Algorithms and Models For Combinatorial Optimization Problems

In this thesis we present some combinatorial optimization problems, suggest models and algorithms for their effective solution. For each problem,we give its description, followed by a short literature review, provide methods to solve it and, finally, present computational results and comparisons with previous works to show the effectiveness of the proposed approaches. The considered problems are: the Generalized Traveling Salesman Problem (GTSP), the Bin Packing Problem with Conflicts(BPPC) and the Fair Layout Problem (FLOP).

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Generazione di istanze difficili per problemi di impaccamento e routing

La presente tesi è il frutto di un lavoro di ricerca sugli aspetti che rendono gli algoritmi esatti per CVRP presenti in letteratura poco efficienti su certi tipi di istanze. L'ipotesi iniziale era che gli algoritmi incontrassero difficoltà di risoluzione su istanze di CVRP dotate di un numero limitato di soluzioni di Bin Packing. Allo scopo di verificare la validità di tale supposizione, sono state create istanze di Bin Packing aventi poche soluzioni ottime e sono stati aggiunti tre differenti schemi di routing. Le istanze CVRP sono state risolte con l'algoritmo del dr. Roberti, già presente in letteratura.

Algorithms for on-line image registration from multiple views

Images of a scene, static or dynamic, are generally acquired at different epochs from different viewpoints. They potentially gather information about the whole scene and its relative motion with respect to the acquisition device. Data from different (in the spatial or temporal domain) visual sources can be fused together to provide a unique consistent representation of the whole scene, even recovering the third dimension, permitting a more complete understanding of the scene content. Moreover, the pose of the acquisition device can be achieved by estimating the relative motion parameters linking different views, thus providing localization information for automatic guidance purposes. Image registration is based on the use of pattern recognition techniques to match among corresponding parts of different views of the acquired scene. Depending on hypotheses or prior information about the sensor model, the motion model and/or the scene model, this information can be used to estimate global or local geometrical mapping functions between different images or different parts of them. These mapping functions contain relative motion parameters between the scene and the sensor(s) and can be used to integrate accordingly informations coming from the different sources to build a wider or even augmented representation of the scene. Accordingly, for their scene reconstruction and pose estimation capabilities, nowadays image registration techniques from multiple views are increasingly stirring up the interest of the scientific and industrial community. Depending on the applicative domain, accuracy, robustness, and computational payload of the algorithms represent important issues to be addressed and generally a trade-off among them has to be reached. Moreover, on-line performance is desirable in order to guarantee the direct interaction of the vision device with human actors or control systems. This thesis follows a general research approach to cope with these issues, almost independently from the scene content, under the constraint of rigid motions. This approach has been motivated by the portability to very different domains as a very desirable property to achieve. A general image registration approach suitable for on-line applications has been devised and assessed through two challenging case studies in different applicative domains. The first case study regards scene reconstruction through on-line mosaicing of optical microscopy cell images acquired with non automated equipment, while moving manually the microscope holder. By registering the images the field of view of the microscope can be widened, preserving the resolution while reconstructing the whole cell culture and permitting the microscopist to interactively explore the cell culture. In the second case study, the registration of terrestrial satellite images acquired by a camera integral with the satellite is utilized to estimate its three-dimensional orientation from visual data, for automatic guidance purposes. Critical aspects of these applications are emphasized and the choices adopted are motivated accordingly. Results are discussed in view of promising future developments.

Enabling Techniques and Algorithms for Integrated Communication and Navigation Satellite Systems

This thesis presents the outcomes of my Ph.D. course in telecommunications engineering. The focus of my research has been on Global Navigation Satellite Systems (GNSS) and in particular on the design of aiding schemes operating both at position and physical level and the evaluation of their feasibility and advantages. Assistance techniques at the position level are considered to enhance receiver availability in challenging scenarios where satellite visibility is limited. Novel positioning techniques relying on peer-to-peer interaction and exchange of information are thus introduced. More specifically two different techniques are proposed: the Pseudorange Sharing Algorithm (PSA), based on the exchange of GNSS data, that allows to obtain coarse positioning where the user has scarce satellite visibility, and the Hybrid approach, which also permits to improve the accuracy of the positioning solution. At the physical level, aiding schemes are investigated to improve the receiver’s ability to synchronize with satellite signals. An innovative code acquisition strategy for dual-band receivers, the Cross-Band Aiding (CBA) technique, is introduced to speed-up initial synchronization by exploiting the exchange of time references between the two bands. In addition vector configurations for code tracking are analyzed and their feedback generation process thoroughly investigated.

Fingerprint Recognition: Enhancement, Feature Extraction and Automatic Evaluation of Algorithms

The identification of people by measuring some traits of individual anatomy or physiology has led to a specific research area called biometric recognition. This thesis is focused on improving fingerprint recognition systems considering three important problems: fingerprint enhancement, fingerprint orientation extraction and automatic evaluation of fingerprint algorithms. An effective extraction of salient fingerprint features depends on the quality of the input fingerprint. If the fingerprint is very noisy, we are not able to detect a reliable set of features. A new fingerprint enhancement method, which is both iterative and contextual, is proposed. This approach detects high-quality regions in fingerprints, selectively applies contextual filtering and iteratively expands like wildfire toward low-quality ones. A precise estimation of the orientation field would greatly simplify the estimation of other fingerprint features (singular points, minutiae) and improve the performance of a fingerprint recognition system. The fingerprint orientation extraction is improved following two directions. First, after the introduction of a new taxonomy of fingerprint orientation extraction methods, several variants of baseline methods are implemented and, pointing out the role of pre- and post- processing, we show how to improve the extraction. Second, the introduction of a new hybrid orientation extraction method, which follows an adaptive scheme, allows to improve significantly the orientation extraction in noisy fingerprints. Scientific papers typically propose recognition systems that integrate many modules and therefore an automatic evaluation of fingerprint algorithms is needed to isolate the contributions that determine an actual progress in the state-of-the-art. The lack of a publicly available framework to compare fingerprint orientation extraction algorithms, motivates the introduction of a new benchmark area called FOE (including fingerprints and manually-marked orientation ground-truth) along with fingerprint matching benchmarks in the FVC-onGoing framework. The success of such framework is discussed by providing relevant statistics: more than 1450 algorithms submitted and two international competitions.

Metaheuristics for Search Problems in Genomics - New Algorithms and Applications

In this thesis we made the first steps towards the systematic application of a methodology for automatically building formal models of complex biological systems. Such a methodology could be useful also to design artificial systems possessing desirable properties such as robustness and evolvability. The approach we follow in this thesis is to manipulate formal models by means of adaptive search methods called metaheuristics. In the first part of the thesis we develop state-of-the-art hybrid metaheuristic algorithms to tackle two important problems in genomics, namely, the Haplotype Inference by parsimony and the Founder Sequence Reconstruction Problem. We compare our algorithms with other effective techniques in the literature, we show strength and limitations of our approaches to various problem formulations and, finally, we propose further enhancements that could possibly improve the performance of our algorithms and widen their applicability. In the second part, we concentrate on Boolean network (BN) models of gene regulatory networks (GRNs). We detail our automatic design methodology and apply it to four use cases which correspond to different design criteria and address some limitations of GRN modeling by BNs. Finally, we tackle the Density Classification Problem with the aim of showing the learning capabilities of BNs. Experimental evaluation of this methodology shows its efficacy in producing network that meet our design criteria. Our results, coherently to what has been found in other works, also suggest that networks manipulated by a search process exhibit a mixture of characteristics typical of different dynamical regimes.

Low Correlated Sequences & Architectures and Algorithms for Analog-to-Information Converters: Theory, Design, Implementation and Applications.

Most electronic systems can be described in a very simplified way as an assemblage of analog and digital components put all together in order to perform a certain function. Nowadays, there is an increasing tendency to reduce the analog components, and to replace them by operations performed in the digital domain. This tendency has led to the emergence of new electronic systems that are more flexible, cheaper and robust. However, no matter the amount of digital process implemented, there will be always an analog part to be sorted out and thus, the step of converting digital signals into analog signals and vice versa cannot be avoided. This conversion can be more or less complex depending on the characteristics of the signals. Thus, even if it is desirable to replace functions carried out by analog components by digital processes, it is equally important to do so in a way that simplifies the conversion from digital to analog signals and vice versa. In the present thesis, we have study strategies based on increasing the amount of processing in the digital domain in such a way that the implementation of analog hardware stages can be simplified. To this aim, we have proposed the use of very low quantized signals, i.e. 1-bit, for the acquisition and for the generation of particular classes of signals.

Spectrum Sensing Algorithms for Cognitive Radio Applications

Future wireless communications systems are expected to be extremely dynamic, smart and capable to interact with the surrounding radio environment. To implement such advanced devices, cognitive radio (CR) is a promising paradigm, focusing on strategies for acquiring information and learning. The first task of a cognitive systems is spectrum sensing, that has been mainly studied in the context of opportunistic spectrum access, in which cognitive nodes must implement signal detection techniques to identify unused bands for transmission. In the present work, we study different spectrum sensing algorithms, focusing on their statistical description and evaluation of the detection performance. Moving from traditional sensing approaches we consider the presence of practical impairments, and analyze algorithm design. Far from the ambition of cover the broad spectrum of spectrum sensing, we aim at providing contributions to the main classes of sensing techniques. In particular, in the context of energy detection we studied the practical design of the test, considering the case in which the noise power is estimated at the receiver. This analysis allows to deepen the phenomenon of the SNR wall, providing the conditions for its existence and showing that presence of the SNR wall is determined by the accuracy of the noise power estimation process. In the context of the eigenvalue based detectors, that can be adopted by multiple sensors systems, we studied the practical situation in presence of unbalances in the noise power at the receivers. Then, we shift the focus from single band detectors to wideband sensing, proposing a new approach based on information theoretic criteria. This technique is blind and, requiring no threshold setting, can be adopted even if the statistical distribution of the observed data in not known exactly. In the last part of the thesis we analyze some simple cooperative localization techniques based on weighted centroid strategies.

Implementation of network entropy algorithms on hpc machines, with application to high-dimensional experimental data

Network Theory is a prolific and lively field, especially when it approaches Biology. New concepts from this theory find application in areas where extensive datasets are already available for analysis, without the need to invest money to collect them. The only tools that are necessary to accomplish an analysis are easily accessible: a computing machine and a good algorithm. As these two tools progress, thanks to technology advancement and human efforts, wider and wider datasets can be analysed. The aim of this paper is twofold. Firstly, to provide an overview of one of these concepts, which originates at the meeting point between Network Theory and Statistical Mechanics: the entropy of a network ensemble. This quantity has been described from different angles in the literature. Our approach tries to be a synthesis of the different points of view. The second part of the work is devoted to presenting a parallel algorithm that can evaluate this quantity over an extensive dataset. Eventually, the algorithm will also be used to analyse high-throughput data coming from biology.

