Run-Time Scalable Hardware for Reconfigurable Systems

La optimización de parámetros tales como el consumo de potencia, la cantidad de recursos lógicos empleados o la ocupación de memoria ha sido siempre una de las preocupaciones principales a la hora de diseñar sistemas embebidos. Esto es debido a que se trata de sistemas dotados de una cantidad de recursos limitados, y que han sido tradicionalmente empleados para un propósito específico, que permanece invariable a lo largo de toda la vida útil del sistema. Sin embargo, el uso de sistemas embebidos se ha extendido a áreas de aplicación fuera de su ámbito tradicional, caracterizadas por una mayor demanda computacional. Así, por ejemplo, algunos de estos sistemas deben llevar a cabo un intenso procesado de señales multimedia o la transmisión de datos mediante sistemas de comunicaciones de alta capacidad. Por otra parte, las condiciones de operación del sistema pueden variar en tiempo real. Esto sucede, por ejemplo, si su funcionamiento depende de datos medidos por el propio sistema o recibidos a través de la red, de las demandas del usuario en cada momento, o de condiciones internas del propio dispositivo, tales como la duración de la batería. Como consecuencia de la existencia de requisitos de operación dinámicos es necesario ir hacia una gestión dinámica de los recursos del sistema. Si bien el software es inherentemente flexible, no ofrece una potencia computacional tan alta como el hardware. Por lo tanto, el hardware reconfigurable aparece como una solución adecuada para tratar con mayor flexibilidad los requisitos variables dinámicamente en sistemas con alta demanda computacional. La flexibilidad y adaptabilidad del hardware requieren de dispositivos reconfigurables que permitan la modificación de su funcionalidad bajo demanda. En esta tesis se han seleccionado las FPGAs (Field Programmable Gate Arrays) como los dispositivos más apropiados, hoy en día, para implementar sistemas basados en hardware reconfigurable De entre todas las posibilidades existentes para explotar la capacidad de reconfiguración de las FPGAs comerciales, se ha seleccionado la reconfiguración dinámica y parcial. Esta técnica consiste en substituir una parte de la lógica del dispositivo, mientras el resto continúa en funcionamiento. La capacidad de reconfiguración dinámica y parcial de las FPGAs es empleada en esta tesis para tratar con los requisitos de flexibilidad y de capacidad computacional que demandan los dispositivos embebidos. La propuesta principal de esta tesis doctoral es el uso de arquitecturas de procesamiento escalables espacialmente, que son capaces de adaptar su funcionalidad y rendimiento en tiempo real, estableciendo un compromiso entre dichos parámetros y la cantidad de lógica que ocupan en el dispositivo. A esto nos referimos con arquitecturas con huellas escalables. En particular, se propone el uso de arquitecturas altamente paralelas, modulares, regulares y con una alta localidad en sus comunicaciones, para este propósito. El tamaño de dichas arquitecturas puede ser modificado mediante la adición o eliminación de algunos de los módulos que las componen, tanto en una dimensión como en dos. Esta estrategia permite implementar soluciones escalables, sin tener que contar con una versión de las mismas para cada uno de los tamaños posibles de la arquitectura. De esta manera se reduce significativamente el tiempo necesario para modificar su tamaño, así como la cantidad de memoria necesaria para almacenar todos los archivos de configuración. En lugar de proponer arquitecturas para aplicaciones específicas, se ha optado por patrones de procesamiento genéricos, que pueden ser ajustados para solucionar distintos problemas en el estado del arte. A este respecto, se proponen patrones basados en esquemas sistólicos, así como de tipo wavefront. Con el objeto de poder ofrecer una solución integral, se han tratado otros aspectos relacionados con el diseño y el funcionamiento de las arquitecturas, tales como el control del proceso de reconfiguración de la FPGA, la integración de las arquitecturas en el resto del sistema, así como las técnicas necesarias para su implementación. Por lo que respecta a la implementación, se han tratado distintos aspectos de bajo nivel dependientes del dispositivo. Algunas de las propuestas realizadas a este respecto en la presente tesis doctoral son un router que es capaz de garantizar el correcto rutado de los módulos reconfigurables dentro del área destinada para ellos, así como una estrategia para la comunicación entre módulos que no introduce ningún retardo ni necesita emplear recursos configurables del dispositivo. El flujo de diseño propuesto se ha automatizado mediante una herramienta denominada DREAMS. La herramienta se encarga de la modificación de las netlists correspondientes a cada uno de los módulos reconfigurables del sistema, y que han sido generadas previamente mediante herramientas comerciales. Por lo tanto, el flujo propuesto se entiende como una