O problema da árvore de suporte de custo mínimo com restrições de peso

Nesta tese abordam-se várias formulações e diferentes métodos para resolver o Problema da Árvore de Suporte de Custo Mínimo com Restrições de Peso (WMST – Weight-constrained Minimum Spanning Tree Problem). Este problema, com aplicações no desenho de redes de comunicações e telecomunicações, é um problema de Otimização Combinatória NP-difícil. O Problema WMST consiste em determinar, numa rede com custos e pesos associados às arestas, uma árvore de suporte de custo mínimo de tal forma que o seu peso total não exceda um dado limite especificado. Apresentam-se e comparam-se várias formulações para o problema. Uma delas é usada para desenvolver um procedimento com introdução de cortes baseado em separação e que se tornou bastante útil na obtenção de soluções para o problema. Tendo como propósito fortalecer as formulações apresentadas, introduzem-se novas classes de desigualdades válidas que foram adaptadas das conhecidas desigualdades de cobertura, desigualdades de cobertura estendida e desigualdades de cobertura levantada. As novas desigualdades incorporam a informação de dois conjuntos de soluções: o conjunto das árvores de suporte e o conjunto saco-mochila. Apresentam-se diversos algoritmos heurísticos de separação que nos permitem usar as desigualdades válidas propostas de forma eficiente. Com base na decomposição Lagrangeana, apresentam-se e comparam-se algoritmos simples, mas eficientes, que podem ser usados para calcular limites inferiores e superiores para o valor ótimo do WMST. Entre eles encontram-se dois novos algoritmos: um baseado na convexidade da função Lagrangeana e outro que faz uso da inclusão de desigualdades válidas. Com o objetivo de obter soluções aproximadas para o Problema WMST usam-se métodos heurísticos para encontrar uma solução inteira admissível. Os métodos heurísticos apresentados são baseados nas estratégias Feasibility Pump e Local Branching. Apresentam-se resultados computacionais usando todos os métodos apresentados. Os resultados mostram que os diferentes métodos apresentados são bastante eficientes para encontrar soluções para o Problema WMST.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.

A Multi-Objective Antenna Placement Genetic Algorithm for Matched Array Synthesis on Complex Platforms

A Multi-Objective Antenna Placement Genetic Algorithm (MO-APGA) has been proposed for the synthesis of matched antenna arrays on complex platforms. The total number of antennas required, their position on the platform, location of loads, loading circuit parameters, decoupling and matching network topology, matching network parameters and feed network parameters are optimized simultaneously. The optimization goal was to provide a given minimum gain, specific gain discrimination between the main and back lobes and broadband performance. This algorithm is developed based on the non-dominated sorting genetic algorithm (NSGA-II) and Minimum Spanning Tree (MST) technique for producing diverse solutions when the number of objectives is increased beyond two. The proposed method is validated through the design of a wideband airborne SAR

Estimating Dependency Structure as a Hidden Variable

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EMand the Minimum Spanning Tree algorithm to find the ML and MAP mixtureof trees for a variety of priors, including the Dirichlet and the MDL priors.

Estimating Dependency Structure as a Hidden Variable

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors. We also show that the single tree classifier acts like an implicit feature selector, thus making the classification performance insensitive to irrelevant attributes. Experimental results demonstrate the excellent performance of the new model both in density estimation and in classification.

Efficient topology estimation for large scale optical mapping

Large scale image mosaicing methods are in great demand among scientists who study different aspects of the seabed, and have been fostered by impressive advances in the capabilities of underwater robots in gathering optical data from the seafloor. Cost and weight constraints mean that lowcost Remotely operated vehicles (ROVs) usually have a very limited number of sensors. When a low-cost robot carries out a seafloor survey using a down-looking camera, it usually follows a predetermined trajectory that provides several non time-consecutive overlapping image pairs. Finding these pairs (a process known as topology estimation) is indispensable to obtaining globally consistent mosaics and accurate trajectory estimates, which are necessary for a global view of the surveyed area, especially when optical sensors are the only data source. This thesis presents a set of consistent methods aimed at creating large area image mosaics from optical data obtained during surveys with low-cost underwater vehicles. First, a global alignment method developed within a Feature-based image mosaicing (FIM) framework, where nonlinear minimisation is substituted by two linear steps, is discussed. Then, a simple four-point mosaic rectifying method is proposed to reduce distortions that might occur due to lens distortions, error accumulation and the difficulties of optical imaging in an underwater medium. The topology estimation problem is addressed by means of an augmented state and extended Kalman filter combined framework, aimed at minimising the total number of matching attempts and simultaneously obtaining the best possible trajectory. Potential image pairs are predicted by taking into account the uncertainty in the trajectory. The contribution of matching an image pair is investigated using information theory principles. Lastly, a different solution to the topology estimation problem is proposed in a bundle adjustment framework. Innovative aspects include the use of fast image similarity criterion combined with a Minimum spanning tree (MST) solution, to obtain a tentative topology. This topology is improved by attempting image matching with the pairs for which there is the most overlap evidence. Unlike previous approaches for large-area mosaicing, our framework is able to deal naturally with cases where time-consecutive images cannot be matched successfully, such as completely unordered sets. Finally, the efficiency of the proposed methods is discussed and a comparison made with other state-of-the-art approaches, using a series of challenging datasets in underwater scenarios

