-tolerance can be achieved by the creation of checkpoints during the execution of a parallel program. Checkpoint/Restart (C/R) mechanisms allow for both task migration (even if there were no hardware faults) and restarting of tasks after the occurrence of hardware faults. Affected tasks are then migrated to other nodes which may result in unfortunate process placement and/or oversubscription of compute resources. In this paper we analyze the impact of unfortunate process placement and oversubscription of compute resources on the performance and scalability of two typical HPC application workloads, CP2K and MOM5. Results are given for a Cray XC30/40 with Aries dragonfly topology. Our results indicate that unfortunate process placement has only little negative impact while oversubscription substantially degrades the performance. The latter might be only (partially) beneficial when placing multiple applications with different computational characteristics on the same node. T3 - ZIB-Report - 15-05 KW - Fault-tolerance KW - Process placement KW - Oversubscription Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53560 SN - 1438-0064 ER - TY - GEN A1 - Kuhn, Alexander A1 - Engelke, Wito A1 - Flatken, Markus A1 - Hege, Hans-Christian A1 - Hotz, Ingrid T1 - Topology-based Analysis for Multimodal Atmospheric Data of Volcano Eruptions N2 - Many scientific applications deal with data from a multitude of different sources, e.g., measurements, imaging and simulations. Each source provides an additional perspective on the phenomenon of interest, but also comes with specific limitations, e.g. regarding accuracy, spatial and temporal availability. Effectively combining and analyzing such multimodal and partially incomplete data of limited accuracy in an integrated way is challenging. In this work, we outline an approach for an integrated analysis and visualization of the atmospheric impact of volcano eruptions. The data sets comprise observation and imaging data from satellites as well as results from numerical particle simulations. To analyze the clouds from the volcano eruption in the spatiotemporal domain we apply topological methods. Extremal structures reveal structures in the data that support clustering and comparison. We further discuss the robustness of those methods with respect to different properties of the data and different parameter setups. Finally we outline open challenges for the effective integrated visualization using topological methods. T3 - ZIB-Report - 16-03 KW - multi-modal, intergrated data analysis, topology Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57043 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 - Shinano, Yuji T1 - The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound N2 - Mixed integer linear programming (MIP) is a general form to model combinatorial optimization problems and has many industrial applications. The performance of MIP solvers has improved tremendously in the last two decades and these solvers have been used to solve many real-word problems. However, against the backdrop of modern computer technology, parallelization is of pivotal importance. In this way, ParaSCIP is the most successful parallel MIP solver in terms of solving previously unsolvable instances from the well-known benchmark instance set MIPLIB by using supercomputers. It solved two instances from MIPLIB2003 and 12 from MIPLIB2010 for the first time to optimality by using up to 80,000 cores on supercomputers. ParaSCIP has been developed by using the Ubiquity Generator (UG) framework, which is a general software package to parallelize any state-of-the-art branch-and-bound based solver. This paper discusses 7 years of progress in parallelizing branch-and-bound solvers with UG. T3 - ZIB-Report - 17-60 KW - Parallelization, Branch-and-bound, Mixed Integer Programming, UG, ParaSCIP, FiberSCIP, ParaXpress, FiberXpress, SCIP-Jack Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65545 SN - 1438-0064 ER - TY - GEN A1 - Pulaj, Jonad T1 - Cutting Planes for Families Implying Frankl's Conjecture N2 - We find previously unknown families which imply Frankl’s conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non–Frankl-Complete (Non–FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non–FC-families. T3 - ZIB-Report - 16-51 KW - extremal combinatorics, extremal set theory, cutting plane, exact integer programming Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60626 SN - 1438-0064 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 -