Jeux de policiers et voleurs, Modèles et applications

Les jeux de policiers et voleurs sont étudiés depuis une trentaine d’années en informatique et en mathématiques. Comme dans les jeux de poursuite en général, des poursuivants (les policiers) cherchent à capturer des évadés (les voleurs), cependant ici les joueurs agissent tour à tour et sont contraints de se déplacer sur une structure discrète. On suppose toujours que les joueurs connaissent les positions exactes de leurs opposants, autrement dit le jeu se déroule à information parfaite. La première définition d’un jeu de policiers-voleurs remonte à celle de Nowakowski et Winkler [39] et, indépendamment, Quilliot [46]. Cette première définition présente un jeu opposant un seul policier et un seul voleur avec des contraintes sur leurs vitesses de déplacement. Des extensions furent graduellement proposées telles que l’ajout de policiers et l’augmentation des vitesses de mouvement. En 2014, Bonato et MacGillivray [6] proposèrent une généralisation des jeux de policiers-voleurs pour permettre l’étude de ceux-ci dans leur globalité. Cependant, leur modèle ne couvre aucunement les jeux possédant des composantes stochastiques tels que ceux dans lesquels les voleurs peuvent bouger de manière aléatoire. Dans ce mémoire est donc présenté un nouveau modèle incluant des aspects stochastiques. En second lieu, on présente dans ce mémoire une application concrète de l’utilisation de ces jeux sous la forme d’une méthode de résolution d’un problème provenant de la théorie de la recherche. Alors que les jeux de policiers et voleurs utilisent l’hypothèse de l’information parfaite, les problèmes de recherches ne peuvent faire cette supposition. Il appert cependant que le jeu de policiers et voleurs peut être analysé comme une relaxation de contraintes d’un problème de recherche. Ce nouvel angle de vue est exploité pour la conception d’une borne supérieure sur la fonction objectif d’un problème de recherche pouvant être mise à contribution dans une méthode dite de branch and bound.

LARGE MOTION VISUALIZATION AND ESTIMATION FOR FLAPPING WING SYSTEMS

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. Motion capture of a free flying insect is considered by using three synchronized high-speed cameras. A solid finite element representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. An objective function is formulated, and various shape difference definitions are considered. The proposed methodology is first studied for a synthetic case of a flexible cantilever structure undergoing large deformations, and then applied to a Manduca Sexta (hawkmoth) in free flight. The three-dimensional motions of this flapping system are reconstructed from image date collected by using three cameras. The complete deformation geometry of this system is analyzed. Finally, a computational investigation is carried out to understand the flow physics and aerodynamic performance by prescribing the body and wing motions in a fluid-body code. This thesis work contains one of the first set of such motion visualization and deformation analyses carried out for a hawkmoth in free flight. The tools and procedures used in this work are widely applicable to the studies of other flying animals with flexible wings as well as synthetic systems with flexible body elements.

Conversor de energia das ondas em energia elétrica com dispositivo de coluna de água oscilante: simulação numérica e estudo geométrico

Os oceanos representam um dos maiores recursos naturais, possuindo expressivo potencial energético, podendo suprir parte da demanda energética mundial. Nas últimas décadas, alguns dispositivos destinados à conversão da energia das ondas dos oceanos em energia elétrica têm sido estudados. No presente trabalho, o princípio de funcionamento do conversor do tipo Coluna de Água Oscilante, do inglês Oscillating Water Colum, (OWC) foi analisado numericamente. As ondas incidentes na câmara hidro-pneumática da OWC, causam um movimento alternado da coluna de água no interior da câmara, o qual produz um fluxo alternado de ar que passa pela chaminé. O ar passa e aciona uma turbina a qual transmite energia para um gerador elétrico. O objetivo do presente estudo foi investigar a influência de diferentes formas geométricas da câmara sobre o fluxo resultante de ar que passa pela turbina, que influencia no desempenho do dispositivo. Para isso, geometrias diferentes para o conversor foram analisadas empregando modelos computacionais 2D e 3D. Um modelo computacional desenvolvido nos softwares GAMBIT e FLUENT foi utilizado, em que o conversor OWC foi acoplado a um tanque de ondas. O método Volume of Fluid (VOF) e a teoria de 2ª ordem Stokes foram utilizados para gerar ondas regulares, permitindo uma interação mais realista entre o conversor, água, ar e OWC. O Método dos Volumes Finitos (MVF) foi utilizado para a discretização das equações governantes. Neste trabalho o Contructal Design (baseado na Teoria Constructal) foi aplicado pela primeira vez em estudos numéricos tridimensionais de OWC para fim de encontrar uma geometria que mais favorece o desempenho do dispositivo. A função objetivo foi a maximização da vazão mássica de ar que passa através da chaminé do dispositivo OWC, analisado através do método mínimos quadrados, do inglês Root Mean Square (RMS). Os resultados indicaram que a forma geométrica da câmara influencia na transformação da energia das ondas em energia elétrica. As geometrias das câmaras analisadas que apresentaram maior área da face de incidência das ondas (sendo altura constante), apresentaram também maior desempenho do conversor OWC. A melhor geometria, entre os casos desse estudo, ofereceu um ganho no desempenho do dispositivo em torno de 30% maior.