etapa de post-procesamiento, que adapta esas netlists a los requisitos de la reconfiguración dinámica y parcial. Dicha modificación la lleva a cabo la herramienta de una forma completamente automática, por lo que la productividad del proceso de diseño aumenta de forma evidente. Para facilitar dicho proceso, se ha dotado a la herramienta de una interfaz gráfica. El flujo de diseño propuesto, y la herramienta que lo soporta, tienen características específicas para abordar el diseño de las arquitecturas dinámicamente escalables propuestas en esta tesis. Entre ellas está el soporte para el realojamiento de módulos reconfigurables en posiciones del dispositivo distintas a donde el módulo es originalmente implementado, así como la generación de estructuras de comunicación compatibles con la simetría de la arquitectura. El router has sido empleado también en esta tesis para obtener un rutado simétrico entre nets equivalentes. Dicha posibilidad ha sido explotada para aumentar la protección de circuitos con altos requisitos de seguridad, frente a ataques de canal lateral, mediante la implantación de lógica complementaria con rutado idéntico. Para controlar el proceso de reconfiguración de la FPGA, se propone en esta tesis un motor de reconfiguración especialmente adaptado a los requisitos de las arquitecturas dinámicamente escalables. Además de controlar el puerto de reconfiguración, el motor de reconfiguración ha sido dotado de la capacidad de realojar módulos reconfigurables en posiciones arbitrarias del dispositivo, en tiempo real. De esta forma, basta con generar un único bitstream por cada módulo reconfigurable del sistema, independientemente de la posición donde va a ser finalmente reconfigurado. La estrategia seguida para implementar el proceso de realojamiento de módulos es diferente de las propuestas existentes en el estado del arte, pues consiste en la composición de los archivos de configuración en tiempo real. De esta forma se consigue aumentar la velocidad del proceso, mientras que se reduce la longitud de los archivos de configuración parciales a almacenar en el sistema. El motor de reconfiguración soporta módulos reconfigurables con una altura menor que la altura de una región de reloj del dispositivo. Internamente, el motor se encarga de la combinación de los frames que describen el nuevo módulo, con la configuración existente en el dispositivo previamente. El escalado de las arquitecturas de procesamiento propuestas en esta tesis también se puede beneficiar de este mecanismo. Se ha incorporado también un acceso directo a una memoria externa donde se pueden almacenar bitstreams parciales. Para acelerar el proceso de reconfiguración se ha hecho funcionar el ICAP por encima de la máxima frecuencia de reloj aconsejada por el fabricante. Así, en el caso de Virtex-5, aunque la máxima frecuencia del reloj deberían ser 100 MHz, se ha conseguido hacer funcionar el puerto de reconfiguración a frecuencias de operación de hasta 250 MHz, incluyendo el proceso de realojamiento en tiempo real. Se ha previsto la posibilidad de portar el motor de reconfiguración a futuras familias de FPGAs. Por otro lado, el motor de reconfiguración se puede emplear para inyectar fallos en el propio dispositivo hardware, y así ser capaces de evaluar la tolerancia ante los mismos que ofrecen las arquitecturas reconfigurables. Los fallos son emulados mediante la generación de archivos de configuración a los que intencionadamente se les ha introducido un error, de forma que se modifica su funcionalidad. Con el objetivo de comprobar la validez y los beneficios de las arquitecturas propuestas en esta tesis, se han seguido dos líneas principales de aplicación. En primer lugar, se propone su uso como parte de una plataforma adaptativa basada en hardware evolutivo, con capacidad de escalabilidad, adaptabilidad y recuperación ante fallos. En segundo lugar, se ha desarrollado un deblocking filter escalable, adaptado a la codificación de vídeo escalable, como ejemplo de aplicación de las arquitecturas de tipo wavefront propuestas. El hardware evolutivo consiste en el uso de algoritmos evolutivos para diseñar hardware de forma autónoma, explotando la flexibilidad que ofrecen los dispositivos reconfigurables. En este caso, los elementos de procesamiento que componen la arquitectura son seleccionados de una biblioteca de elementos presintetizados, de acuerdo con las decisiones tomadas por el algoritmo evolutivo, en lugar de definir la configuración de las mismas en tiempo de diseño. De esta manera, la configuración del core puede cambiar cuando lo hacen las condiciones del entorno, en tiempo real, por lo que se consigue un control autónomo del proceso de reconfiguración dinámico. Así, el sistema es capaz de optimizar, de forma autónoma, su propia configuración. El hardware evolutivo tiene una capacidad inherente de auto-reparación. Se ha probado que las arquitecturas evolutivas propuestas en esta tesis son tolerantes ante fallos, tanto transitorios, como