Metodi euristici per il Vehicle Routing Problem

Il problema della consegna di prodotti da un deposito/impianto ai clienti mediante una flotta di automezzi è un problema centrale nella gestione di una catena di produzione e distribuzione (supply chain). Questo problema, noto in letteratura come Vehicle Routing Problem (VRP), nella sua versione più semplice consiste nel disegnare per ogni veicolo disponibile presso un dato deposito aziendale un viaggio (route) di consegna dei prodotti ai clienti, che tali prodotti richiedono, in modo tale che (i) la somma delle quantità richieste dai clienti assegnati ad ogni veicolo non superi la capacità del veicolo, (ii) ogni cliente sia servito una ed una sola volta, (iii) sia minima la somma dei costi dei viaggi effettuati dai veicoli. Il VRP è un problema trasversale ad una molteplicità di settori merceologici dove la distribuzione dei prodotti e/o servizi avviene mediante veicoli su gomma, quali ad esempio: distribuzione di generi alimentari, distribuzione di prodotti petroliferi, raccolta e distribuzione della posta, organizzazione del servizio scuolabus, pianificazione della manutenzione di impianti, raccolta rifiuti, etc. In questa tesi viene considerato il Multi-Trip VRP, in cui ogni veicolo può eseguire un sottoinsieme di percorsi, chiamato vehicle schedule (schedula del veicolo), soggetto a vincoli di durata massima. Nonostante la sua importanza pratica, il MTVRP ha ricevuto poca attenzione in letteratura: sono stati proposti diversi metodi euristici e un solo algoritmo esatto di risoluzione, presentato da Mingozzi, Roberti e Toth. In questa tesi viene presentato un metodo euristico in grado di risolvere istanze di MTVRP in presenza di vincoli reali, quali flotta di veicoli non omogenea e time windows. L’euristico si basa sul modello di Prins. Sono presentati inoltre due approcci di local search per migliorare la soluzione finale. I risultati computazionali evidenziano l’efficienza di tali approcci.

Permutation classes, sorting algorithms, and lattice paths

A permutation is said to avoid a pattern if it does not contain any subsequence which is order-isomorphic to it. Donald Knuth, in the first volume of his celebrated book "The art of Computer Programming", observed that the permutations that can be computed (or, equivalently, sorted) by some particular data structures can be characterized in terms of pattern avoidance. In more recent years, the topic was reopened several times, while often in terms of sortable permutations rather than computable ones. The idea to sort permutations by using one of Knuth’s devices suggests to look for a deterministic procedure that decides, in linear time, if there exists a sequence of operations which is able to convert a given permutation into the identical one. In this thesis we show that, for the stack and the restricted deques, there exists an unique way to implement such a procedure. Moreover, we use these sorting procedures to create new sorting algorithms, and we prove some unexpected commutation properties between these procedures and the base step of bubblesort. We also show that the permutations that can be sorted by a combination of the base steps of bubblesort and its dual can be expressed, once again, in terms of pattern avoidance. In the final chapter we give an alternative proof of some enumerative results, in particular for the classes of permutations that can be sorted by the two restricted deques. It is well-known that the permutations that can be sorted through a restricted deque are counted by the Schrӧder numbers. In the thesis, we show how the deterministic sorting procedures yield a bijection between sortable permutations and Schrӧder paths.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Brain-Computer Interfaces for augmented communication: Asynchronous and adaptive algorithms and evaluation with end users

This thesis aimed at addressing some of the issues that, at the state of the art, avoid the P300-based brain computer interface (BCI) systems to move from research laboratories to end users’ home. An innovative asynchronous classifier has been defined and validated. It relies on the introduction of a set of thresholds in the classifier, and such thresholds have been assessed considering the distributions of score values relating to target, non-target stimuli and epochs of voluntary no-control. With the asynchronous classifier, a P300-based BCI system can adapt its speed to the current state of the user and can automatically suspend the control when the user diverts his attention from the stimulation interface. Since EEG signals are non-stationary and show inherent variability, in order to make long-term use of BCI possible, it is important to track changes in ongoing EEG activity and to adapt BCI model parameters accordingly. To this aim, the asynchronous classifier has been subsequently improved by introducing a self-calibration algorithm for the continuous and unsupervised recalibration of the subjective control parameters. Finally an index for the online monitoring of the EEG quality has been defined and validated in order to detect potential problems and system failures. This thesis ends with the description of a translational work involving end users (people with amyotrophic lateral sclerosis-ALS). Focusing on the concepts of the user centered design approach, the phases relating to the design, the development and the validation of an innovative assistive device have been described. The proposed assistive technology (AT) has been specifically designed to meet the needs of people with ALS during the different phases of the disease (i.e. the degree of motor abilities impairment). Indeed, the AT can be accessed with several input devices either conventional (mouse, touchscreen) or alterative (switches, headtracker) up to a P300-based BCI.