Paleoamerican Morphology in the Context of European and East Asian Late Pleistocene Variation: Implications for Human Dispersion Into the New World

Early American crania show a different morphological pattern from the one shared by late Native Americans. Although the origin of the diachronic morphological diversity seen on the continents is still debated, the distinct morphology of early Americans is well documented and widely dispersed. This morphology has been described extensively for South America, where larger samples are available. Here we test the hypotheses that the morphology of Early Americans results from retention of the morphological pattern of Late Pleistocene modern humans and that the occupation of the New World precedes the morphological differentiation that gave rise to recent Eurasian and American morphology. We compare Early American samples with European Upper Paleolithic skulls, the East Asian Zhoukoudian Upper Cave specimens and a series of 20 modern human reference crania. Canonical Analysis and Minimum Spanning Tree were used to assess the morphological affinities among the series, while Mantel and Dow-Cheverud tests based on Mahalanobis Squared Distances were used to test different evolutionary scenarios. Our results show strong morphological affinities among the early series irrespective of geographical origin, which together with the matrix analyses results favor the scenario of a late morphological differentiation of modern humans. We conclude that the geographic differentiation of modern human morphology is a late phenomenon that occurred after the initial settlement of the Americas. Am J Phys Anthropol 144:442-453, 2011. (c) 2010 Wiley-Liss, Inc.

Uma abordagem por nuvem de partículas para problemas de otimização combinatória

Combinatorial optimization problems have the goal of maximize or minimize functions defined over a finite domain. Metaheuristics are methods designed to find good solutions in this finite domain, sometimes the optimum solution, using a subordinated heuristic, which is modeled for each particular problem. This work presents algorithms based on particle swarm optimization (metaheuristic) applied to combinatorial optimization problems: the Traveling Salesman Problem and the Multicriteria Degree Constrained Minimum Spanning Tree Problem. The first problem optimizes only one objective, while the other problem deals with many objectives. In order to evaluate the performance of the algorithms proposed, they are compared, in terms of the quality of the solutions found, to other approaches

Evaluation of ERIC-PCR as Genotyping Method for Corynebacterium pseudotuberculosis Isolates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A path- and label-cost propagation approach to speedup the training of the optimum-path forest classifier

In general, pattern recognition techniques require a high computational burden for learning the discriminating functions that are responsible to separate samples from distinct classes. As such, there are several studies that make effort to employ machine learning algorithms in the context of big data classification problems. The research on this area ranges from Graphics Processing Units-based implementations to mathematical optimizations, being the main drawback of the former approaches to be dependent on the graphic video card. Here, we propose an architecture-independent optimization approach for the optimum-path forest (OPF) classifier, that is designed using a theoretical formulation that relates the minimum spanning tree with the minimum spanning forest generated by the OPF over the training dataset. The experiments have shown that the approach proposed can be faster than the traditional one in five public datasets, being also as accurate as the original OPF. (C) 2014 Elsevier B. V. All rights reserved.

Efficient Forest Data Structure for Evolutionary Algorithms Applied to Network Design

The design of a network is a solution to several engineering and science problems. Several network design problems are known to be NP-hard, and population-based metaheuristics like evolutionary algorithms (EAs) have been largely investigated for such problems. Such optimization methods simultaneously generate a large number of potential solutions to investigate the search space in breadth and, consequently, to avoid local optima. Obtaining a potential solution usually involves the construction and maintenance of several spanning trees, or more generally, spanning forests. To efficiently explore the search space, special data structures have been developed to provide operations that manipulate a set of spanning trees (population). For a tree with n nodes, the most efficient data structures available in the literature require time O(n) to generate a new spanning tree that modifies an existing one and to store the new solution. We propose a new data structure, called node-depth-degree representation (NDDR), and we demonstrate that using this encoding, generating a new spanning forest requires average time O(root n). Experiments with an EA based on NDDR applied to large-scale instances of the degree-constrained minimum spanning tree problem have shown that the implementation adds small constants and lower order terms to the theoretical bound.

Maximum Series-Parallel Subgraph

Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G with the maximum number of edges. The algorithm that, given a connected graph G, outputs a spanning tree of G, is a 1/2-approximation. Indeed, if n is the number of vertices in G, any spanning tree in G has n-1 edges and any series-parallel graph on n vertices has at most 2n-3 edges. We present a 7/12 -approximation for this problem and results showing the limits of our approach.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Chemische Zusammensetzung der Aerosole : Design und Datenauswertung eines Einzelpartikel-Laserablationsmassenspektrometers

Atmosphärische Aerosolpartikel wirken in vielerlei Hinsicht auf die Menschen und die Umwelt ein. Eine genaue Charakterisierung der Partikel hilft deren Wirken zu verstehen und dessen Folgen einzuschätzen. Partikel können hinsichtlich ihrer Größe, ihrer Form und ihrer chemischen Zusammensetzung charakterisiert werden. Mit der Laserablationsmassenspektrometrie ist es möglich die Größe und die chemische Zusammensetzung einzelner Aerosolpartikel zu bestimmen. Im Rahmen dieser Arbeit wurde das SPLAT (Single Particle Laser Ablation Time-of-flight mass spectrometer) zur besseren Analyse insbesondere von atmosphärischen Aerosolpartikeln weiterentwickelt. Der Aerosoleinlass wurde dahingehend optimiert, einen möglichst weiten Partikelgrößenbereich (80 nm - 3 µm) in das SPLAT zu transferieren und zu einem feinen Strahl zu bündeln. Eine neue Beschreibung für die Beziehung der Partikelgröße zu ihrer Geschwindigkeit im Vakuum wurde gefunden. Die Justage des Einlasses wurde mithilfe von Schrittmotoren automatisiert. Die optische Detektion der Partikel wurde so verbessert, dass Partikel mit einer Größe < 100 nm erfasst werden können. Aufbauend auf der optischen Detektion und der automatischen Verkippung des Einlasses wurde eine neue Methode zur Charakterisierung des Partikelstrahls entwickelt. Die Steuerelektronik des SPLAT wurde verbessert, so dass die maximale Analysefrequenz nur durch den Ablationslaser begrenzt wird, der höchsten mit etwa 10 Hz ablatieren kann. Durch eine Optimierung des Vakuumsystems wurde der Ionenverlust im Massenspektrometer um den Faktor 4 verringert.rnrnNeben den hardwareseitigen Weiterentwicklungen des SPLAT bestand ein Großteil dieser Arbeit in der Konzipierung und Implementierung einer Softwarelösung zur Analyse der mit dem SPLAT gewonnenen Rohdaten. CRISP (Concise Retrieval of Information from Single Particles) ist ein auf IGOR PRO (Wavemetrics, USA) aufbauendes Softwarepaket, das die effiziente Auswertung der Einzelpartikel Rohdaten erlaubt. CRISP enthält einen neu entwickelten Algorithmus zur automatischen Massenkalibration jedes einzelnen Massenspektrums, inklusive der Unterdrückung von Rauschen und von Problemen mit Signalen die ein intensives Tailing aufweisen. CRISP stellt Methoden zur automatischen Klassifizierung der Partikel zur Verfügung. Implementiert sind k-means, fuzzy-c-means und eine Form der hierarchischen Einteilung auf Basis eines minimal aufspannenden Baumes. CRISP bietet die Möglichkeit die Daten vorzubehandeln, damit die automatische Einteilung der Partikel schneller abläuft und die Ergebnisse eine höhere Qualität aufweisen. Daneben kann CRISP auf einfache Art und Weise Partikel anhand vorgebener Kriterien sortieren. Die CRISP zugrundeliegende Daten- und Infrastruktur wurde in Hinblick auf Wartung und Erweiterbarkeit erstellt. rnrnIm Rahmen der Arbeit wurde das SPLAT in mehreren Kampagnen erfolgreich eingesetzt und die Fähigkeiten von CRISP konnten anhand der gewonnen Datensätze gezeigt werden.rnrnDas SPLAT ist nun in der Lage effizient im Feldeinsatz zur Charakterisierung des atmosphärischen Aerosols betrieben zu werden, während CRISP eine schnelle und gezielte Auswertung der Daten ermöglicht.