permanentes y acumulativos. La plataforma evolutiva se ha empleado para implementar filtros de eliminación de ruido. La escalabilidad también ha sido aprovechada en esta aplicación. Las arquitecturas evolutivas escalables permiten la adaptación autónoma de los cores de procesamiento ante fluctuaciones en la cantidad de recursos disponibles en el sistema. Por lo tanto, constituyen un ejemplo de escalabilidad dinámica para conseguir un determinado nivel de calidad, que puede variar en tiempo real. Se han propuesto dos variantes de sistemas escalables evolutivos. El primero consiste en un único core de procesamiento evolutivo, mientras que el segundo está formado por un número variable de arrays de procesamiento. La codificación de vídeo escalable, a diferencia de los codecs no escalables, permite la decodificación de secuencias de vídeo con diferentes niveles de calidad, de resolución temporal o de resolución espacial, descartando la información no deseada. Existen distintos algoritmos que soportan esta característica. En particular, se va a emplear el estándar Scalable Video Coding (SVC), que ha sido propuesto como una extensión de H.264/AVC, ya que este último es ampliamente utilizado tanto en la industria, como a nivel de investigación. Para poder explotar toda la flexibilidad que ofrece el estándar, hay que permitir la adaptación de las características del decodificador en tiempo real. El uso de las arquitecturas dinámicamente escalables es propuesto en esta tesis con este objetivo. El deblocking filter es un algoritmo que tiene como objetivo la mejora de la percepción visual de la imagen reconstruida, mediante el suavizado de los "artefactos" de bloque generados en el lazo del codificador. Se trata de una de las tareas más intensivas en procesamiento de datos de H.264/AVC y de SVC, y además, su carga computacional es altamente dependiente del nivel de escalabilidad seleccionado en el decodificador. Por lo tanto, el deblocking filter ha sido seleccionado como prueba de concepto de la aplicación de las arquitecturas dinámicamente escalables para la compresión de video. La arquitectura propuesta permite añadir o eliminar unidades de computación, siguiendo un esquema de tipo wavefront. La arquitectura ha sido propuesta conjuntamente con un esquema de procesamiento en paralelo del deblocking filter a nivel de macrobloque, de tal forma que cuando se varía del tamaño de la arquitectura, el orden de filtrado de los macrobloques varia de la misma manera. El patrón propuesto se basa en la división del procesamiento de cada macrobloque en dos etapas independientes, que se corresponden con el filtrado horizontal y vertical de los bloques dentro del macrobloque. Las principales contribuciones originales de esta tesis son las siguientes: - El uso de arquitecturas altamente regulares, modulares, paralelas y con una intensa localidad en sus comunicaciones, para implementar cores de procesamiento dinámicamente reconfigurables. - El uso de arquitecturas bidimensionales, en forma de malla, para construir arquitecturas dinámicamente escalables, con una huella escalable. De esta forma, las arquitecturas permiten establecer un compromiso entre el área que ocupan en el dispositivo, y las prestaciones que ofrecen en cada momento. Se proponen plantillas de procesamiento genéricas, de tipo sistólico o wavefront, que pueden ser adaptadas a distintos problemas de procesamiento. - Un flujo de diseño y una herramienta que lo soporta, para el diseño de sistemas reconfigurables dinámicamente, centradas en el diseño de las arquitecturas altamente paralelas, modulares y regulares propuestas en esta tesis. - Un esquema de comunicaciones entre módulos reconfigurables que no introduce ningún retardo ni requiere el uso de recursos lógicos propios. - Un router flexible, capaz de resolver los conflictos de rutado asociados con el diseño de sistemas reconfigurables dinámicamente. - Un algoritmo de optimización para sistemas formados por múltiples cores escalables que optimice, mediante un algoritmo genético, los parámetros de dicho sistema. Se basa en un modelo conocido como el problema de la mochila. - Un motor de reconfiguración adaptado a los requisitos de las arquitecturas altamente regulares y modulares. Combina una alta velocidad de reconfiguración, con la capacidad de realojar módulos en tiempo real, incluyendo el soporte para la reconfiguración de regiones que ocupan menos que una región de reloj, así como la réplica de un módulo reconfigurable en múltiples posiciones del dispositivo. - Un mecanismo de inyección de fallos que, empleando el motor de reconfiguración del sistema, permite evaluar los efectos de fallos permanentes y transitorios en arquitecturas reconfigurables. - La demostración de las posibilidades de las arquitecturas propuestas en esta tesis para la implementación de sistemas de hardware evolutivos, con una alta capacidad de procesamiento de datos. - La implementación de sistemas de hardware evolutivo escalables, que son capaces de tratar