Regularization meets GreenAI: a new framework for image reconstruction in life sciences applications

Ill-conditioned inverse problems frequently arise in life sciences, particularly in the context of image deblurring and medical image reconstruction. These problems have been addressed through iterative variational algorithms, which regularize the reconstruction by adding prior knowledge about the problem's solution. Despite the theoretical reliability of these methods, their practical utility is constrained by the time required to converge. Recently, the advent of neural networks allowed the development of reconstruction algorithms that can compute highly accurate solutions with minimal time demands. Regrettably, it is well-known that neural networks are sensitive to unexpected noise, and the quality of their reconstructions quickly deteriorates when the input is slightly perturbed. Modern efforts to address this challenge have led to the creation of massive neural network architectures, but this approach is unsustainable from both ecological and economic standpoints. The recently introduced GreenAI paradigm argues that developing sustainable neural network models is essential for practical applications. In this thesis, we aim to bridge the gap between theory and practice by introducing a novel framework that combines the reliability of model-based iterative algorithms with the speed and accuracy of end-to-end neural networks. Additionally, we demonstrate that our framework yields results comparable to state-of-the-art methods while using relatively small, sustainable models. In the first part of this thesis, we discuss the proposed framework from a theoretical perspective. We provide an extension of classical regularization theory, applicable in scenarios where neural networks are employed to solve inverse problems, and we show there exists a trade-off between accuracy and stability. Furthermore, we demonstrate the effectiveness of our methods in common life science-related scenarios. In the second part of the thesis, we initiate an exploration extending the proposed method into the probabilistic domain. We analyze some properties of deep generative models, revealing their potential applicability in addressing ill-posed inverse 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.

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.

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.

