Progettazione e sviluppo di un RVE (Reconfigurable Virtual Environment) per applicazioni nei settori dell’ingegneria industriale

Il presente elaborato descrive la realizzazione, presso il Laboratorio di Realtà Virtuale e Simulazione della Seconda Facoltà di Ingegneria, di un RVE (Reconfigurable Virtual Environment), per applicazioni nei settori dell’ingegneria industriale. La tesi ripercorre la fase di progettazione del sistema basato sull'integrazione di componenti COTS. E' definito, inoltre, un insieme di applicazioni target nei settori dell'ingegneria industriale di cui si valuta la compatibilità con il Virtual Environment. L'elaborato si conclude con la presentazione dei risultati e dei possibili sviluppi futuri.

Polarization observables in virtual compton scattering

Virtual Compton Scattering (VCS) is an important reaction for understanding nucleon structure at low energies. By studying this process, the generalized polarizabilities of the nucleon can be measured. These observables are a generalization of the already known polarizabilities and will permit theoretical models to be challenged on a new level. More specifically, there exist six generalized polarizabilities and in order to disentangle them all, a double polarization experiment must be performed. Within this work, the VCS reaction p(e,e p)gamma was measured at MAMI using the A1 Collaboration three spectrometer setup with Q2=0.33 (GeV/c)2. Using the highly polarized MAMI beam and a recoil proton polarimeter, it was possible to measure both the VCS cross section and the double polarization observables. Already in 2000, the unpolarized VCS cross section was measured at MAMI. In this new experiment, we could confirm the old data and furthermore the double polarization observables were measured for the first time. The data were taken in five periods between 2005 and 2006. In this work, the data were analyzed to extract the cross section and the proton polarization. For the analysis, a maximum likelihood algorithm was developed together with the full simulation of all the analysis steps. The experiment is limited by the low statistics due mainly to the focal plane proton polarimeter efficiency. To overcome this problem, a new determination and parameterization of the carbon analyzing power was performed. The main result of the experiment is the extraction of a new combination of the generalized polarizabilities using the double polarization observables.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Anwendung der geoelektrischen 3D-Tomographie für die Analyse thermisch induzierter Strömungen im Labor

Sowohl in der Natur als auch in der Industrie existieren thermisch induzierte Strömungen. Von Interesse für diese Forschungsarbeit sind dabei die Konvektionen im Erdmantel sowie in den Glasschmelzwannen. Der dort stattfindende Materialtransport resultiert aus Unterschieden in der Dichte, der Temperatur und der chemischen Konzentration innerhalb des konvektierenden Materials. Um das Verständnis für die ablaufenden Prozesse zu verbessern, werden von zahlreichen Forschergruppen numerische Modellierungen durchgeführt. Die Verifikation der dafür verwendeten Algorithmen erfolgt meist über die Analyse von Laborexperimenten. Im Vordergrund dieser Forschungsarbeit steht die Entwicklung einer Methode zur Bestimmung der dreidimensionalen Temperaturverteilung für die Untersuchung von thermisch induzierten Strömungen in einem Versuchsbecken. Eine direkte Temperaturmessung im Inneren des Versuchsmaterials bzw. der Glasschmelze beeinflusst allerdings das Strömungsverhalten. Deshalb wird die geodynamisch störungsfrei arbeitende Impedanztomographie verwendet. Die Grundlage dieser Methode bildet der erweiterte Arrhenius-Zusammenhang zwischen Temperatur und spezifischer elektrischer Leitfähigkeit. Während der Laborexperimente wird ein zähflüssiges Polyethylenglykol-Wasser-Gemisch in einem Becken von unten her erhitzt. Die auf diese Weise generierten Strömungen stellen unter Berücksichtigung der Skalierung ein Analogon sowohl zu dem Erdmantel als auch zu den Schmelzwannen dar. Über mehrere Elektroden, die an den Beckenwänden installiert sind, erfolgen die geoelektrischen Messungen. Nach der sich anschließenden dreidimensionalen Inversion der elektrischen Widerstände liegt das Modell mit der Verteilung der spezifischen elektrischen Leitfähigkeit im Inneren des Versuchsbeckens vor. Diese wird mittels der erweiterten Arrhenius-Formel in eine Temperaturverteilung umgerechnet. Zum Nachweis der Eignung dieser Methode für die nichtinvasive Bestimmung der dreidimensionalen Temperaturverteilung wurden mittels mehrerer Thermoelemente an den Beckenwänden zusätzlich direkte Temperaturmessungen durchgeführt und die Werte miteinander verglichen. Im Wesentlichen sind die Innentemperaturen gut rekonstruierbar, wobei die erreichte Messgenauigkeit von der räumlichen und zeitlichen Auflösung der Gleichstromgeoelektrik abhängt.

