Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

Topological analysis of singularity loci for serial and parallel manipulators

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

Numerical simulation of ion transport through ion channels and solid-state nanopores

Ion channels are pore-forming proteins that regulate the flow of ions across biological cell membranes. Ion channels are fundamental in generating and regulating the electrical activity of cells in the nervous system and the contraction of muscolar cells. Solid-state nanopores are nanometer-scale pores located in electrically insulating membranes. They can be adopted as detectors of specific molecules in electrolytic solutions. Permeation of ions from one electrolytic solution to another, through a protein channel or a synthetic pore is a process of considerable importance and realistic analysis of the main dependencies of ion current on the geometrical and compositional characteristics of these structures are highly required. The project described by this thesis is an effort to improve the understanding of ion channels by devising methods for computer simulation that can predict channel conductance from channel structure. This project describes theory, algorithms and implementation techniques used to develop a novel 3-D numerical simulator of ion channels and synthetic nanopores based on the Brownian Dynamics technique. This numerical simulator could represent a valid tool for the study of protein ion channel and synthetic nanopores, allowing to investigate at the atomic-level the complex electrostatic interactions that determine channel conductance and ion selectivity. Moreover it will provide insights on how parameters like temperature, applied voltage, and pore shape could influence ion translocation dynamics. Furthermore it will help making predictions of conductance of given channel structures and it will add information like electrostatic potential or ionic concentrations throughout the simulation domain helping the understanding of ion flow through membrane pores.

Parallel modeling of the electric field distribution in the brain

The term "Brain Imaging" identi�es a set of techniques to analyze the structure and/or functional behavior of the brain in normal and/or pathological situations. These techniques are largely used in the study of brain activity. In addition to clinical usage, analysis of brain activity is gaining popularity in others recent �fields, i.e. Brain Computer Interfaces (BCI) and the study of cognitive processes. In this context, usage of classical solutions (e.g. f MRI, PET-CT) could be unfeasible, due to their low temporal resolution, high cost and limited portability. For these reasons alternative low cost techniques are object of research, typically based on simple recording hardware and on intensive data elaboration process. Typical examples are ElectroEncephaloGraphy (EEG) and Electrical Impedance Tomography (EIT), where electric potential at the patient's scalp is recorded by high impedance electrodes. In EEG potentials are directly generated from neuronal activity, while in EIT by the injection of small currents at the scalp. To retrieve meaningful insights on brain activity from measurements, EIT and EEG relies on detailed knowledge of the underlying electrical properties of the body. This is obtained from numerical models of the electric �field distribution therein. The inhomogeneous and anisotropic electric properties of human tissues make accurate modeling and simulation very challenging, leading to a tradeo�ff between physical accuracy and technical feasibility, which currently severely limits the capabilities of these techniques. Moreover elaboration of data recorded requires usage of regularization techniques computationally intensive, which influences the application with heavy temporal constraints (such as BCI). This work focuses on the parallel implementation of a work-flow for EEG and EIT data processing. The resulting software is accelerated using multi-core GPUs, in order to provide solution in reasonable times and address requirements of real-time BCI systems, without over-simplifying the complexity and accuracy of the head models.

Theoretical and numerical study of the laser-plasma ion acceleration

The laser driven ion acceleration is a burgeoning field of resarch and is attracting a growing number of scientists since the first results reported in 2000 obtained irradiating thin solid foils by high power laser pulses. The growing interest is driven by the peculiar characteristics of the produced bunches, the compactness of the whole accelerating system and the very short accelerating length of this all-optical accelerators. A fervent theoretical and experimental work has been done since then. An important part of the theoretical study is done by means of numerical simulations and the most widely used technique exploits PIC codes (“Particle In Cell'”). In this thesis the PIC code AlaDyn, developed by our research group considering innovative algorithms, is described. My work has been devoted to the developement of the code and the investigation of the laser driven ion acceleration for different target configurations. Two target configurations for the proton acceleration are presented together with the results of the 2D and 3D numerical investigation. One target configuration consists of a solid foil with a low density layer attached on the irradiated side. The nearly critical plasma of the foam layer allows a very high energy absorption by the target and an increase of the proton energy up to a factor 3, when compared to the ``pure'' TNSA configuration. The differences of the regime with respect to the standard TNSA are described The case of nearly critical density targets has been investigated with 3D simulations. In this case the laser travels throughout the plasma and exits on the rear side. During the propagation, the laser drills a channel and induce a magnetic vortex that expanding on the rear side of the targer is source of a very intense electric field. The protons of the plasma are strongly accelerated up to energies of 100 MeV using a 200PW laser.

A numerical methodology for the multi-objective optimization of the DI Diesel engine combustion

DI Diesel engine are widely used both for industrial and automotive applications due to their durability and fuel economy. Nonetheless, increasing environmental concerns force that type of engine to comply with increasingly demanding emission limits, so that, it has become mandatory to develop a robust design methodology of the DI Diesel combustion system focused on reduction of soot and NOx simultaneously while maintaining a reasonable fuel economy. In recent years, genetic algorithms and CFD three-dimensional combustion simulations have been successfully applied to that kind of problem. However, combining GAs optimization with actual CFD three-dimensional combustion simulations can be too onerous since a large number of calculations is usually needed for the genetic algorithm to converge, resulting in a high computational cost and, thus, limiting the suitability of this method for industrial processes. In order to make the optimization process less time-consuming, CFD simulations can be more conveniently used to generate a training set for the learning process of an artificial neural network which, once correctly trained, can be used to forecast the engine outputs as a function of the design parameters during a GA optimization performing a so-called virtual optimization. In the current work, a numerical methodology for the multi-objective virtual optimization of the combustion of an automotive DI Diesel engine, which relies on artificial neural networks and genetic algorithms, was developed.

