A fast and reliable hybrid algorithm for numerical nonlinear global optimization

PreprintHighly nonlinear and ill-conditioned numerical optimization problems take their toll on the convergence of existing resolution methods. Stochastic methods such as Evolutionary Algorithms carry out an efficient exploration of the searchspace at low cost, but get often trapped in local minima and do not prove the optimality of the solution. Deterministic methods such as Interval Branch and Bound algorithms guarantee bounds on the solution, yet struggle to converge within a reasonable time on high-dimensional problems. The contribution of this paper is a hybrid algorithm in which a Differential Evolution algorithm and an Interval Branch and Contract algorithm cooperate. Bounds and solutions are exchanged through shared memory to accelerate the proof of optimality. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate the efficiency of this algorithm on two currently unsolved problems: first by presenting new certified optimal results for the Michalewicz function for up to 75 dimensions and then by proving that the putative minimum of Lennard-Jones clusters of 5 atoms is optimal

Rapid gravity filtration operational performance assessment and diagnosis for preventative maintenance from on-line data

Rapid gravity filters, the final particulate barrier in many water treatment systems, are typically monitored using on-line turbidity, flow and head loss instrumentation. Current metrics for assessing filtration performance from on-line turbidity data were critically assessed and observed not to effectively and consistently summarise the important properties of a turbidity distribution and the associated water quality risk. In the absence of a consistent risk function for turbidity in treated water, using on-line turbidity as an indicative rather than a quantitative variable appears to be more practical. Best practice suggests that filtered water turbidity should be maintained below 0.1 NTU, at higher turbidity we can be less confident of an effective particle and pathogen barrier. Based on this simple distinction filtration performance has been described in terms of reliability and resilience by characterising the likelihood, frequency and duration of turbidity spikes greater than 0.1 NTU. This view of filtration performance is then used to frame operational diagnosis of unsatisfactory performance in terms of a machine learning classification problem. Through calculation of operationally relevant predictor variables and application of the Classification and Regression Tree (CART) algorithm the conditions associated with the greatest risk of poor filtration performance can be effectively modelled and communicated in operational terms. This provides a method for an evidence based decision support which can be used to efficiently manage individual pathogen barriers in a multi-barrier system

Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

The joint workshop of the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, and the Vision and Fusion Laboratory (Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)), is organized annually since 2005 with the aim to report on the latest research and development findings of the doctoral students of both institutions. This book provides a collection of 16 technical reports on the research results presented on the 2009 workshop

On interval branch-and-bound for additively separable functions with common variables

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis

Efficient processing of large-scale spatio-temporal data

Millionen Geräte, wie z.B. Mobiltelefone, Autos und Umweltsensoren senden ihre Positionen zusammen mit einem Zeitstempel und weiteren Nutzdaten an einen Server zu verschiedenen Analysezwecken. Die Positionsinformationen und übertragenen Ereignisinformationen werden als Punkte oder Polygone dargestellt. Eine weitere Art räumlicher Daten sind Rasterdaten, die zum Beispiel von Kameras und Sensoren produziert werden. Diese großen räumlich-zeitlichen Datenmengen können nur auf skalierbaren Plattformen wie Hadoop und Apache Spark verarbeitet werden, die jedoch z.B. die Nachbarschaftsinformation nicht ausnutzen können - was die Ausführung bestimmter Anfragen praktisch unmöglich macht. Die wiederholten Ausführungen der Analyseprogramme während ihrer Entwicklung und durch verschiedene Nutzer resultieren in langen Ausführungszeiten und hohen Kosten für gemietete Ressourcen, die durch die Wiederverwendung von Zwischenergebnissen reduziert werden können. Diese Arbeit beschäftigt sich mit den beiden oben beschriebenen Herausforderungen. Wir präsentieren zunächst das STARK Framework für die Verarbeitung räumlich-zeitlicher Vektor- und Rasterdaten in Apache Spark. Wir identifizieren verschiedene Algorithmen für Operatoren und analysieren, wie diese von den Eigenschaften der zugrundeliegenden Plattform profitieren können. Weiterhin wird untersucht, wie Indexe in der verteilten und parallelen Umgebung realisiert werden können. Außerdem vergleichen wir Partitionierungsmethoden, die unterschiedlich gut mit ungleichmäßiger Datenverteilung und der Größe der Datenmenge umgehen können und präsentieren einen Ansatz um die auf Operatorebene zu verarbeitende Datenmenge frühzeitig zu reduzieren. Um die Ausführungszeit von Programmen zu verkürzen, stellen wir einen Ansatz zur transparenten Materialisierung von Zwischenergebnissen vor. Dieser Ansatz benutzt ein Entscheidungsmodell, welches auf den tatsächlichen Operatorkosten basiert. In der Evaluierung vergleichen wir die verschiedenen Implementierungs- sowie Konfigurationsmöglichkeiten in STARK und identifizieren Szenarien wann Partitionierung und Indexierung eingesetzt werden sollten. Außerdem vergleichen wir STARK mit verwandten Systemen. Im zweiten Teil der Evaluierung zeigen wir, dass die transparente Wiederverwendung der materialisierten Zwischenergebnisse die Ausführungszeit der Programme signifikant verringern kann.Millions of location-aware devices, such as mobile phones, cars, and environmental sensors constantly report their positions often in combination with a timestamp to a server for different kinds of analyses. While the location information of the devices and reported events is represented as points and polygons, raster data is another type of spatial data, which is for example produced by cameras and sensors. This Big spatio-temporal Data needs to be processed on scalable platforms, such as Hadoop and Apache Spark, which, however, are unaware of, e.g., spatial neighborhood, what makes them practically impossible to use for this kind of data. The repeated executions of the programs during development and by different users result in long execution times and potentially high costs in rented clusters, which can be reduced by reusing commonly computed intermediate results. Within this thesis, we tackle the two challenges described above. First, we present the STARK framework for processing spatio-temporal vector and raster data on the Apache Spark stack. For operators, we identify several possible algorithms and study how they can benefit from the underlying platform's properties. We further investigate how indexes can be realized in the distributed and parallel architecture of Big Data processing engines and compare methods for data partitioning, which perform differently well with respect to data skew and data set size. Furthermore, an approach to reduce the amount of data to process at operator level is presented. In order to reduce the execution times, we introduce an approach to transparently recycle intermediate results of dataflow programs, based on operator costs. To compute the costs, we instrument the programs with profiling code to gather the execution time and result size of the operators. In the evaluation, we first compare the various implementation and configuration possibilities in STARK and identify scenarios when and how partitioning and indexing should be applied. We further compare STARK to related systems and show that we can achieve significantly better execution times, not only when exploiting existing partitioning information. In the second part of the evaluation, we show that with the transparent cost-based materialization and recycling of intermediate results, the execution times of programs can be reduced significantly