3D-electron microscopy of different conformations of cephalopod hemocyanins

Die Hämocyanine der Cephalopoden Nautilus pompilius und Sepia officinalis sorgen für den Sauerstofftransport zwischen den Kiemen und den Geweben. Sie bestehen aus einem zylindrischen Dekamer mit interner Kragenstruktur. Während eine Untereinheit (also eine Polypeptidkette) bei NpH aus sieben paralogen funktionellen Domänen (FU-a bis FU-g) besteht, führte ein Genduplikationsereignis der FU-d zu acht FUs in SoH (a, b, c, d, d´, e, f, g). In allen Mollusken Hämocyaninen bilden sechs dieser FUs den äußeren Ring und die restlichen die interne Kragenstruktur. rnrnIn dieser Arbeit wurde ein dreidimensionales Modell des Hämocyanins von Sepia officinalis (SoH) erstellt. Die Rekonstruktion, mit einer Auflösung von 8,8Å (FSC=0,5), erlaubt das Einpassen von Homolologiemodellen und somit das Erstellen eines molekularen Modells mit pseudo atomarer Auflösung. Des Weiteren wurden zwei Rekonstruktionen des Hämocyanins von Nautilus pompilius (NpH) in verschiedenen Oxygenierungszuständen erstellt. Die auf 10 und 8,1Å aufgelösten Modelle zeigen zwei verschiedene Konformationen des Proteins. Daraus ließ sich eine Modellvorstellung über die allosterische Funktionsweise ableiten. Die hier erreichte Auflösung von 8Å ist die momentan höchste eines Molluskenhämocyanins. rnAuf Grundlage des molekularen Modells von SoH konnte die Topologie des Proteins aufgeklärt werden. Es wurde gezeigt, dass die zusätzliche FU-d´ in den Kragen integriert ist und somit die prinzipielle Wandarchitektur aller Mollusken Hämocyanine identisch ist. Wie die Analyse des erstellten molekularen Modells zeigt werden sind die beiden Isoformen (SoH1 und SoH2) in den Bereichen der Interfaces nahezu identisch; auch der Vergleich mit NpH zeigt grosse Übereinstimmungen. Des weiteren konnte eine Fülle von Informationen bezüglich der allosterischen Signalübertragung innerhalb des Moleküls gewonnen werden. rnDer Versuch, NpH in verschiedenen Oxygenierungszuständen zu zeigen, war erfolgreich. Die Datensätze, die unter zwei atmosphärischen Bedingungen präpariert wurden, führten reproduzierbar zu zwei unterschiedlichen Rekonstruktionen. Dies zeigt, daß der hier entwickelte experimentelle Ansatz funktioniert. Er kann nun routinemäßig auf andere Proteine angewandt werden. Wie der strukturelle Vergleich zeigte, verändert sich die Orientierung der FUs durch die Oxygenierung leicht. Dies wiederum beeinflusst die Anordnung innerhalb der Interfaces sowie die Abstände zwischen den beteiligten Aminosäuren. Aus dieser Analyse konnte eine Modellvorstellung zum allosterischen Signaltransfer innerhalb des Moleküls abgeleitet werden, die auf einer Umordnung von Salzbrücken basiert.