Parameters and algorithms to evaluate cardiac mechanics by conductance catheter

This work is structured as follows: In Section 1 we discuss the clinical problem of heart failure. In particular, we present the phenomenon known as ventricular mechanical dyssynchrony: its impact on cardiac function, the therapy for its treatment and the methods for its quantification. Specifically, we describe the conductance catheter and its use for the measurement of dyssynchrony. At the end of the Section 1, we propose a new set of indexes to quantify the dyssynchrony that are studied and validated thereafter. In Section 2 we describe the studies carried out in this work: we report the experimental protocols, we present and discuss the results obtained. Finally, we report the overall conclusions drawn from this work and we try to envisage future works and possible clinical applications of our results. Ancillary studies that were carried out during this work mainly to investigate several aspects of cardiac resynchronization therapy (CRT) are mentioned in Appendix. -------- Ventricular mechanical dyssynchrony plays a regulating role already in normal physiology but is especially important in pathological conditions, such as hypertrophy, ischemia, infarction, or heart failure (Chapter 1,2.). Several prospective randomized controlled trials supported the clinical efficacy and safety of cardiac resynchronization therapy (CRT) in patients with moderate or severe heart failure and ventricular dyssynchrony. CRT resynchronizes ventricular contraction by simultaneous pacing of both left and right ventricle (biventricular pacing) (Chapter 1.). Currently, the conductance catheter method has been used extensively to assess global systolic and diastolic ventricular function and, more recently, the ability of this instrument to pick-up multiple segmental volume signals has been used to quantify mechanical ventricular dyssynchrony. Specifically, novel indexes based on volume signals acquired with the conductance catheter were introduced to quantify dyssynchrony (Chapter 3,4.). Present work was aimed to describe the characteristics of the conductancevolume signals, to investigate the performance of the indexes of ventricular dyssynchrony described in literature and to introduce and validate improved dyssynchrony indexes. Morevoer, using the conductance catheter method and the new indexes, the clinical problem of the ventricular pacing site optimization was addressed and the measurement protocol to adopt for hemodynamic tests on cardiac pacing was investigated. In accordance to the aims of the work, in addition to the classical time-domain parameters, a new set of indexes has been extracted, based on coherent averaging procedure and on spectral and cross-spectral analysis (Chapter 4.). Our analyses were carried out on patients with indications for electrophysiologic study or device implantation (Chapter 5.). For the first time, besides patients with heart failure, indexes of mechanical dyssynchrony based on conductance catheter were extracted and studied in a population of patients with preserved ventricular function, providing information on the normal range of such a kind of values. By performing a frequency domain analysis and by applying an optimized coherent averaging procedure (Chapter 6.a.), we were able to describe some characteristics of the conductance-volume signals (Chapter 6.b.). We unmasked the presence of considerable beat-to-beat variations in dyssynchrony that seemed more frequent in patients with ventricular dysfunction and to play a role in discriminating patients. These non-recurrent mechanical ventricular non-uniformities are probably the expression of the substantial beat-to-beat hemodynamic variations, often associated with heart failure and due to cardiopulmonary interaction and conduction disturbances. We investigated how the coherent averaging procedure may affect or refine the conductance based indexes; in addition, we proposed and tested a new set of indexes which quantify the non-periodic components of the volume signals. Using the new set of indexes we studied the acute effects of the CRT and the right ventricular pacing, in patients with heart failure and patients with preserved ventricular function. In the overall population we observed a correlation between the hemodynamic changes induced by the pacing and the indexes of dyssynchrony, and this may have practical implications for hemodynamic-guided device implantation. The optimal ventricular pacing site for patients with conventional indications for pacing remains controversial. The majority of them do not meet current clinical indications for CRT pacing. Thus, we carried out an analysis to compare the impact of several ventricular pacing sites on global and regional ventricular function and dyssynchrony (Chapter 6.c.). We observed that right ventricular pacing worsens cardiac function in patients with and without ventricular dysfunction unless the pacing site is optimized. CRT preserves left ventricular function in patients with normal ejection fraction and improves function in patients with poor ejection fraction despite no clinical indication for CRT. Moreover, the analysis of the results obtained using new indexes of regional dyssynchrony, suggests that pacing site may influence overall global ventricular function depending on its relative effects on regional function and synchrony. Another clinical problem that has been investigated in this work is the optimal right ventricular lead location for CRT (Chapter 6.d.). Similarly to the previous analysis, using novel parameters describing local synchrony and efficiency, we tested the hypothesis and we demonstrated that biventricular pacing with alternative right ventricular pacing sites produces acute improvement of ventricular systolic function and improves mechanical synchrony when compared to standard right ventricular pacing. Although no specific right ventricular location was shown to be superior during CRT, the right ventricular pacing site that produced the optimal acute hemodynamic response varied between patients. Acute hemodynamic effects of cardiac pacing are conventionally evaluated after stabilization episodes. The applied duration of stabilization periods in most cardiac pacing studies varied considerably. With an ad hoc protocol (Chapter 6.e.) and indexes of mechanical dyssynchrony derived by conductance catheter we demonstrated that the usage of stabilization periods during evaluation of cardiac pacing may mask early changes in systolic and diastolic intra-ventricular dyssynchrony. In fact, at the onset of ventricular pacing, the main dyssynchrony and ventricular performance changes occur within a 10s time span, initiated by the changes in ventricular mechanical dyssynchrony induced by aberrant conduction and followed by a partial or even complete recovery. It was already demonstrated in normal animals that ventricular mechanical dyssynchrony may act as a physiologic modulator of cardiac performance together with heart rate, contractile state, preload and afterload. The present observation, which shows the compensatory mechanism of mechanical dyssynchrony, suggests that ventricular dyssynchrony may be regarded as an intrinsic cardiac property, with baseline dyssynchrony at increased level in heart failure patients. To make available an independent system for cardiac output estimation, in order to confirm the results obtained with conductance volume method, we developed and validated a novel technique to apply the Modelflow method (a method that derives an aortic flow waveform from arterial pressure by simulation of a non-linear three-element aortic input impedance model, Wesseling et al. 1993) to the left ventricular pressure signal, instead of the arterial pressure used in the classical approach (Chapter 7.). The results confirmed that in patients without valve abnormalities, undergoing conductance catheter evaluations, the continuous monitoring of cardiac output using the intra-ventricular pressure signal is reliable. Thus, cardiac output can be monitored quantitatively and continuously with a simple and low-cost method. During this work, additional studies were carried out to investigate several areas of uncertainty of CRT. The results of these studies are briefly presented in Appendix: the long-term survival in patients treated with CRT in clinical practice, the effects of CRT in patients with mild symptoms of heart failure and in very old patients, the limited thoracotomy as a second choice alternative to transvenous implant for CRT delivery, the evolution and prognostic significance of diastolic filling pattern in CRT, the selection of candidates to CRT with echocardiographic criteria and the prediction of response to the therapy.