con la fluctuación de la cantidad de recursos disponibles en el sistema, de una forma autónoma. - Una estrategia de procesamiento en paralelo para el deblocking filter compatible con los estándares H.264/AVC y SVC que reduce el número de ciclos de macrobloque necesarios para procesar un frame de video. - Una arquitectura dinámicamente escalable que permite la implementación de un nuevo deblocking filter, totalmente compatible con los estándares H.264/AVC y SVC, que explota el paralelismo a nivel de macrobloque. El presente documento se organiza en siete capítulos. En el primero se ofrece una introducción al marco tecnológico de esta tesis, especialmente centrado en la reconfiguración dinámica y parcial de FPGAs. También se motiva la necesidad de las arquitecturas dinámicamente escalables propuestas en esta tesis. En el capítulo 2 se describen las arquitecturas dinámicamente escalables. Dicha descripción incluye la mayor parte de las aportaciones a nivel arquitectural realizadas en esta tesis. Por su parte, el flujo de diseño adaptado a dichas arquitecturas se propone en el capítulo 3. El motor de reconfiguración se propone en el 4, mientras que el uso de dichas arquitecturas para implementar sistemas de hardware evolutivo se aborda en el 5. El deblocking filter escalable se describe en el 6, mientras que las conclusiones finales de esta tesis, así como la descripción del trabajo futuro, son abordadas en el capítulo 7. ABSTRACT The optimization of system parameters, such as power dissipation, the amount of hardware resources and the memory footprint, has been always a main concern when dealing with the design of resource-constrained embedded systems. This situation is even more demanding nowadays. Embedded systems cannot anymore be considered only as specific-purpose computers, designed for a particular functionality that remains unchanged during their lifetime. Differently, embedded systems are now required to deal with more demanding and complex functions, such as multimedia data processing and high-throughput connectivity. In addition, system operation may depend on external data, the user requirements or internal variables of the system, such as the battery life-time. All these conditions may vary at run-time, leading to adaptive scenarios. As a consequence of both the growing computational complexity and the existence of dynamic requirements, dynamic resource management techniques for embedded systems are needed. Software is inherently flexible, but it cannot meet the computing power offered by hardware solutions. Therefore, reconfigurable hardware emerges as a suitable technology to deal with the run-time variable requirements of complex embedded systems. Adaptive hardware requires the use of reconfigurable devices, where its functionality can be modified on demand. In this thesis, Field Programmable Gate Arrays (FPGAs) have been selected as the most appropriate commercial technology existing nowadays to implement adaptive hardware systems. There are different ways of exploiting reconfigurability in reconfigurable devices. Among them is dynamic and partial reconfiguration. This is a technique which consists in substituting part of the FPGA logic on demand, while the rest of the device continues working. The strategy followed in this thesis is to exploit the dynamic and partial reconfiguration of commercial FPGAs to deal with the flexibility and complexity demands of state-of-the-art embedded systems. The proposal of this thesis to deal with run-time variable system conditions is the use of spatially scalable processing hardware IP cores, which are able to adapt their functionality or performance at run-time, trading them off with the amount of logic resources they occupy in the device. This is referred to as a scalable footprint in the context of this thesis. The distinguishing characteristic of the proposed cores is that they rely on highly parallel, modular and regular architectures, arranged in one or two dimensions. These architectures can be scaled by means of the addition or removal of the composing blocks. This strategy avoids implementing a full version of the core for each possible size, with the corresponding benefits in terms of scaling and adaptation time, as well as bitstream storage memory requirements. Instead of providing specific-purpose architectures, generic architectural templates, which can be tuned to solve different problems, are proposed in this thesis. Architectures following both systolic and wavefront templates have been selected. Together with the proposed scalable architectural templates, other issues needed to ensure the proper design and operation of the scalable cores, such as the device reconfiguration control, the run-time management of the architecture and the implementation techniques have been also addressed in this thesis. With regard to the implementation of dynamically reconfigurable architectures, device dependent low-level details are addressed. Some of the aspects covered in