3D-Strukturanalyse von Molluskenhämocyaninen aus elektronenmikroskopischen Bildern

Diese Arbeit präsentiert die bislang höchst aufgelösten KryoEM-Strukturen für ein Cephalopoden hämocyanin Dekamer (Nautilus pompilus Hämocyanin, NpH) und ein Gastropoden Hämocyanin Didekamer (keyhole limpet hemocyanin isoform 1). Durch die Methoden des “molecular modelling” und “rigid-body-fiting” wurde auch eine detaillierte Beschreibung beider Strukturen auf atomarem Niveau erstmalig möglich. Hämocyanine sind kupferhaltige Sauerstoff-Transportproteine die frei gelöst in Blut zahlreicher Arthropoden und Mollusken vorkommen. Allgemein sind Molluskenhämocyanine als Dekamere (Hohlzylinder aus 5 Untereinheiten-dimere) oder Didecamere (Zusammenlagerung von zwei Dekameren) zu finden. Durch Anlagerung weiterer Dekamere bilden sich teilweise tubuläre Multidekamere. Hämocyanine der Cephalopoden bestehen ausschließlich aus solitären Decameren. In Octopus und Nautilus bestehen die 10 Untereinheiten aus 7 funktionellen Einheiten(FU-a bis FU-g), wobei jede FU ein Sauerstoffmolekül binden kann. FUs a-f bilden die Wand des ringförmigen Moleküls und 10 Kopien der FU-g bilden einen sogenannten „inneren Kragenkomplex“. Das im Rahmen dieser Arbeit erstelltes molekulares Modell von NpH klärt die Struktur des Dekamers vollständig auf. Wir waren zum ersten Mal in der Lage das Untereinheiten-dimer, den Verlauf der Polypeptidkette und 15 unterschiedliche Kontaktstellen zwischen FUs zu identifizieren. Viele der inter-FU-Kontakte weisen Aminosäurenkonstellationen auf, die die Basis für die Übertragung allosterischer Wechselwirkungen zwischen FUs darstellen könnten und Hinweise für den Aufbau der allosterische Einheit geben. Potentielle Bindungsstellen für N-glykosidische Zucker und bivalente Kationen wurden auch identifiziert. Im Gegensatz zu NpH, kommen Gastropoden Hämocyanine (inkl. KLH) hauptsächlich als Didekamere vor und der Kragenkomplex wird in diesem Fall aus 2 FUs gebildet (Fu-g und FU-h). Die zusätzliche C'-terminale FU-h zeichnet sich durch eine spezielle Verlängerung von ~ 100 Aminosäuren aus. KLH stammt aus der kalifornische Schnecke Megathura crenulata und kommt seit mehreren Jahrzehnten als Immunostimulator in der immunologischen Grundlagenforschung und klinischen Anwendung zum Einsatz. KLH weist zwei Isoformen auf, KLH1 und KLH2. Das vorliegende Modell von KLH1 erlaubt die komplexe Architektur dieses riesigen Proteins in allen Details zu verstehen, sowie einen Vergleich zum dem NpH Dekamer auf atomare Ebene. Es wurde gefunden, dass das Untereinheitensegment a-b-c-d-e-f-g, sowie die equivalenten Kontaktstellen zwichen FUs stark konserviert sind. Dies deutet darauf hin, dass in Bezug auf die Übertragung allosterische Signale zwischen benachbarten FUs, grundlegende Mechanismen in beiden Molekülen beibehalten wurden. Weiterhin, konnten die Verbindungen zwischen den zwei Dekameren ertsmalig identifiziert werden. Schließlich, wurde die Topologie der N-glycosidischen Zucker, welche für die immunologische Eigenschaften von KLH1 von großer Bedeutung sind, auch aufgeklärt. Somit leistet die vorliegende Arbeit einen wesentlichen Schritt zum Verständnis der Quartärstruktur und Funktion der Molluskenhämocyanine.rn

A proposal for a virtual museum of computer science

A proposal for a virtual museum of computer science

Computational strategies to include protein flexibility in Ligand Docking and Virtual Screening

The dynamic character of proteins strongly influences biomolecular recognition mechanisms. With the development of the main models of ligand recognition (lock-and-key, induced fit, conformational selection theories), the role of protein plasticity has become increasingly relevant. In particular, major structural changes concerning large deviations of protein backbones, and slight movements such as side chain rotations are now carefully considered in drug discovery and development. It is of great interest to identify multiple protein conformations as preliminary step in a screening campaign. Protein flexibility has been widely investigated, in terms of both local and global motions, in two diverse biological systems. On one side, Replica Exchange Molecular Dynamics has been exploited as enhanced sampling method to collect multiple conformations of Lactate Dehydrogenase A (LDHA), an emerging anticancer target. The aim of this project was the development of an Ensemble-based Virtual Screening protocol, in order to find novel potent inhibitors. On the other side, a preliminary study concerning the local flexibility of Opioid Receptors has been carried out through ALiBERO approach, an iterative method based on Elastic Network-Normal Mode Analysis and Monte Carlo sampling. Comparison of the Virtual Screening performances by using single or multiple conformations confirmed that the inclusion of protein flexibility in screening protocols has a positive effect on the probability to early recognize novel or known active compounds.

Temperature Variation Aware Energy Optimization in Heterogeneous MPSoCs

Thermal effects are rapidly gaining importance in nanometer heterogeneous integrated systems. Increased power density, coupled with spatio-temporal variability of chip workload, cause lateral and vertical temperature non-uniformities (variations) in the chip structure. The assumption of an uniform temperature for a large circuit leads to inaccurate determination of key design parameters. To improve design quality, we need precise estimation of temperature at detailed spatial resolution which is very computationally intensive. Consequently, thermal analysis of the designs needs to be done at multiple levels of granularity. To further investigate the flow of chip/package thermal analysis we exploit the Intel Single Chip Cloud Computer (SCC) and propose a methodology for calibration of SCC on-die temperature sensors. We also develop an infrastructure for online monitoring of SCC temperature sensor readings and SCC power consumption. Having the thermal simulation tool in hand, we propose MiMAPT, an approach for analyzing delay, power and temperature in digital integrated circuits. MiMAPT integrates seamlessly into industrial Front-end and Back-end chip design flows. It accounts for temperature non-uniformities and self-heating while performing analysis. Furthermore, we extend the temperature variation aware analysis of designs to 3D MPSoCs with Wide-I/O DRAM. We improve the DRAM refresh power by considering the lateral and vertical temperature variations in the 3D structure and adapting the per-DRAM-bank refresh period accordingly. We develop an advanced virtual platform which models the performance, power, and thermal behavior of a 3D-integrated MPSoC with Wide-I/O DRAMs in detail. Moving towards real-world multi-core heterogeneous SoC designs, a reconfigurable heterogeneous platform (ZYNQ) is exploited to further study the performance and energy efficiency of various CPU-accelerator data sharing methods in heterogeneous hardware architectures. A complete hardware accelerator featuring clusters of OpenRISC CPUs, with dynamic address remapping capability is built and verified on a real hardware.

Towards Centrifugal Compressor Stages Virtual Testing

Flow features inside centrifugal compressor stages are very complicated to simulate with numerical tools due to the highly complex geometry and varying gas conditions all across the machine. For this reason, a big effort is currently being made to increase the fidelity of the numerical models during the design and validation phases. Computational Fluid Dynamics (CFD) plays an increasing role in the assessment of the performance prediction of centrifugal compressor stages. Historically, CFD was considered reliable for performance prediction on a qualitatively level, whereas tests were necessary to predict compressors performance on a quantitatively basis. In fact "standard" CFD with only the flow-path and blades included into the computational domain is known to be weak in capturing efficiency level and operating range accurately due to the under-estimation of losses and the lack of secondary flows modeling. This research project aims to fill the gap in accuracy between "standard" CFD and tests data by including a high fidelity reproduction of the gas domain and the use of advanced numerical models and tools introduced in the author's OEM in-house CFD code. In other words, this thesis describes a methodology by which virtual tests can be conducted on single stages and multistage centrifugal compressors in a similar fashion to a typical rig test that guarantee end users to operate machines with a confidence level not achievable before. Furthermore, the new "high fidelity" approach allowed understanding flow phenomena not fully captured before, increasing aerodynamicists capability and confidence in designing high efficiency and high reliable centrifugal compressor stages.

Kinematic models of interseismic deformation from inversion of GPS and InSAR measurements to estimate fault parameters and coupling degree