Management and routing algorithms for ad-hoc and sensor networks

Large scale wireless adhoc networks of computers, sensors, PDAs etc. (i.e. nodes) are revolutionizing connectivity and leading to a paradigm shift from centralized systems to highly distributed and dynamic environments. An example of adhoc networks are sensor networks, which are usually composed by small units able to sense and transmit to a sink elementary data which are successively processed by an external machine. Recent improvements in the memory and computational power of sensors, together with the reduction of energy consumptions, are rapidly changing the potential of such systems, moving the attention towards datacentric sensor networks. A plethora of routing and data management algorithms have been proposed for the network path discovery ranging from broadcasting/floodingbased approaches to those using global positioning systems (GPS). We studied WGrid, a novel decentralized infrastructure that organizes wireless devices in an adhoc manner, where each node has one or more virtual coordinates through which both message routing and data management occur without reliance on either flooding/broadcasting operations or GPS. The resulting adhoc network does not suffer from the deadend problem, which happens in geographicbased routing when a node is unable to locate a neighbor closer to the destination than itself. WGrid allow multidimensional data management capability since nodes' virtual coordinates can act as a distributed database without needing neither special implementation or reorganization. Any kind of data (both single and multidimensional) can be distributed, stored and managed. We will show how a location service can be easily implemented so that any search is reduced to a simple query, like for any other data type. WGrid has then been extended by adopting a replication methodology. We called the resulting algorithm WRGrid. Just like WGrid, WRGrid acts as a distributed database without needing neither special implementation nor reorganization and any kind of data can be distributed, stored and managed. We have evaluated the benefits of replication on data management, finding out, from experimental results, that it can halve the average number of hops in the network. The direct consequence of this fact are a significant improvement on energy consumption and a workload balancing among sensors (number of messages routed by each node). Finally, thanks to the replications, whose number can be arbitrarily chosen, the resulting sensor network can face sensors disconnections/connections, due to failures of sensors, without data loss. Another extension to {WGrid} is {W*Grid} which extends it by strongly improving network recovery performance from link and/or device failures that may happen due to crashes or battery exhaustion of devices or to temporary obstacles. W*Grid guarantees, by construction, at least two disjoint paths between each couple of nodes. This implies that the recovery in W*Grid occurs without broadcasting transmissions and guaranteeing robustness while drastically reducing the energy consumption. An extensive number of simulations shows the efficiency, robustness and traffic road of resulting networks under several scenarios of device density and of number of coordinates. Performance analysis have been compared to existent algorithms in order to validate the results.

Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Multiobjective genetic algorithms applied to heat transfer problems

In the present work, the multi-objective optimization by genetic algorithms is investigated and applied to heat transfer problems. Firstly, the work aims to compare different reproduction processes employed by genetic algorithms and two new promising processes are suggested. Secondly, in this work two heat transfer problems are studied under the multi-objective point of view. Specifically, the two cases studied are the wavy fins and the corrugated wall channel. Both these cases have already been studied by a single objective optimizer. Therefore, this work aims to extend the previous works in a more comprehensive study.