this thesis are the area constrained routing for reconfigurable modules, or an inter-module communication strategy which does not introduce either extra delay or logic overhead. The system implementation, from the hardware description to the device configuration bitstream, has been fully automated by modifying the netlists corresponding to each of the system modules, which are previously generated using the vendor tools. This modification is therefore envisaged as a post-processing step. Based on these implementation proposals, a design tool called DREAMS (Dynamically Reconfigurable Embedded and Modular Systems) has been created, including a graphic user interface. The tool has specific features to cope with modular and regular architectures, including the support for module relocation and the inter-module communications scheme based on the symmetry of the architecture. The core of the tool is a custom router, which has been also exploited in this thesis to obtain symmetric routed nets, with the aim of enhancing the protection of critical reconfigurable circuits against side channel attacks. This is achieved by duplicating the logic with an exactly equal routing. In order to control the reconfiguration process of the FPGA, a Reconfiguration Engine suited to the specific requirements set by the proposed architectures was also proposed. Therefore, in addition to controlling the reconfiguration port, the Reconfiguration Engine has been enhanced with the online relocation ability, which allows employing a unique configuration bitstream for all the positions where the module may be placed in the device. Differently to the existing relocating solutions, which are based on bitstream parsers, the proposed approach is based on the online composition of bitstreams. This strategy allows increasing the speed of the process, while the length of partial bitstreams is also reduced. The height of the reconfigurable modules can be lower than the height of a clock region. The Reconfiguration Engine manages the merging process of the new and the existing configuration frames within each clock region. The process of scaling up and down the hardware cores also benefits from this technique. A direct link to an external memory where partial bitstreams can be stored has been also implemented. In order to accelerate the reconfiguration process, the ICAP has been overclocked over the speed reported by the manufacturer. In the case of Virtex-5, even though the maximum frequency of the ICAP is reported to be 100 MHz, valid operations at 250 MHz have been achieved, including the online relocation process. Portability of the reconfiguration solution to today's and probably, future FPGAs, has been also considered. The reconfiguration engine can be also used to inject faults in real hardware devices, and this way being able to evaluate the fault tolerance offered by the reconfigurable architectures. Faults are emulated by introducing partial bitstreams intentionally modified to provide erroneous functionality. To prove the validity and the benefits offered by the proposed architectures, two demonstration application lines have been envisaged. First, scalable architectures have been employed to develop an evolvable hardware platform with adaptability, fault tolerance and scalability properties. Second, they have been used to implement a scalable deblocking filter suited to scalable video coding. Evolvable Hardware is the use of evolutionary algorithms to design hardware in an autonomous way, exploiting the flexibility offered by reconfigurable devices. In this case, processing elements composing the architecture are selected from a presynthesized library of processing elements, according to the decisions taken by the algorithm, instead of being decided at design time. This way, the configuration of the array may change as run-time environmental conditions do, achieving autonomous control of the dynamic reconfiguration process. Thus, the self-optimization property is added to the native self-configurability of the dynamically scalable architectures. In addition, evolvable hardware adaptability inherently offers self-healing features. The proposal has proved to be self-tolerant, since it is able to self-recover from both transient and cumulative permanent faults. The proposed evolvable architecture has been used to implement noise removal image filters. Scalability has been also exploited in this application. Scalable evolvable hardware architectures allow the autonomous adaptation of the processing cores to a fluctuating amount of resources available in the system. Thus, it constitutes an example of the dynamic quality scalability tackled in this thesis. Two variants have been proposed. The first one consists in a single dynamically scalable evolvable core, and the second one contains a variable number of processing cores. Scalable video is a flexible approach for video compression, which offers scalability at different levels. Differently to non-scalable