O problema de alocação de berços: um estudo das heurísticas simulated annealing e algoritmo genético

Este trabalho apresenta um estudo de caso das heurísticas Simulated Annealing e Algoritmo Genético para um problema de grande relevância encontrado no sistema portuário, o Problema de Alocação em Berços. Esse problema aborda a programação e a alocação de navios às áreas de atracação ao longo de um cais. A modelagem utilizada nesta pesquisa é apresentada por Mauri (2008) [28] que trata do problema como uma Problema de Roteamento de Veículos com Múltiplas Garagens e sem Janelas de Tempo. Foi desenvolvido um ambiente apropriado para testes de simulação, onde o cenário de análise foi constituido a partir de situações reais encontradas na programação de navios de um terminal de contêineres. Os testes computacionais realizados mostram a performance das heurísticas em relação a função objetivo e o tempo computacional, a m de avaliar qual das técnicas apresenta melhores resultados.

Leveraging Multiple Features for Image Retrieval and Matching

The goal of image retrieval and matching is to find and locate object instances in images from a large-scale image database. While visual features are abundant, how to combine them to improve performance by individual features remains a challenging task. In this work, we focus on leveraging multiple features for accurate and efficient image retrieval and matching. We first propose two graph-based approaches to rerank initially retrieved images for generic image retrieval. In the graph, vertices are images while edges are similarities between image pairs. Our first approach employs a mixture Markov model based on a random walk model on multiple graphs to fuse graphs. We introduce a probabilistic model to compute the importance of each feature for graph fusion under a naive Bayesian formulation, which requires statistics of similarities from a manually labeled dataset containing irrelevant images. To reduce human labeling, we further propose a fully unsupervised reranking algorithm based on a submodular objective function that can be efficiently optimized by greedy algorithm. By maximizing an information gain term over the graph, our submodular function favors a subset of database images that are similar to query images and resemble each other. The function also exploits the rank relationships of images from multiple ranked lists obtained by different features. We then study a more well-defined application, person re-identification, where the database contains labeled images of human bodies captured by multiple cameras. Re-identifications from multiple cameras are regarded as related tasks to exploit shared information. We apply a novel multi-task learning algorithm using both low level features and attributes. A low rank attribute embedding is joint learned within the multi-task learning formulation to embed original binary attributes to a continuous attribute space, where incorrect and incomplete attributes are rectified and recovered. To locate objects in images, we design an object detector based on object proposals and deep convolutional neural networks (CNN) in view of the emergence of deep networks. We improve a Fast RCNN framework and investigate two new strategies to detect objects accurately and efficiently: scale-dependent pooling (SDP) and cascaded rejection classifiers (CRC). The SDP improves detection accuracy by exploiting appropriate convolutional features depending on the scale of input object proposals. The CRC effectively utilizes convolutional features and greatly eliminates negative proposals in a cascaded manner, while maintaining a high recall for true objects. The two strategies together improve the detection accuracy and reduce the computational cost.

Simulation Optimization of the Crossdock Door Assignmnet Problem

The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model - simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Modelo para distribuição de recursos nos municípios brasileiros baseado na lei de diretrizes orçamentárias, análise multicritério e programação linear

The municipal management in any country of the globe requires planning and allocation of resources evenly. In Brazil, the Law of Budgetary Guidelines (LDO) guides municipal managers toward that balance. This research develops a model that seeks to find the balance of the allocation of public resources in Brazilian municipalities, considering the LDO as a parameter. For this using statistical techniques and multicriteria analysis as a first step in order to define allocation strategies, based on the technical aspects arising from the municipal manager. In a second step, presented in linear programming based optimization where the objective function is derived from the preference of the results of the manager and his staff. The statistical representation is presented to support multicriteria development in the definition of replacement rates through time series. The multicriteria analysis was structured by defining the criteria, alternatives and the application of UTASTAR methods to calculate replacement rates. After these initial settings, an application of linear programming was developed to find the optimal allocation of enforcement resources of the municipal budget. Data from the budget of a municipality in southwestern Paraná were studied in the application of the model and analysis of results.

Simulation Optimization of the Crossdock Door Assignmnet Problem

The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model - simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.

Optimisation of a crossdocking distribution centre simulation model

This paper reports on continuing research into the modelling of an order picking process within a Crossdocking distribution centre using Simulation Optimisation. The aim of this project is to optimise a discrete event simulation model and to understand factors that affect finding its optimal performance. Our initial investigation revealed that the precision of the selected simulation output performance measure and the number of replications required for the evaluation of the optimisation objective function through simulation influences the ability of the optimisation technique. We experimented with Common Random Numbers, in order to improve the precision of our simulation output performance measure, and intended to use the number of replications utilised for this purpose as the initial number of replications for the optimisation of our Crossdocking distribution centre simulation model. Our results demonstrate that we can improve the precision of our selected simulation output performance measure value using Common Random Numbers at various levels of replications. Furthermore, after optimising our Crossdocking distribution centre simulation model, we are able to achieve optimal performance using fewer simulations runs for the simulation model which uses Common Random Numbers as compared to the simulation model which does not use Common Random Numbers.