We have used kinematic models in two Italian regions to reproduce surface interseismic velocities obtained from InSAR and GPS measurements. We have considered a Block modeling, BM, approach to evaluate which fault system is actively accommodating the occurring deformation in both considered areas. We have performed a study for the Umbria-Marche Apennines, obtaining that the tectonic extension observed by GPS measurements is explained by the active contribution of at least two fault systems, one of which is the Alto Tiberina fault, ATF. We have estimated also the interseismic coupling distribution for the ATF using a 3D surface and the result shows an interesting correlation between the microseismicity and the uncoupled fault portions. The second area analyzed concerns the Gargano promontory for which we have used jointly the available InSAR and GPS velocities. Firstly we have attached the two datasets to the same terrestrial reference frame and then using a simple dislocation approach, we have estimated the best fault parameters reproducing the available data, providing a solution corresponding to the Mattinata fault. Subsequently we have considered within a BM analysis both GPS and InSAR datasets in order to evaluate if the Mattinata fault may accommodate the deformation occurring in the central Adriatic due to the relative motion between the North-Adriatic and South-Adriatic plates. We obtain that the deformation occurring in that region should be accommodated by more that one fault system, that is however difficult to detect since the poor coverage of geodetic measurement offshore of the Gargano promontory. Finally we have performed also the estimate of the interseismic coupling distribution for the Mattinata fault, obtaining a shallow coupling pattern. Both of coupling distributions found using the BM approach have been tested by means of resolution checkerboard tests and they demonstrate that the coupling patterns depend on the geodetic data positions.

Towards the 3D attenuation imaging of active volcanoes: methods and tests on real and simulated data

The purpose of my PhD thesis has been to face the issue of retrieving a three dimensional attenuation model in volcanic areas. To this purpose, I first elaborated a robust strategy for the analysis of seismic data. This was done by performing several synthetic tests to assess the applicability of spectral ratio method to our purposes. The results of the tests allowed us to conclude that: 1) spectral ratio method gives reliable differential attenuation (dt*) measurements in smooth velocity models; 2) short signal time window has to be chosen to perform spectral analysis; 3) the frequency range over which to compute spectral ratios greatly affects dt* measurements. Furthermore, a refined approach for the application of spectral ratio method has been developed and tested. Through this procedure, the effects caused by heterogeneities of propagation medium on the seismic signals may be removed. The tested data analysis technique was applied to the real active seismic SERAPIS database. It provided a dataset of dt* measurements which was used to obtain a three dimensional attenuation model of the shallowest part of Campi Flegrei caldera. Then, a linearized, iterative, damped attenuation tomography technique has been tested and applied to the selected dataset. The tomography, with a resolution of 0.5 km in the horizontal directions and 0.25 km in the vertical direction, allowed to image important features in the off-shore part of Campi Flegrei caldera. High QP bodies are immersed in a high attenuation body (Qp=30). The latter is well correlated with low Vp and high Vp/Vs values and it is interpreted as a saturated marine and volcanic sediments layer. High Qp anomalies, instead, are interpreted as the effects either of cooled lava bodies or of a CO2 reservoir. A pseudo-circular high Qp anomaly was detected and interpreted as the buried rim of NYT caldera.

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Evaluation of 3D cell culture systems for host-pathogen interaction studies

Traditional cell culture models have limitations in extrapolating functional mechanisms that underlie strategies of microbial virulence. Indeed during the infection the pathogens adapt to different tissue-specific environmental factors. The development of in vitro models resembling human tissue physiology might allow the replacement of inaccurate or aberrant animal models. Three-dimensional (3D) cell culture systems are more reliable and more predictive models that can be used for the meaningful dissection of host–pathogen interactions. The lung and gut mucosae often represent the first site of exposure to pathogens and provide a physical barrier against their entry. Within this context, the tracheobronchial and small intestine tract were modelled by tissue engineering approach. The main work was focused on the development and the extensive characterization of a human organotypic airway model, based on a mechanically supported co-culture of normal primary cells. The regained morphological features, the retrieved environmental factors and the presence of specific epithelial subsets resembled the native tissue organization. In addition, the respiratory model enabled the modular insertion of interesting cell types, such as innate immune cells or multipotent stromal cells, showing a functional ability to release pertinent cytokines differentially. Furthermore this model responded imitating known events occurring during the infection by Non-typeable H. influenzae. Epithelial organoid models, mimicking the small intestine tract, were used for a different explorative analysis of tissue-toxicity. Further experiments led to detection of a cell population targeted by C. difficile Toxin A and suggested a role in the impairment of the epithelial homeostasis by the bacterial virulence machinery. The described cell-centered strategy can afford critical insights in the evaluation of the host defence and pathogenic mechanisms. The application of these two models may provide an informing step that more coherently defines relevant molecular interactions happening during the infection.

Models and Algorihtm for the Optimization of Real-World Routing and Logistics Problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.