The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot. This thesis addresses heuristics algorithms based on the well-know granular search idea introduced by Toth and Vigo (2003) to solve the CLRP and the MDVRP. Extensive computational experiments on benchmark instances for both problems have been performed to determine the effectiveness of the proposed algorithms. This work is organized as follows: Chapter 1 describes a detailed overview and a methodological review of the literature for the the Capacitated Location-Routing Problem (CLRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). Chapter 2 describes a two-phase hybrid heuristic algorithm to solve the CLRP. Chapter 3 shows a computational comparison of heuristic algorithms for the CLRP. Chapter 4 presents a hybrid granular tabu search approach for solving the MDVRP.

This Ph.D thesis focuses on iterative regularization methods for regularizing linear and nonlinear ill-posed problems. Regarding linear problems, three new stopping rules for the Conjugate Gradient method applied to the normal equations are proposed and tested in many numerical simulations, including some tomographic images reconstruction problems. Regarding nonlinear problems, convergence and convergence rate results are provided for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting.

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.

In the present thesis, we discuss the main notions of an axiomatic approach for an invariant Harnack inequality. This procedure, originated from techniques for fully nonlinear elliptic operators, has been developed by Di Fazio, Gutiérrez, and Lanconelli in the general settings of doubling Hölder quasi-metric spaces. The main tools of the approach are the so-called double ball property and critical density property: the validity of these properties implies an invariant Harnack inequality. We are mainly interested in the horizontally elliptic operators, i.e. some second order linear degenerate-elliptic operators which are elliptic with respect to the horizontal directions of a Carnot group. An invariant Harnack inequality of Krylov-Safonov type is still an open problem in this context. In the thesis we show how the double ball property is related to the solvability of a kind of exterior Dirichlet problem for these operators. More precisely, it is a consequence of the existence of some suitable interior barrier functions of Bouligand-type. By following these ideas, we prove the double ball property for a generic step two Carnot group. Regarding the critical density, we generalize to the setting of H-type groups some arguments by Gutiérrez and Tournier for the Heisenberg group. We recognize that the critical density holds true in these peculiar contexts by assuming a Cordes-Landis type condition for the coefficient matrix of the operator. By the axiomatic approach, we thus prove an invariant Harnack inequality in H-type groups which is uniform in the class of the coefficient matrices with prescribed bounds for the eigenvalues and satisfying such a Cordes-Landis condition.

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.

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Intelligent Transport Systems (ITS) consists in the application of ICT to transport to offer new and improved services to the mobility of people and freights. While using ITS, travellers produce large quantities of data that can be collected and analysed to study their behaviour and to provide information to decision makers and planners. The thesis proposes innovative deployments of classification algorithms for Intelligent Transport System with the aim to support the decisions on traffic rerouting, bus transport demand and behaviour of two wheelers vehicles. The first part of this work provides an overview and a classification of a selection of clustering algorithms that can be implemented for the analysis of ITS data. The first contribution of this thesis is an innovative use of the agglomerative hierarchical clustering algorithm to classify similar travels in terms of their origin and destination, together with the proposal for a methodology to analyse drivers’ route choice behaviour using GPS coordinates and optimal alternatives. The clusters of repetitive travels made by a sample of drivers are then analysed to compare observed route choices to the modelled alternatives. The results of the analysis show that drivers select routes that are more reliable but that are more expensive in terms of travel time. Successively, different types of users of a service that provides information on the real time arrivals of bus at stop are classified using Support Vector Machines. The results shows that the results of the classification of different types of bus transport users can be used to update or complement the census on bus transport flows. Finally, the problem of the classification of accidents made by two wheelers vehicles is presented together with possible future application of clustering methodologies aimed at identifying and classifying the different types of accidents.

In this thesis we focus on optimization and simulation techniques applied to solve strategic, tactical and operational problems rising in the healthcare sector. At first we present three applications to Emilia-Romagna Public Health System (SSR) developed in collaboration with Agenzia Sanitaria e Sociale dell'Emilia-Romagna (ASSR), a regional center for innovation and improvement in health. Agenzia launched a strategic campaign aimed at introducing Operations Research techniques as decision making tools to support technological and organizational innovations. The three applications focus on forecast and fund allocation of medical specialty positions, breast screening program extension and operating theater planning. The case studies exploit the potential of combinatorial optimization, discrete event simulation and system dynamics techniques to solve resource constrained problem arising within Emilia-Romagna territory. We then present an application in collaboration with Dipartimento di Epidemiologia del Lazio that focuses on population demand of service allocation to regional emergency departments. Finally, a simulation-optimization approach, developed in collaboration with INESC TECH center of Porto, to evaluate matching policies for the kidney exchange problem is discussed.

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.