Models for capacitated lot-sizing problem with backlogging, setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.

Design methodology of piezoelectric energy-harvesting skin using topology optimization

Abstract This paper describes a design methodology for piezoelectric energy harvester s that thinly encapsulate the mechanical devices and expl oit resonances from higher- order vibrational modes. The direction of polarization determines the sign of the pi ezoelectric tensor to avoid cancellations of electric fields from opposite polarizations in the same circuit. The resultant modified equations of state are solved by finite element method (FEM). Com- bining this method with the solid isotropic material with penalization (SIMP) method for piezoelectric material, we have developed an optimization methodology that optimizes the piezoelectric material layout and polarization direc- tion. Updating the density function of the SIMP method is performed based on sensitivity analysis, the sequen- tial linear programming on the early stage of the opti- mization, and the phase field method on the latter stage

Development of heat sink device by using topology optimization

Small scale fluid flow systems have been studied for various applications, such as chemical reagent dosages and cooling devices of compact electronic components. This work proposes to present the complete cycle development of an optimized heat sink designed by using Topology Optimization Method (TOM) for best performance, including minimization of pressure drop in fluid flow and maximization of heat dissipation effects, aiming small scale applications. The TOM is applied to a domain, to obtain an optimized channel topology, according to a given multi-objective function that combines pressure drop minimization and heat transfer maximization. Stokes flow hypothesis is adopted. Moreover, both conduction and forced convection effects are included in the steady-state heat transfer model. The topology optimization procedure combines the Finite Element Method (to carry out the physical analysis) with Sequential Linear Programming (as the optimization algorithm). Two-dimensional topology optimization results of channel layouts obtained for a heat sink design are presented as example to illustrate the design methodology. 3D computational simulations and prototype manufacturing have been carried out to validate the proposed design methodology.

Numerical Model for the Dynamic Analysis of Pile Foundations

Programa de doctorado: Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería Instituto Universitario (SIANI)

Structural analysis of combinatorial optimization problem characteristics and their resolution using hybrid approaches

Many combinatorial problems coming from the real world may not have a clear and well defined structure, typically being dirtied by side constraints, or being composed of two or more sub-problems, usually not disjoint. Such problems are not suitable to be solved with pure approaches based on a single programming paradigm, because a paradigm that can effectively face a problem characteristic may behave inefficiently when facing other characteristics. In these cases, modelling the problem using different programming techniques, trying to ”take the best” from each technique, can produce solvers that largely dominate pure approaches. We demonstrate the effectiveness of hybridization and we discuss about different hybridization techniques by analyzing two classes of problems with particular structures, exploiting Constraint Programming and Integer Linear Programming solving tools and Algorithm Portfolios and Logic Based Benders Decomposition as integration and hybridization frameworks.