Road Estimation Using GPS Traces and Real Time Kinematic Data

Advance Driver Assistance System (ADAS) are becoming the main issue in today’s automotive industry. The new generation of ADAS aims at focusing on more details and obtaining more accuracy. To achieve this objective, the research and development parts of the automobile industry intend to utilize Global Positioning System (GPS) by integrating it with other existing tools in ADAS. There are several driving assistance systems which are served by a digital map as a primary or a secondary sensor. The traditional techniques of digital map generation are expensive and time consuming and require extensive manual effort. Therefore, having frequently updated maps is an issue. Furthermore, the existing commercial digital maps are not highly accurate. This Master thesis presents several algorithms for automatically converting raw Universal Serial Bus (USB)-GPS and Real Time Kinematic (RTK) GPS traces into a routable road network. The traces are gathered by driving 20 times on a highway. This work begins by pruning raw GPS traces using four different algorithms. The first step tries to minimize the number of outliers. After the traces are smoothed, they tend to consolidate into smooth paths. So in order to merge all 20 trips together and estimate the road network a Trace Merging algorithm is applied. Finally, a Non-Uniform Rational B-Spline (NURBS) curve is implemented as an approximation curve to smooth the road shape and decrease the effect of noisy data further. Since the RTK-GPS receiver provides highly accurate data, the curve resulted from its GPS data is the most sufficient road shape. Therefore, it is used as a ground truth to compare the result of each pruning algorithm based on data from USB-GPS. Lastly, the results of this work are demonstrated and a quality evaluation is done for all methods

Hybrid Dynamic Modelling of Engine Emissions on Multi-Physics Simulation Platform. A Framework Combining Dynamic and Statistical Modelling to Develop Surrogate Models of System of Internal Combustion Engine for Emission Modelling

The data-driven models used for the design of powertrain controllers are typically based on the data obtained from steady-state experiments. However, they are only valid under stable conditions and do not provide any information on the dynamic behaviour of the system. In order to capture this behaviour, dynamic modelling techniques are intensively studied to generate alternative solutions for engine mapping and calibration problem, aiming to address the need to increase productivity (reduce development time) and to develop better models for the actual behaviour of the engine under real-world conditions. In this thesis, a dynamic modelling approach is presented undertaken for the prediction of NOx emissions for a 2.0 litre Diesel engine, based on a coupled pre-validated virtual Diesel engine model (GT- Suite ® 1-D air path model) and in-cylinder combustion model (CMCL ® Stochastic Reactor Model Engine Suite). In the context of the considered Engine Simulation Framework, GT Suite + Stochastic Reactor Model (SRM), one fundamental problem is to establish a real time stochastic simulation capability. This problem can be addressed by replacing the slow combustion chemistry solver (SRM) with an appropriate NOx surrogate model. The approach taken in this research for the development of this surrogate model was based on a combination of design of dynamic experiments run on the virtual diesel engine model (GT- Suite), with a dynamic model fitted for the parameters required as input to the SRM, with a zonal design of experiments (DoEs), using Optimal Latin Hypercubes (OLH), run on the SRM model. A response surface model was fitted on the predicted NOx from the SRM OLH DoE data. This surrogate NOx model was then used to replace the computationally expensive SRM simulation, enabling real-time simulations of transient drive cycles to be executed. The performance of the approach was validated on a simulated NEDC drive cycle, against experimental data collected for the engine case study. The capability of methodology to capture the transient trends of the system shows promising results and will be used for the development of global surrogate prediction models for engine-out emissions

