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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Optimisation non-linéaire mixte en nombres entiers pour la conception de réseaux en télécommunications / Mixed integer non-linear optimization approaches for network design in telecommunications

Hijazi, Hassan 18 November 2010 (has links)
Dans cette thèse, nous nous basons sur les outils apportés par la programmation mathématique afin de modéliser et résoudre des problèmes relevant du domaine des télécommunications. Notre premier objectif consiste à se conformer aux contraintes réelles, prenant en compte les aléas courants, afin de définir des stratégies optimales de routage et de planification dans les réseaux. Les contributions théoriques concernent l'optimisation convexe non linéaire mixte en nombres entiers. Parmi les résultats majeurs, nous établissons en particulier : *une formulation compacte des contraintes de type "on/off" qui s'écrivent f(x) ≤ 0 si z = 1,I ≤ x ≤ u si z = 0, basée sur une nouvelle caractérisation de l'enveloppe convexe de l'union d'un hyper-rectangle et d'un ensemble convexe dans l'espace des variables d'origine. * Une prise en compte de l'incertitude au niveau des fonctions additives ∑i(fi(xi) + vi) ≤ 0 où vi représente une perturbation bornée de chaque fonction univarée fi(xi). * Un algorithme spécialisé pour les problèmes d'optimisation non-linéaires mixtes en nombres entiers faisant intervenir des fonctions additives. D'un point de vue industriel, ces apports théoriques nous permettent de nous rapprocher de notre objectif consistant à définir des stratégies de gestion optimales pour des réseaux de télécommunications plus fiables. La qualité de service perçue par le client est modélisée par une fonction délai de bout en bout, différentiée selon le type de service et dépendant de la congestion au niveau de chaque lien / In our work, we rely on the powerful arsenal of mathematical programming theory to model telecommunication problems and devise efficient methods for solving them. Our goal is to comply to real life constraints when defining optimal routing strategies and designing efficient capacity planning tools. Theoretical contributions apply the field of Mixed Integer Non-Linear Optimization. Among relevant results, let us mention :Explicit formulations of convex hulls in disjunctive programming, generalizing the famous perspective formulationsTractable compact formulations of problems featuring inerval uncertainty in Robust OptimizationAn efficient Outer-Inner approximation algorithm for solving large families of separable mixed Integer Non-Linear Programs (MINLPs) and Second Order Cone Programs (SOCPs), outperforming state-of-the-art commercial solvers.In the application part, our work aims at introducing reliable telecommunication networks, offering appropriate and guaranteed Quality of Service to all its customers. Today, Wide Access Networks (WAN), Virtual Private Networks (VPN) or IP-based Backbones carry a wide range services, namely: voice, video streaming and data traffic. Each one of these contents has its own performance requirements. Unfortunately, best effort algorithms are implemented at all levels, offering no guarantee for delay sensitive applications. Is it possible to build routing strategies guaranteeing upper bounds on source-to-destination delays? Can we make these routing protocols to delay variation ? Does service differentiation affect capacity planning decisions ? Answers to these questions will be developed in this thesis.
2

New relaxations for composite functions

Taotao He (7047464) 13 August 2019 (has links)
Mixed-integer nonlinear programs are typically solved using branch-and-bound algorithms. A key determinant of the success of such methods is their ability to construct tight and tractable relaxations. The predominant relaxation strategy used by most state-of-the-art solvers is the factorable programming technique. This technique recursively traverses the expression tree for each nonlinear function and relaxes each operator over a bounding box that covers the ranges for all the operands. While it is versatile, and allows finer control over the number of introduced variables, the factorable programming technique often leads to weak relaxations because it ignores operand structure while constructing the relaxation for the operator.<div>In this thesis, we introduce new relaxations, called composite relaxations, for composite functions by convexifying the outer-function over a polytope, which models an ordering structure of outer-approximators of inner functions. We devise a fast combinatorial algorithm to separate the hypograph of concave-extendable supermodular outer-functions over the polytope, although the separation problem is NP-Hard in general. As a consequence, we obtain large classes of inequalities that tighten prevalent factorable programming relaxations. The limiting composite relaxation obtained with infinitely many outer-approximators for each inner-function is shown to be related to the solution of an optimal transport problem. Moreover, composite relaxations can be seamlessly embedded into a discretization scheme to relax nonlinear programs with mixed-integer linear programs. Combined with linearization, composite relaxations provide a framework for deriving cutting planes used in relaxation hierarchies and more.<br></div>
3