codecs, a scalable video bitstream can be decoded with different levels of quality, spatial or temporal resolutions, by discarding the undesired information. The interest in this technology has been fostered by the development of the Scalable Video Coding (SVC) standard, as an extension of H.264/AVC. In order to exploit all the flexibility offered by the standard, it is necessary to adapt the characteristics of the decoder to the requirements of each client during run-time. The use of dynamically scalable architectures is proposed in this thesis with this aim. The deblocking filter algorithm is the responsible of improving the visual perception of a reconstructed image, by smoothing blocking artifacts generated in the encoding loop. This is one of the most computationally intensive tasks of the standard, and furthermore, it is highly dependent on the selected scalability level in the decoder. Therefore, the deblocking filter has been selected as a proof of concept of the implementation of dynamically scalable architectures for video compression. The proposed architecture allows the run-time addition or removal of computational units working in parallel to change its level of parallelism, following a wavefront computational pattern. Scalable architecture is offered together with a scalable parallelization strategy at the macroblock level, such that when the size of the architecture changes, the macroblock filtering order is modified accordingly. The proposed pattern is based on the division of the macroblock processing into two independent stages, corresponding to the horizontal and vertical filtering of the blocks within the macroblock. The main contributions of this thesis are: - The use of highly parallel, modular, regular and local architectures to implement dynamically reconfigurable processing IP cores, for data intensive applications with flexibility requirements. - The use of two-dimensional mesh-type arrays as architectural templates to build dynamically reconfigurable IP cores, with a scalable footprint. The proposal consists in generic architectural templates, which can be tuned to solve different computational problems. •A design flow and a tool targeting the design of DPR systems, focused on highly parallel, modular and local architectures. - An inter-module communication strategy, which does not introduce delay or area overhead, named Virtual Borders. - A custom and flexible router to solve the routing conflicts as well as the inter-module communication problems, appearing during the design of DPR systems. - An algorithm addressing the optimization of systems composed of multiple scalable cores, which size can be decided individually, to optimize the system parameters. It is based on a model known as the multi-dimensional multi-choice Knapsack problem. - A reconfiguration engine tailored to the requirements of highly regular and modular architectures. It combines a high reconfiguration throughput with run-time module relocation capabilities, including the support for sub-clock reconfigurable regions and the replication in multiple positions. - A fault injection mechanism which takes advantage of the system reconfiguration engine, as well as the modularity of the proposed reconfigurable architectures, to evaluate the effects of transient and permanent faults in these architectures. - The demonstration of the possibilities of the architectures proposed in this thesis to implement evolvable hardware systems, while keeping a high processing throughput. - The implementation of scalable evolvable hardware systems, which are able to adapt to the fluctuation of the amount of resources available in the system, in an autonomous way. - A parallelization strategy for the H.264/AVC and SVC deblocking filter, which reduces the number of macroblock cycles needed to process the whole frame. - A dynamically scalable architecture that permits the implementation of a novel deblocking filter module, fully compliant with the H.264/AVC and SVC standards, which exploits the macroblock level parallelism of the algorithm. This document is organized in seven chapters. In the first one, an introduction to the technology framework of this thesis, specially focused on dynamic and partial reconfiguration, is provided. The need for the dynamically scalable processing architectures proposed in this work is also motivated in this chapter. In chapter 2, dynamically scalable architectures are described. Description includes most of the architectural contributions of this work. The design flow tailored to the scalable architectures, together with the DREAMs tool provided to implement them, are described in chapter 3. The reconfiguration engine is described in chapter 4. The use of the proposed scalable archtieectures to implement evolvable hardware systems is described in chapter 5, while the scalable deblocking filter is described in chapter 6. Final conclusions of this thesis, and the description of future work, are addressed in chapter 7.