Experimental and Numerical Analysis of Gas Forced Convection through Microtubes and Micro Heat Exchangers

The last decade has witnessed very fast development in microfabrication technologies. The increasing industrial applications of microfluidic systems call for more intensive and systematic knowledge on this newly emerging field. Especially for gaseous flow and heat transfer at microscale, the applicability of conventional theories developed at macro scale is not yet completely validated; this is mainly due to scarce experimental data available in literature for gas flows. The objective of this thesis is to investigate these unclear elements by analyzing forced convection for gaseous flows through microtubes and micro heat exchangers. Experimental tests have been performed with microtubes having various inner diameters, namely 750 m, 510 m and 170 m, over a wide range of Reynolds number covering the laminar region, the transitional zone and also the onset region of the turbulent regime. The results show that conventional theory is able to predict the flow friction factor when flow compressibility does not appear and the effect of fluid temperature-dependent properties is insignificant. A double-layered microchannel heat exchanger has been designed in order to study experimentally the efficiency of a gas-to-gas micro heat exchanger. This microdevice contains 133 parallel microchannels machined into polished PEEK plates for both the hot side and the cold side. The microchannels are 200 µm high, 200 µm wide and 39.8 mm long. The design of the micro device has been made in order to be able to test different materials as partition foil with flexible thickness. Experimental tests have been carried out for five different partition foils, with various mass flow rates and flow configurations. The experimental results indicate that the thermal performance of the countercurrent and cross flow micro heat exchanger can be strongly influenced by axial conduction in the partition foil separating the hot gas flow and cold gas flow.

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.

Shape memory and elastoplastic materials: from constitutive and numerical to fatigue modeling

Shape memory materials (SMMs) represent an important class of smart materials that have the ability to return from a deformed state to their original shape. Thanks to such a property, SMMs are utilized in a wide range of innovative applications. The increasing number of applications and the consequent involvement of industrial players in the field have motivated researchers to formulate constitutive models able to catch the complex behavior of these materials and to develop robust computational tools for design purposes. Such a research field is still under progress, especially in the prediction of shape memory polymer (SMP) behavior and of important effects characterizing shape memory alloy (SMA) applications. Moreover, the frequent use of shape memory and metallic materials in biomedical devices, particularly in cardiovascular stents, implanted in the human body and experiencing millions of in-vivo cycles by the blood pressure, clearly indicates the need for a deeper understanding of fatigue/fracture failure in microsize components. The development of reliable stent designs against fatigue is still an open subject in scientific literature. Motivated by the described framework, the thesis focuses on several research issues involving the advanced constitutive, numerical and fatigue modeling of elastoplastic and shape memory materials. Starting from the constitutive modeling, the thesis proposes to develop refined phenomenological models for reliable SMA and SMP behavior descriptions. Then, concerning the numerical modeling, the thesis proposes to implement the models into numerical software by developing implicit/explicit time-integration algorithms, to guarantee robust computational tools for practical purposes. The described modeling activities are completed by experimental investigations on SMA actuator springs and polyethylene polymers. Finally, regarding the fatigue modeling, the thesis proposes the introduction of a general computational approach for the fatigue-life assessment of a classical stent design, in order to exploit computer-based simulations to prevent failures and modify design, without testing numerous devices.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.

Numerical and Analytical Methods for Laser-Plasma Acceleration Physics

Theories and numerical modeling are fundamental tools for understanding, optimizing and designing present and future laser-plasma accelerators (LPAs). Laser evolution and plasma wave excitation in a LPA driven by a weakly relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, is studied analytically in 3D including the effects of pulse steepening and energy depletion. At higher laser intensities, the process of electron self-injection in the nonlinear bubble wake regime is studied by means of fully self-consistent Particle-in-Cell simulations. Considering a non-evolving laser driver propagating with a prescribed velocity, the geometrical properties of the non-evolving bubble wake are studied. For a range of parameters of interest for laser plasma acceleration, The dependence of the threshold for self-injection in the non-evolving wake on laser intensity and wake velocity is characterized. Due to the nonlinear and complex nature of the Physics involved, computationally challenging numerical simulations are required to model laser-plasma accelerators operating at relativistic laser intensities. The numerical and computational optimizations, that combined in the codes INF&RNO and INF&RNO/quasi-static give the possibility to accurately model multi-GeV laser wakefield acceleration stages with present supercomputing architectures, are discussed. The PIC code jasmine, capable of efficiently running laser-plasma simulations on Graphics Processing Units (GPUs) clusters, is presented. GPUs deliver exceptional performance to PIC codes, but the core algorithms had to be redesigned for satisfying the constraints imposed by the intrinsic parallelism of the architecture. The simulation campaigns, run with the code jasmine for modeling the recent LPA experiments with the INFN-FLAME and CNR-ILIL laser systems, are also presented.

Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods

In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases.