Incerteza intervalar em otimização e controle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modelagem matemática: uma abordagem do método gráfico e do método simplex na resolução de problemas de otimização

Pós-graduação em Matemática em Rede Nacional - IBILCE

Image Reconstruction Using Interval Simulated Annealing in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging technique that attempts to reconstruct the impedance distribution inside an object from the impedance between electrodes placed on the object surface. The EIT reconstruction problem can be approached as a nonlinear nonconvex optimization problem in which one tries to maximize the matching between a simulated impedance problem and the observed data. This nonlinear optimization problem is often ill-posed, and not very suited to methods that evaluate derivatives of the objective function. It may be approached by simulated annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function, which involves a full simulation of the impedance problem at each iteration. A variation of SA is proposed in which the objective function is evaluated only partially, while ensuring boundaries on the behavior of the modified algorithm.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Tecniche per il controllo dinamico del consumo di potenza per piattaforme system-on-chip

Providing support for multimedia applications on low-power mobile devices remains a significant research challenge. This is primarily due to two reasons: • Portable mobile devices have modest sizes and weights, and therefore inadequate resources, low CPU processing power, reduced display capabilities, limited memory and battery lifetimes as compared to desktop and laptop systems. • On the other hand, multimedia applications tend to have distinctive QoS and processing requirementswhichmake themextremely resource-demanding. This innate conflict introduces key research challenges in the design of multimedia applications and device-level power optimization. Energy efficiency in this kind of platforms can be achieved only via a synergistic hardware and software approach. In fact, while System-on-Chips are more and more programmable thus providing functional flexibility, hardwareonly power reduction techniques cannot maintain consumption under acceptable bounds. It is well understood both in research and industry that system configuration andmanagement cannot be controlled efficiently only relying on low-level firmware and hardware drivers. In fact, at this level there is lack of information about user application activity and consequently about the impact of power management decision on QoS. Even though operating system support and integration is a requirement for effective performance and energy management, more effective and QoSsensitive power management is possible if power awareness and hardware configuration control strategies are tightly integratedwith domain-specificmiddleware services. The main objective of this PhD research has been the exploration and the integration of amiddleware-centric energymanagement with applications and operating-system. We choose to focus on the CPU-memory and the video subsystems, since they are the most power-hungry components of an embedded system. A second main objective has been the definition and implementation of software facilities (like toolkits, API, and run-time engines) in order to improve programmability and performance efficiency of such platforms. Enhancing energy efficiency and programmability ofmodernMulti-Processor System-on-Chips (MPSoCs) Consumer applications are characterized by tight time-to-market constraints and extreme cost sensitivity. The software that runs on modern embedded systems must be high performance, real time, and even more important low power. Although much progress has been made on these problems, much remains to be done. Multi-processor System-on-Chip (MPSoC) are increasingly popular platforms for high performance embedded applications. This leads to interesting challenges in software development since efficient software development is a major issue for MPSoc designers. An important step in deploying applications on multiprocessors is to allocate and schedule concurrent tasks to the processing and communication resources of the platform. The problem of allocating and scheduling precedenceconstrained tasks on processors in a distributed real-time system is NP-hard. There is a clear need for deployment technology that addresses thesemulti processing issues. This problem can be tackled by means of specific middleware which takes care of allocating and scheduling tasks on the different processing elements and which tries also to optimize the power consumption of the entire multiprocessor platform. This dissertation is an attempt to develop insight into efficient, flexible and optimalmethods for allocating and scheduling concurrent applications tomultiprocessor architectures. It is a well-known problem in literature: this kind of optimization problems are very complex even in much simplified variants, therefore most authors propose simplified models and heuristic approaches to solve it in reasonable time. Model simplification is often achieved by abstracting away platform implementation ”details”. As a result, optimization problems become more tractable, even reaching polynomial time complexity. Unfortunately, this approach creates an abstraction gap between the optimization model and the real HW-SW platform. The main issue with heuristic or, more in general, with incomplete search is that they introduce an optimality gap of unknown size. They provide very limited or no information on the distance between the best computed solution and the optimal one. The goal of this work is to address both abstraction and optimality gaps, formulating accurate models which accounts for a number of ”non-idealities” in real-life hardware platforms, developing novel mapping algorithms that deterministically find optimal solutions, and implementing software infrastructures required by developers to deploy applications for the targetMPSoC platforms. Energy Efficient LCDBacklightAutoregulation on Real-LifeMultimediaAp- plication Processor Despite the ever increasing advances in Liquid Crystal Display’s (LCD) technology, their power consumption is still one of the major limitations to the battery life of mobile appliances such as smart phones, portable media players, gaming and navigation devices. There is a clear trend towards the increase of LCD size to exploit the multimedia capabilities of portable devices that can receive and render high definition video and pictures. Multimedia applications running on these devices require LCD screen sizes of 2.2 to 3.5 inches andmore to display video sequences and pictures with the required quality. LCD power consumption is dependent on the backlight and pixel matrix driving circuits and is typically proportional to the panel area. As a result, the contribution is also likely to be considerable in future mobile appliances. To address this issue, companies are proposing low power technologies suitable for mobile applications supporting low power states and image control techniques. On the research side, several power saving schemes and algorithms can be found in literature. Some of them exploit software-only techniques to change the image content to reduce the power associated with the crystal polarization, some others are aimed at decreasing the backlight level while compensating the luminance reduction by compensating the user perceived quality degradation using pixel-by-pixel image processing algorithms. The major limitation of these techniques is that they rely on the CPU to perform pixel-based manipulations and their impact on CPU utilization and power consumption has not been assessed. This PhDdissertation shows an alternative approach that exploits in a smart and efficient way the hardware image processing unit almost integrated in every current multimedia application processors to implement a hardware assisted image compensation that allows dynamic scaling of the backlight with a negligible impact on QoS. The proposed approach overcomes CPU-intensive techniques by saving system power without requiring either a dedicated display technology or hardware modification. Thesis Overview The remainder of the thesis is organized as follows. The first part is focused on enhancing energy efficiency and programmability of modern Multi-Processor System-on-Chips (MPSoCs). Chapter 2 gives an overview about architectural trends in embedded systems, illustrating the principal features of new technologies and the key challenges still open. Chapter 3 presents a QoS-driven methodology for optimal allocation and frequency selection for MPSoCs. The methodology is based on functional simulation and full system power estimation. Chapter 4 targets allocation and scheduling of pipelined stream-oriented applications on top of distributed memory architectures with messaging support. We tackled the complexity of the problem by means of decomposition and no-good generation, and prove the increased computational efficiency of this approach with respect to traditional ones. Chapter 5 presents a cooperative framework to solve the allocation, scheduling and voltage/frequency selection problem to optimality for energyefficient MPSoCs, while in Chapter 6 applications with conditional task graph are taken into account. Finally Chapter 7 proposes a complete framework, called Cellflow, to help programmers in efficient software implementation on a real architecture, the Cell Broadband Engine processor. The second part is focused on energy efficient software techniques for LCD displays. Chapter 8 gives an overview about portable device display technologies, illustrating the principal features of LCD video systems and the key challenges still open. Chapter 9 shows several energy efficient software techniques present in literature, while Chapter 10 illustrates in details our method for saving significant power in an LCD panel. Finally, conclusions are drawn, reporting the main research contributions that have been discussed throughout this dissertation.

Risikomaße in der Finanzmathematik

„Risikomaße in der Finanzmathematik“ Der Value-at -Risk (VaR) ist ein Risikomaß, dessen Verwendung von der Bankenaufsicht gefordert wird. Der Vorteil des VaR liegt – als Quantil der Ertrags- oder Verlustverteilung - vor allem in seiner einfachen Interpretierbarkeit. Nachteilig ist, dass der linke Rand der Wahrscheinlichkeitsverteilung nicht beachtet wird. Darüber hinaus ist die Berechnung des VaR schwierig, da Quantile nicht additiv sind. Der größte Nachteil des VaR ist in der fehlenden Subadditivität zu sehen. Deswegen werden Alternativen wie Expected Shortfall untersucht. In dieser Arbeit werden zunächst finanzielle Risikomaße eingeführt und einige ihre grundlegenden Eigenschaften festgehalten. Wir beschäftigen uns mit verschiedenen parametrischen und nichtparametrischen Methoden zur Ermittlung des VaR, unter anderen mit ihren Vorteilen und Nachteilen. Des Weiteren beschäftigen wir uns mit parametrischen und nichtparametrischen Schätzern vom VaR in diskreter Zeit. Wir stellen Portfoliooptimierungsprobleme im Black Scholes Modell mit beschränktem VaR und mit beschränkter Varianz vor. Der Vorteil des erstens Ansatzes gegenüber dem zweiten wird hier erläutert. Wir lösen Nutzenoptimierungsprobleme in Bezug auf das Endvermögen mit beschränktem VaR und mit beschränkter Varianz. VaR sagt nichts über den darüber hinausgehenden Verlust aus, während dieser von Expected Shortfall berücksichtigt wird. Deswegen verwenden wir hier den Expected Shortfall anstelle des von Emmer, Korn und Klüppelberg (2001) betrachteten Risikomaßes VaR für die Optimierung des Portfolios im Black Scholes Modell.

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm.

Portfolio Approaches in Constraint Programming

Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of —possibly on-average slower— algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance. In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core. We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.

Packing a trunk : a physically based approach with full motional freedom

Geometric packing problems may be formulated mathematically as constrained optimization problems. But finding a good solution is a challenging task. The more complicated the geometry of the container or the objects to be packed, the more complex the non-penetration constraints become. In this work we propose the use of a physics engine that simulates a system of colliding rigid bodies. It is a tool to resolve interpenetration conflicts and to optimize configurations locally. We develop an efficient and easy-to-implement physics engine that is specialized for collision detection and contact handling. In succession of the development of this engine a number of novel algorithms for distance calculation and intersection volume were designed and imple- mented, which are presented in this work. They are highly specialized to pro- vide fast responses for cuboids and triangles as input geometry whereas the concepts they are based on can easily be extended to other convex shapes. Especially noteworthy in this context is our ε-distance algorithm - a novel application that is not only very robust and fast but also compact in its im- plementation. Several state-of-the-art third party implementations are being presented and we show that our implementations beat them in runtime and robustness. The packing algorithm that lies on top of the physics engine is a Monte Carlo based approach implemented for packing cuboids into a container described by a triangle soup. We give an implementation for the SAE J1100 variant of the trunk packing problem. We compare this implementation to several established approaches and we show that it gives better results in faster time than these existing implementations.

Parallel algorithm for solving integer linear programs

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for solving ILPs. We discuss a serial algorithm using a breadth-first branch-and-bound search to check the feasible solution space, and then extend it into a parallel algorithm using a client-server model. In the parallel mode, the search may not be truly breadth-first, depending on the solution time for each node in the solution tree. Our search takes advantage of pruning, often resulting in super-linear improvements in solution time. Finally, we present results from sample ILPs, describe a few modifications to enhance the algorithm and improve solution time, and offer suggestions for future work.

Resource management in location aware cognitive radio networks

Dynamic spectrum access (DSA) aims at utilizing spectral opportunities both in time and frequency domains at any given location, which arise due to variations in spectrum usage. Recently, Cognitive radios (CRs) have been proposed as a means of implementing DSA. In this work we focus on the aspect of resource management in overlaid CRNs. We formulate resource allocation strategies for cognitive radio networks (CRNs) as mathematical optimization problems. Specifically, we focus on two key problems in resource management: Sum Rate Maximization and Maximization of Number of Admitted Users. Since both the above mentioned problems are NP hard due to presence of binary assignment variables, we propose novel graph based algorithms to optimally solve these problems. Further, we analyze the impact of location awareness on network performance of CRNs by considering three cases: Full location Aware, Partial location Aware and Non location Aware. Our results clearly show that location awareness has significant impact on performance of overlaid CRNs and leads to increase in spectrum utilization effciency.

Quantification of relativistic perturbation forces on spacecraft trajectories

The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

A review of estimation of distribution algorithms in bioinformatics

Evolutionary search algorithms have become an essential asset in the algorithmic toolbox for solving high-dimensional optimization problems in across a broad range of bioinformatics problems. Genetic algorithms, the most well-known and representative evolutionary search technique, have been the subject of the major part of such applications. Estimation of distribution algorithms (EDAs) offer a novel evolutionary paradigm that constitutes a natural and attractive alternative to genetic algorithms. They make use of a probabilistic model, learnt from the promising solutions, to guide the search process. In this paper, we set out a basic taxonomy of EDA techniques, underlining the nature and complexity of the probabilistic model of each EDA variant. We review a set of innovative works that make use of EDA techniques to solve challenging bioinformatics problems, emphasizing the EDA paradigm's potential for further research in this domain.