Formulations and Metaheuristics for combinatorial optimization problems

Combinatorial optimization problems have been strongly addressed throughout history. Their study involves highly applied problems that must be solved in reasonable times. This doctoral Thesis addresses three Operations Research problems: the first deals with the Traveling Salesman Problem with Pickups and Delivery with Handling cost, which was approached with two metaheuristics based on Iterated Local Search; the results show that the proposed methods are faster and obtain good results respect to the metaheuristics from the literature. The second problem corresponds to the Quadratic Multiple Knapsack Problem, and polynomial formulations and relaxations are presented for new instances of the problem; in addition, a metaheuristic and a matheuristic are proposed that are competitive with state of the art algorithms. Finally, an Open-Pit Mining problem is approached. This problem is solved with a parallel genetic algorithm that allows excavations using truncated cones. Each of these problems was computationally tested with difficult instances from the literature, obtaining good quality results in reasonable computational times, and making significant contributions to the state of the art techniques of Operations Research.

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

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Ecological Literacy And Beyond: Problem-based Learning For Future Professionals.

Ecological science contributes to solving a broad range of environmental problems. However, lack of ecological literacy in practice often limits application of this knowledge. In this paper, we highlight a critical but often overlooked demand on ecological literacy: to enable professionals of various careers to apply scientific knowledge when faced with environmental problems. Current university courses on ecology often fail to persuade students that ecological science provides important tools for environmental problem solving. We propose problem-based learning to improve the understanding of ecological science and its usefulness for real-world environmental issues that professionals in careers as diverse as engineering, public health, architecture, social sciences, or management will address. Courses should set clear learning objectives for cognitive skills they expect students to acquire. Thus, professionals in different fields will be enabled to improve environmental decision-making processes and to participate effectively in multidisciplinary work groups charged with tackling environmental issues.

A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

Work disability remains a major problem in rheumatoid arthritis in the 2000s: data from 32 countries in the QUEST-RA Study

Introduction: Work disability is a major consequence of rheumatoid arthritis (RA), associated not only with traditional disease activity variables, but also more significantly with demographic, functional, occupational, and societal variables. Recent reports suggest that the use of biologic agents offers potential for reduced work disability rates, but the conclusions are based on surrogate disease activity measures derived from studies primarily from Western countries. Methods: The Quantitative Standard Monitoring of Patients with RA (QUEST-RA) multinational database of 8,039 patients in 86 sites in 32 countries, 16 with high gross domestic product (GDP) (>24K US dollars (USD) per capita) and 16 low-GDP countries (<11K USD), was analyzed for work and disability status at onset and over the course of RA and clinical status of patients who continued working or had stopped working in high-GDP versus low-GDP countries according to all RA Core Data Set measures. Associations of work disability status with RA Core Data Set variables and indices were analyzed using descriptive statistics and regression analyses. Results: At the time of first symptoms, 86% of men (range 57%-100% among countries) and 64% (19%-87%) of women <65 years were working. More than one third (37%) of these patients reported subsequent work disability because of RA. Among 1,756 patients whose symptoms had begun during the 2000s, the probabilities of continuing to work were 80% (95% confidence interval (CI) 78%-82%) at 2 years and 68% (95% CI 65%-71%) at 5 years, with similar patterns in high-GDP and low-GDP countries. Patients who continued working versus stopped working had significantly better clinical status for all clinical status measures and patient self-report scores, with similar patterns in high-GDP and low-GDP countries. However, patients who had stopped working in high-GDP countries had better clinical status than patients who continued working in low-GDP countries. The most significant identifier of work disability in all subgroups was Health Assessment Questionnaire (HAQ) functional disability score. Conclusions: Work disability rates remain high among people with RA during this millennium. In low-GDP countries, people remain working with high levels of disability and disease activity. Cultural and economic differences between societies affect work disability as an outcome measure for RA.

An analytical approach to the dwarf galaxies cusp problem

Aims. An analytical solution for the discrepancy between observed core-like profiles and predicted cusp profiles in dark matter halos is studied. Methods. We calculate the distribution function for Navarro-Frenk-White halos and extract energy from the distribution, taking into account the effects of baryonic physics processes. Results. We show with a simple argument that we can reproduce the evolution of a cusp to a flat density profile by a decrease of the initial potential energy.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure. (C) 2008 Published by Elsevier B.V.