Optimisation massivement multi-tâche sur grappes de calcul hétérogènes – Application aux problèmes de permutation

Branch-and-Bound (B&B) is a frequently used tree-search exploratory method for the exact resolution of combinatorial optimization problems (COPs). However, in practice, only small problem instances can be solved on a sequential computer, as B&B generates often generates a huge amount of subproblems to be evaluated. In order to solve large COPs, we revisit the design and implementation of massively parallel B&B on top of large heterogeneous clusters, integrating multi-core CPUs, many-core processors and GPUs.For the efficient storage and management of subproblems an original data structure (IVM) dedicated to permutation problems is used. Because of the highly irregular and unpredictable shape of the B&B tree, dynamic load balancing between parallel exploration processes is one of the main issues addressed in this thesis. Based on a compact encoding of the search space in the form of intervals, work stealing strategies for multi-core and GPU are proposed, as well as hierarchical approaches for load balancing in distributed memory multi-CPU/multi-GPU systems. Three permutation problems, the Flowshop Scheduling Problem (FSP), the Quadratic Assignment Problem (QAP) and the n-Queens puzzle problem are used as test-cases.The resolution, in 9 hours, of a FSP instance with an estimated sequential execution time of 22 years demonstrates the scalability of the proposed algorithms on a cluster composed of 36 GPUs.L'algorithme Branch-and-Bound (B&B) est une méthode de recherche arborescente fréquemment utilisé pour la résolution exacte de problèmes d'optimisation combinatoire (POC). Néanmoins, seules des petites instances peuvent être effectivement résolues sur une machine séquentielle, le nombre de sous-problèmes à évaluer étant souvent très grand. Visant la resolution de POC de grande taille, nous réexaminons la conception et l'implémentation d'algorithmes B&B massivement parallèles sur de larges plateformes hétérogènes de calcul, intégrant des processeurs multi-coeurs, many-cores et et processeurs graphiques (GPUs). Pour une représentation compacte en mémoire des sous-problèmes une structure de données originale (IVM), dédiée aux problèmes de permutation est utilisée. En raison de la forte irrégularité de l'arbre de recherche, l'équilibrage de charge dynamique entre processus d'exploration parallèles occupe une place centrale dans cette thèse. Basés sur un encodage compact de l'espace de recherche sous forme d'intervalles, des stratégies de vol de tâches sont proposées pour processeurs multi-core et GPU, ainsi une approche hiérarchique pour l'équilibrage de charge dans les systèmes multi-GPU et multi-CPU à mémoire distribuée. Trois problèmes d'optimisation définis sur l'ensemble des permutations, le problème d'ordonnancement Flow-Shop (FSP), d'affectation quadratique (QAP) et le problème des n-dames sont utilisés comme cas d'étude. La resolution en 9 heures d'une instance du FSP dont le temps de résolution séquentiel est estimé à 22 ans demontre la capacité de passage à l'échelle des algorithmes proposés sur une grappe de calcul composé de 36 GPUs

Enabling Technology in Optical Fiber Communications: From Device, System to Networking

This book explores the enabling technology in optical fiber communications. It focuses on the state-of-the-art advances from fundamental theories, devices, and subsystems to networking applications as well as future perspectives of optical fiber communications. The topics cover include integrated photonics, fiber optics, fiber and free-space optical communications, and optical networking

CUDA implementation of the solution of a system of linear equations arising in an hp-Finite Element code

El método de elementos finitos (FEM) ha probado ser uno de los métodos mas eficientes para resolver ecuaciones diferenciales. Diseñado para aprovechar las capacidades de calculo de los ordenadores, las mejores realizadas a lo largo de los años han permitido solucionar problemas cada vez mas grandes. Una de las ultimas mejoras ha sido el desarrollo de las tarjetas gráficas (GPU). La programación científica con GPUs era extremadamente compleja hasta que en 2006 la compañía NVIDIA desarrolló CUDA. Es un lenguaje genérico de programación que no requiere de conocimientos de la tradicional programación con GPUs. Estos dispositivos son capaces de realizar grandes cantidades de operaciones simultáneamente. Esta capacidad los hace muy atractivos para el calculo en FEM. Una de las partes del FEM que mas recursos computacionales requiere, es la solución de sistemas de ecuaciones lineales. En este trabajo de fin de máster, se implementará un algoritmo para la solución de sistemas de ecuaciones lineales en CUDA. Dicho sistema provendrá de la aplicación de un método hp-FEM a la ecuación de Laplace. El objetivo es comparar la ejecución del solucionador implementado CUDA frente a una implementación en C y comprobar si CUDA presenta ventajas sobre la programación tradicional