De Novo Design of secondary structures: Synthesis and conformational studies

Chemists have long sought to extrapolate the power of biological catalysis and recognition to synthetic systems. These efforts have focused largely on low molecular weight catalysts and receptors; however, biological systems themselves rely almost exclusively on polymers, proteins and RNA, to perform complex chemical functions. Proteins and RNA are unique in their ability to adopt compact, well-ordered conformations, and specific folding provides precise spatial orientation of the functional groups that comprise the “active site”. These features suggest that identification of new polymer backbones with discrete and predictable folding propensities (“foldamers”) will provide a basis for design of molecular machines with unique capabilities. The foldamer approach complements current efforts to design unnatural properties into polypeptides and polynucleotides. The aim of this thesis is the synthesis and conformational studies of new classes of foldamers, using a peptidomimetic approach. Moreover their attitude to be utilized as ionophores, catalysts, and nanobiomaterials were analyzed in solution and in the solid state. This thesis is divided in thematically chapters that are reported below. It begins with a very general introduction (page 4) which is useful, but not strictly necessary, to the expert reader. It is worth mentioning that paragraph I.3 (page 22) is the starting point of this work and paragraph I.5 (page 32) isrequired to better understand the results of chapters 4 and 5. In chapter 1 (page 39) is reported the synthesis and conformational analysis of a novel class of foldamers containing (S)-β3-homophenylglycine [(S)-β3-hPhg] and D- 4-carboxy-oxazolidin-2-one (D-Oxd) residues in alternate order is reported. The experimental conformational analysis performed in solution by IR, 1HNMR, and CD spectroscopy unambiguously proved that these oligomers fold into ordered structures with increasing sequence length. Theoretical calculations employing ab initio MO theory suggest a helix with 11-membered hydrogenbonded rings as the preferred secondary structure type. The novel structures enrich the field of peptidic foldamers and might be useful in the mimicry of native peptides. In chapter 2 cyclo-(L-Ala-D-Oxd)3 and cyclo-(L-Ala-DOxd) 4 were prepared in the liquid phase with good overall yields and were utilized for bivalent ions chelation (Ca2+, Mg2+, Cu2+, Zn2+ and Hg2+); their chelation skill was analyzed with ESI-MS, CD and 1HNMR techniques and the best results were obtained with cyclo-(L-Ala-D-Oxd)3 and Mg2+ or Ca2+. Chapter 3 describes an application of oligopeptides as catalysts for aldol reactions. Paragraph 3.1 concerns the use of prolinamides as catalysts of the cross aldol addition of hydroxyacetone to aromatic aldeydes, whereas paragraphs 3.2 and 3.3 are about the catalyzed aldol addition of acetone to isatins. By means of DFT and AIM calculations, the steric and stereoelectronic effects that control the enantioselectivity in the cross-aldol addition of acetone to isatin catalysed by L-proline have been studied, also in the presence of small quantities of water. In chapter 4 is reported the synthesis and the analysis of a new fiber-like material, obtained from the selfaggregation of the dipeptide Boc-L-Phe-D-Oxd-OBn, which spontaneously forms uniform fibers consisting of parallel infinite linear chains arising from singleintermolecular N-H···O=C hydrogen bonds. This is the absolute borderline case of a parallel β-sheet structure. Longer oligomers of the same series with general formula Boc-(L-Phe-D-Oxd)n-OBn (where n = 2-5), are described in chapter 5. Their properties in solution and in the solid state were analyzed, in correlation with their attitude to form intramolecular hydrogen bond. In chapter 6 is reported the synthesis of imidazolidin-2- one-4-carboxylate and (tetrahydro)-pyrimidin-2-one-5- carboxylate, via an efficient modification of the Hofmann rearrangement. The reaction affords the desired compounds from protected asparagine or glutamine in good to high yield, using PhI(OAc)2 as source of iodine(III).

Formulations and Algorithms for Routing Problems

Combinatorial Optimization is a branch of optimization that deals with the problems where the set of feasible solutions is discrete. Routing problem is a well studied branch of Combinatorial Optimization that concerns the process of deciding the best way of visiting the nodes (customers) in a network. Routing problems appear in many real world applications including: Transportation, Telephone or Electronic data Networks. During the years, many solution procedures have been introduced for the solution of different Routing problems. Some of them are based on exact approaches to solve the problems to optimality and some others are based on heuristic or metaheuristic search to find optimal or near optimal solutions. There is also a less studied method, which combines both heuristic and exact approaches to face different problems including those in the Combinatorial Optimization area. The aim of this dissertation is to develop some solution procedures based on the combination of heuristic and Integer Linear Programming (ILP) techniques for some important problems in Routing Optimization. In this approach, given an initial feasible solution to be possibly improved, the method follows a destruct-and-repair paradigm, where the given solution is randomly destroyed (i.e., customers are removed in a random way) and repaired by solving an ILP model, in an attempt to find a new improved solution.

Über die Linearität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen

Über die Liniarität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. In meiner Arbeit beschäftige ich mich mit Darstellungen der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. Mein Ansatz hierbei ist, die Teichmüllersche Modulgruppe in eine p-adische Liegruppe einzubetten. Sei nun F die von zwei Elementen erzeugte freie Gruppe und Aut(F) die Automorphismengruppe von F. Inhalt des ersten Kapitels ist es nun zu zeigen, daß folgende Aussagen äquivalent sind: - Die Teichmüllersche Modulgruppe des Torus mit zwei Punktierungen ist linear, - Aut(F)ist linear, - F besitzt eine p-Kongruenzstruktur, deren Folgen- glieder von Aut(F) festgehalten werden, also charak- teristisch sind. Im zweiten Kapitel wird unter anderem gezeigt, daß es eine Einbettung einer Untergruppe endlichen Indexes der Aut(F) in die Automorphismengruppe einer einfachen p-adischen Liegruppe gibt. Bisher ist unbekannt, ob die Buraudarstellung treu ist.In dieser Arbeit wird ein unendliches, lineares Gleichungssystem, dessen Lösungen gerade die Koeffizienten der Wörter des Kernes der Buraudarstellung sind, vorgestellt.Im dritten Kapitel wird mit den Methoden des 1.Kapitels gezeigt, daß der Torus mit zwei Punktierungen genau dann linear ist, wenn die Teichmüllersche Modulgruppe der Sphäre mit 5 Punktierungen es auch ist. Bekanntlich ist die 4. Braidgruppe linear. Nun ist aber die 4. Braidgruppe letztlich die Teichmüllersche Modulgruppe der abgeschlossenen Kreisscheibe mit 5 Punktierungen. Wenn man nun deren Randpunkte miteinander identifiziert und anschließend wegläßt, erhält man die 5-fach punktiereSphäre.Mit der eben beschriebenen Abbildung kann man zeigen, daß die Teichmüllersche Modulgruppe der fünffach punktierten Sphäre linear ist.

Algorithms for UAS insertion in civil air space

One of the most interesting challenge of the next years will be the Air Space Systems automation. This process will involve different aspects as the Air Traffic Management, the Aircrafts and Airport Operations and the Guidance and Navigation Systems. The use of UAS (Uninhabited Aerial System) for civil mission will be one of the most important steps in this automation process. In civil air space, Air Traffic Controllers (ATC) manage the air traffic ensuring that a minimum separation between the controlled aircrafts is always provided. For this purpose ATCs use several operative avoidance techniques like holding patterns or rerouting. The use of UAS in these context will require the definition of strategies for a common management of piloted and piloted air traffic that allow the UAS to self separate. As a first employment in civil air space we consider a UAS surveillance mission that consists in departing from a ground base, taking pictures over a set of mission targets and coming back to the same ground base. During all mission a set of piloted aircrafts fly in the same airspace and thus the UAS has to self separate using the ATC avoidance as anticipated. We consider two objective, the first consists in the minimization of the air traffic impact over the mission, the second consists in the minimization of the impact of the mission over the air traffic. A particular version of the well known Travelling Salesman Problem (TSP) called Time-Dependant-TSP has been studied to deal with traffic problems in big urban areas. Its basic idea consists in a cost of the route between two clients depending on the period of the day in which it is crossed. Our thesis supports that such idea can be applied to the air traffic too using a convenient time horizon compatible with aircrafts operations. The cost of a UAS sub-route will depend on the air traffic that it will meet starting such route in a specific moment and consequently on the avoidance maneuver that it will use to avoid that conflict. The conflict avoidance is a topic that has been hardly developed in past years using different approaches. In this thesis we purpose a new approach based on the use of ATC operative techniques that makes it possible both to model the UAS problem using a TDTSP framework both to use an Air Traffic Management perspective. Starting from this kind of mission, the problem of the UAS insertion in civil air space is formalized as the UAS Routing Problem (URP). For this reason we introduce a new structure called Conflict Graph that makes it possible to model the avoidance maneuvers and to define the arc cost function of the departing time. Two Integer Linear Programming formulations of the problem are proposed. The first is based on a TDTSP formulation that, unfortunately, is weaker then the TSP formulation. Thus a new formulation based on a TSP variation that uses specific penalty to model the holdings is proposed. Different algorithms are presented: exact algorithms, simple heuristics used as Upper Bounds on the number of time steps used, and metaheuristic algorithms as Genetic Algorithm and Simulated Annealing. Finally an air traffic scenario has been simulated using real air traffic data in order to test our algorithms. Graphic Tools have been used to represent the Milano Linate air space and its air traffic during different days. Such data have been provided by ENAV S.p.A (Italian Agency for Air Navigation Services).

Referee Assignment Problem Case: Italian Volleyball Championships

This thesis addresses the formulation of a referee assignment problem for the Italian Volleyball Serie A Championships. The problem has particular constraints such as a referee must be assigned to different teams in a given period of times, and the minimal/maximal level of workload for each referee is obtained by considering cost and profit in the objective function. The problem has been solved through an exact method by using an integer linear programming formulation and a clique based decomposition for improving the computing time. Extensive computational experiments on real-world instances have been performed to determine the effectiveness of the proposed approach.

Riconversione degli impianti saccariferi per la valorizzazione della filiera agro-energetica: analisi di impatto sul comprensorio agricolo

Il presente lavoro trae origine dagli obiettivi e dalle relative misure applicative della riforma dell’OCM zucchero del 2006 e nello specifico dal Piano nazionale per la razionalizzazione e riconversione della produzione bieticolo-saccarifera approvato dal MIPAF nel 2007. Lo studio riguarda la riconversione dello zuccherificio di Finale Emilia (MO), di appartenenza del Gruppo bieticolo-saccarifero Co.Pro.B, in un impianto di generazione di energia elettrica e termica che utilizza biomassa di origine agricola per la combustione diretta. L'alimentazione avviene principalmente dalla coltivazione dedicata del sorgo da fibra (Sorghum bicolor), integrata con risorse agro-forestali. Lo studio mostra la necessità di coltivazione di 4.400 ettari di sorgo da fibra con una produzione annua di circa 97.000 t di prodotto al 75% di sostanza secca necessari per l’alimentazione della centrale a biomassa. L’obiettivo é quello di valutare l’impatto della nuova coltura energetica sul comprensorio agricolo e sulla economia dell’impresa agricola. La metodologia adottata si basa sulla simulazione di modelli aziendali di programmazione lineare che prevedono l’inserimento del sorgo da fibra come coltura energetica nel piano ottimo delle aziende considerate. I modelli predisposti sono stati calibrati su aziende RICA al fine di riprodurre riparti medi reali su tre tipologie dimensionali rappresentative: azienda piccola entro i 20 ha, media da 20 a 50 ha e grande oltre i 50 ha. La superficie di entrata a livello aziendale, se rapportata alla rappresentatività delle aziende dell’area di studio, risulta insufficiente per soddisfare la richiesta di approvvigionamento dell’impianto a biomassa. Infatti con tale incremento la superficie di coltivazione nel comprensorio si attesta sui 2.500 ettari circa contro i 4.400 necessari alla centrale. Lo studio mostra pertanto che occorre un incentivo superiore, di circa 80-90 €/ha, per soddisfare la richiesta della superficie colturale a livello di territorio. A questi livelli, la disponibilità della coltura energetica sul comprensorio risulta circa 9.500 ettari.

Laboruntersuchungen zur Aufnahme von NH 3 durch Eiskristalle bei Gleichgewicht und beim Wachstum

In dieser Arbeit wurde in Laborexperimenten die Aufnahme von NH3 durch wachsende Eiskristalle und Eiskristalle, die in eisgesättigter Umgebung mit ihrer mittleren Fallgeschwindigkeit angeströmt wurden, untersucht. So sollten die Verhältnisse innerhalb der Wolke beim Wachstum der Eiskristalle “in cloud scavenging“ und unterhalb der Wolke beim Anströmen mit eisgesättigter NH3 - Luftmischung simuliert werden. Bei längerer Exposition dendritischer Eiskristalle mit eisgesättigter NH3 - Luftmischung ist die Diffusion des gebildeten NH4+ in den Eiskristall hinein, entscheidend für den Anteil an NH3, der aus der Gasphase nach der Adsorption als NH4+ im Eis zurückbleibt. Die experimentellen Daten konnten mit einer einfachen Annahme zur Diffusion in einen “halb unendlichen“ Festkörper beschrieben werden. In weiteren Experimenten konnte gezeigt werden, dass die Aufnahme des NH3 durch nicht wachsende Eiskristalle von anderen Spurenstoffen im Eis beeinflusst wird. Eiskristalle, die im Vorfeld des Strömungsadsorptionsexperiments mit NH3, mit SO2 exponiert wurden, zeigten eine deutliche Zunahme der NH3 - Aufnahme aus der Gasphase. Die Aufnahme von NH3 durch nicht wachsende Eiskristalle ist für typische atmosphärische NH3 - Volumenmischungsverhältnisse nicht relevant. Dagegen zeigten die Experimente zur NH3 Aufnahme beim Eiskristallwachstum, dass dieser Prozess in der Atmosphäre nicht vernachlässigt werden kann.

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

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.

Optimized scheduling in real-time environments with column generation

Im Bereich sicherheitsrelevanter eingebetteter Systeme stellt sich der Designprozess von Anwendungen als sehr komplex dar. Entsprechend einer gegebenen Hardwarearchitektur lassen sich Steuergeräte aufrüsten, um alle bestehenden Prozesse und Signale pünktlich auszuführen. Die zeitlichen Anforderungen sind strikt und müssen in jeder periodischen Wiederkehr der Prozesse erfüllt sein, da die Sicherstellung der parallelen Ausführung von größter Bedeutung ist. Existierende Ansätze können schnell Designalternativen berechnen, aber sie gewährleisten nicht, dass die Kosten für die nötigen Hardwareänderungen minimal sind. Wir stellen einen Ansatz vor, der kostenminimale Lösungen für das Problem berechnet, die alle zeitlichen Bedingungen erfüllen. Unser Algorithmus verwendet Lineare Programmierung mit Spaltengenerierung, eingebettet in eine Baumstruktur, um untere und obere Schranken während des Optimierungsprozesses bereitzustellen. Die komplexen Randbedingungen zur Gewährleistung der periodischen Ausführung verlagern sich durch eine Zerlegung des Hauptproblems in unabhängige Unterprobleme, die als ganzzahlige lineare Programme formuliert sind. Sowohl die Analysen zur Prozessausführung als auch die Methoden zur Signalübertragung werden untersucht und linearisierte Darstellungen angegeben. Des Weiteren präsentieren wir eine neue Formulierung für die Ausführung mit fixierten Prioritäten, die zusätzlich Prozessantwortzeiten im schlimmsten anzunehmenden Fall berechnet, welche für Szenarien nötig sind, in denen zeitliche Bedingungen an Teilmengen von Prozessen und Signalen gegeben sind. Wir weisen die Anwendbarkeit unserer Methoden durch die Analyse von Instanzen nach, welche Prozessstrukturen aus realen Anwendungen enthalten. Unsere Ergebnisse zeigen, dass untere Schranken schnell berechnet werden können, um die Optimalität von heuristischen Lösungen zu beweisen. Wenn wir optimale Lösungen mit Antwortzeiten liefern, stellt sich unsere neue Formulierung in der Laufzeitanalyse vorteilhaft gegenüber anderen Ansätzen dar. Die besten Resultate werden mit einem hybriden Ansatz erzielt, der heuristische Startlösungen, eine Vorverarbeitung und eine heuristische mit einer kurzen nachfolgenden exakten Berechnungsphase verbindet.