Physical Design Methodologies for Low Power and Reliable 3D ICs

As the semiconductor industry struggles to maintain its momentum down the path following the Moore's Law, three dimensional integrated circuit (3D IC) technology has emerged as a promising solution to achieve higher integration density, better performance, and lower power consumption. However, despite its significant improvement in electrical performance, 3D IC presents several serious physical design challenges. In this dissertation, we investigate physical design methodologies for 3D ICs with primary focus on two areas: low power 3D clock tree design, and reliability degradation modeling and management. Clock trees are essential parts for digital system which dissipate a large amount of power due to high capacitive loads. The majority of existing 3D clock tree designs focus on minimizing the total wire length, which produces sub-optimal results for power optimization. In this dissertation, we formulate a 3D clock tree design flow which directly optimizes for clock power. Besides, we also investigate the design methodology for clock gating a 3D clock tree, which uses shutdown gates to selectively turn off unnecessary clock activities. Different from the common assumption in 2D ICs that shutdown gates are cheap thus can be applied at every clock node, shutdown gates in 3D ICs introduce additional control TSVs, which compete with clock TSVs for placement resources. We explore the design methodologies to produce the optimal allocation and placement for clock and control TSVs so that the clock power is minimized. We show that the proposed synthesis flow saves significant clock power while accounting for available TSV placement area. Vertical integration also brings new reliability challenges including TSV's electromigration (EM) and several other reliability loss mechanisms caused by TSV-induced stress. These reliability loss models involve complex inter-dependencies between electrical and thermal conditions, which have not been investigated in the past. In this dissertation we set up an electrical/thermal/reliability co-simulation framework to capture the transient of reliability loss in 3D ICs. We further derive and validate an analytical reliability objective function that can be integrated into the 3D placement design flow. The reliability aware placement scheme enables co-design and co-optimization of both the electrical and reliability property, thus improves both the circuit's performance and its lifetime. Our electrical/reliability co-design scheme avoids unnecessary design cycles or application of ad-hoc fixes that lead to sub-optimal performance. Vertical integration also enables stacking DRAM on top of CPU, providing high bandwidth and short latency. However, non-uniform voltage fluctuation and local thermal hotspot in CPU layers are coupled into DRAM layers, causing a non-uniform bit-cell leakage (thereby bit flip) distribution. We propose a performance-power-resilience simulation framework to capture DRAM soft error in 3D multi-core CPU systems. In addition, a dynamic resilience management (DRM) scheme is investigated, which adaptively tunes CPU's operating points to adjust DRAM's voltage noise and thermal condition during runtime. The DRM uses dynamic frequency scaling to achieve a resilience borrow-in strategy, which effectively enhances DRAM's resilience without sacrificing performance. The proposed physical design methodologies should act as important building blocks for 3D ICs and push 3D ICs toward mainstream acceptance in the near future.

Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.

Risk management for mathematical optimization under uncertainty

We present a general multistage stochastic mixed 0-1 problem where the uncertainty appears everywhere in the objective function, constraints matrix and right-hand-side. The uncertainty is represented by a scenario tree that can be a symmetric or a nonsymmetric one. The stochastic model is converted in a mixed 0-1 Deterministic Equivalent Model in compact representation. Due to the difficulty of the problem, the solution offered by the stochastic model has been traditionally obtained by optimizing the objective function expected value (i.e., mean) over the scenarios, usually, along a time horizon. This approach (so named risk neutral) has the inconvenience of providing a solution that ignores the variance of the objective value of the scenarios and, so, the occurrence of scenarios with an objective value below the expected one. Alternatively, we present several approaches for risk averse management, namely, a scenario immunization strategy, the optimization of the well known Value-at-Risk (VaR) and several variants of the Conditional Value-at-Risk strategies, the optimization of the expected mean minus the weighted probability of having a "bad" scenario to occur for the given solution provided by the model, the optimization of the objective function expected value subject to stochastic dominance constraints (SDC) for a set of profiles given by the pairs of threshold objective values and either bounds on the probability of not reaching the thresholds or the expected shortfall over them, and the optimization of a mixture of the VaR and SDC strategies.

Train scheduling and rolling stock assignment in high speed trains

The Train Timetabling Problem (TTP) has been widely studied for freight and passenger rail systems. A lesser effort has been devoted to the study of high-speed rail systems. A modeling issue that has to be addressed is to model departure time choice of passengers on railway services. Passengers who use these systems attempt to travel at predetermined hours due to their daily life necessities (e.g., commuter trips). We incorporate all these features into TTP focusing on high-speed railway systems. We propose a Rail Scheduling and Rolling Stock (RSch-RS) model for timetable planning of high-speed railway systems. This model is composed of two essential elements: i) an infrastructure model for representing the railway network: it includes capacity constraints of the rail network and the Rolling-Stock constraints; and ii) a demand model that defines how the passengers choose the departure time. The resulting model is a mixed-integer programming model which objective function attempts to maximize the profit for the rail operator