Tecniche di progettazione tollerante alle variazioni per circuiti digitali in tecnologie nanometriche

The digital electronic market development is founded on the continuous reduction of the transistors size, to reduce area, power, cost and increase the computational performance of integrated circuits. This trend, known as technology scaling, is approaching the nanometer size. The lithographic process in the manufacturing stage is increasing its uncertainty with the scaling down of the transistors size, resulting in a larger parameter variation in future technology generations. Furthermore, the exponential relationship between the leakage current and the threshold voltage, is limiting the threshold and supply voltages scaling, increasing the power density and creating local thermal issues, such as hot spots, thermal runaway and thermal cycles. In addiction, the introduction of new materials and the smaller devices dimension are reducing transistors robustness, that combined with high temperature and frequently thermal cycles, are speeding up wear out processes. Those effects are no longer addressable only at the process level. Consequently the deep sub-micron devices will require solutions which will imply several design levels, as system and logic, and new approaches called Design For Manufacturability (DFM) and Design For Reliability. The purpose of the above approaches is to bring in the early design stages the awareness of the device reliability and manufacturability, in order to introduce logic and system able to cope with the yield and reliability loss. The ITRS roadmap suggests the following research steps to integrate the design for manufacturability and reliability in the standard CAD automated design flow: i) The implementation of new analysis algorithms able to predict the system thermal behavior with the impact to the power and speed performances. ii) High level wear out models able to predict the mean time to failure of the system (MTTF). iii) Statistical performance analysis able to predict the impact of the process variation, both random and systematic. The new analysis tools have to be developed beside new logic and system strategies to cope with the future challenges, as for instance: i) Thermal management strategy that increase the reliability and life time of the devices acting to some tunable parameter,such as supply voltage or body bias. ii) Error detection logic able to interact with compensation techniques as Adaptive Supply Voltage ASV, Adaptive Body Bias ABB and error recovering, in order to increase yield and reliability. iii) architectures that are fundamentally resistant to variability, including locally asynchronous designs, redundancy, and error correcting signal encodings (ECC). The literature already features works addressing the prediction of the MTTF, papers focusing on thermal management in the general purpose chip, and publications on statistical performance analysis. In my Phd research activity, I investigated the need for thermal management in future embedded low-power Network On Chip (NoC) devices.I developed a thermal analysis library, that has been integrated in a NoC cycle accurate simulator and in a FPGA based NoC simulator. The results have shown that an accurate layout distribution can avoid the onset of hot-spot in a NoC chip. Furthermore the application of thermal management can reduce temperature and number of thermal cycles, increasing the systemreliability. Therefore the thesis advocates the need to integrate a thermal analysis in the first design stages for embedded NoC design. Later on, I focused my research in the development of statistical process variation analysis tool that is able to address both random and systematic variations. The tool was used to analyze the impact of self-timed asynchronous logic stages in an embedded microprocessor. As results we confirmed the capability of self-timed logic to increase the manufacturability and reliability. Furthermore we used the tool to investigate the suitability of low-swing techniques in the NoC system communication under process variations. In this case We discovered the superior robustness to systematic process variation of low-swing links, which shows a good response to compensation technique as ASV and ABB. Hence low-swing is a good alternative to the standard CMOS communication for power, speed, reliability and manufacturability. In summary my work proves the advantage of integrating a statistical process variation analysis tool in the first stages of the design flow.

Combinatorial and Robust Optimisation Models and Algorithms for Railway Applications

This thesis deals with an investigation of combinatorial and robust optimisation models to solve railway problems. Railway applications represent a challenging area for operations research. In fact, most problems in this context can be modelled as combinatorial optimisation problems, in which the number of feasible solutions is finite. Yet, despite the astonishing success in the field of combinatorial optimisation, the current state of algorithmic research faces severe difficulties with highly-complex and data-intensive applications such as those dealing with optimisation issues in large-scale transportation networks. One of the main issues concerns imperfect information. The idea of Robust Optimisation, as a way to represent and handle mathematically systems with not precisely known data, dates back to 1970s. Unfortunately, none of those techniques proved to be successfully applicable in one of the most complex and largest in scale (transportation) settings: that of railway systems. Railway optimisation deals with planning and scheduling problems over several time horizons. Disturbances are inevitable and severely affect the planning process. Here we focus on two compelling aspects of planning: robust planning and online (real-time) planning.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.