Integration of Hydrogen and CO2 Management within Refinery Planning

Alhajri, Ibrahim 01 December 2008 (has links)
The petroleum refining industry is considered to be one of the most important industries affecting daily life. However, this industry is facing many new and challenging situations, including such new trends as increased heavy crude markets, a shrinking market for fuel oils, clean-fuel legislation that encourages production of ultra low-sulfur (ULS) gasoline and diesel fuels, and strict green house gas (GHG) regulations to reduce CO2 emissions into the atmosphere. Refineries thus face a serious need to increase the capacity of their conversion units, such as the hydrocracker and fluid catalytic cracking units (FCCs), and to increase their consumption of hydrogen to meet the new requirements. These increases should be planned with reference to allowable CO2 emission limits. Refineries therefore need an appropriate tool for planning their operations and production. This research focuses on refinery planning under hydrogen and carbon management considerations. A systematic method that uses mathematical programming techniques to integrate the management of hydrogen and CO2 for refinery planning is proposed. Three different models for refinery planning, hydrogen management, and CO2 management, are prepared and then properly integrated. Firstly, a Nonlinear Programming (NLP) model that provides a more accurate representation of the refinery processes and which is able to optimize the operating variables such as the Crude Distillation Unit (CDU) cut-point temperatures and the conversion of the FCC unit is developed. The model is able to evaluate properties of the final products to meet market specifications as well as required product demands, thereby achieving maximum refinery profit. A systematic methodology for modeling the integration of hydrogen management and refinery planning was considered next. This resulted in a Mixed Integer Nonlinear Programming (MINLP) model that consists of two main building blocks: a set of nonlinear processing unit models and a hydrogen balance framework. The two blocks are integrated to produce a refinery-wide planning model with hydrogen management. The hydrogen alternatives considered in this research are hydrogen balancing, compressors, and purification processes. The model was illustrated on representative case studies and lead to an improvement in the hidden hydrogen unavailability that prevents refineries from achieving their maximum production and profit. It was found that an additional annual profit equivalent to $7 million could be achieved with a $13 million investment in a new purification unit. The consideration of CO2 management and the integration with refinery planning and the hydrogen network required the formulation of a CO2 management model. This model focused on the refinery emission sources and the mitigation options. The refinery emissions sources are the fuel system, hydrogen plant, and FCC unit, and the mitigation options considered are load shifting, fuel switching, and capturing technology. The model performance was tested on different case studies with various reduction targets. The optimization results showed that CO2 mitigation options worked successfully together to meet a given reduction target. The results show that load shifting can contribute up to a 3% reduction of CO2 emissions, and fuel switching can provide up to 20% reduction. To achieve greater than 30% reductions, a refinery must employ capturing technology solutions. The proposed model provides an efficient tool for assisting production planning in refineries and at the same time determines the optimum hydrogen and CO2 emissions strategies.
4

Production Scheduling Optimization of a Plastics Compounding Plant with Quality Constraints

Leung, Michelle January 2009 (has links)
Production scheduling is a common problem that occurs in multi-product manufacturing facilities where a wide range of products are produced in small quantities, resulting in frequent changeovers. A plastics compounding plant offering tailor-made resins is a representative case. This kind of scheduling problem has already been extensively researched and published in the past. However, the concept of incorporating quality of the finished product has never been visited previously. There are many different factors that may affect the quality of polymer resins produced by extrusion. One such factor is temperature. A production schedule cannot be related to the temperature or quality in any direct manner, and any other indirect relationships are not very apparent. The key to a correlation between the temperature of the processed material and the production schedule is the extruder flow rate. The flow rate affects the temperature of the molten plastic inside the extruder barrel, which means it also directly affects the quality of the final resin. Furthermore, the extruder is the critical machine in the extrusion process. Therefore, it determines the processing time of an order, serving as the basis for the scheduling problem. The extruded polymer resin must undergo quality control testing to ensure that quantitative quality measurements must meet specifications. This is formulated as a constraint, where the extruder flow rate is determined to generate an optimized production schedule while ensuring the quality is within range. The general scheduling problem at a plastics compounding plant is formulated as a mixed integer linear programming (MILP) model for a semi-continuous, multi-product plant with parallel production lines. The incorporation of quality considerations renders the problem a mixed integer nonlinear program (MINLP). Another objective of the proposed research deals with providing insight into the economic aspects of the scheduling process under consideration. The scheduling problem is analyzed and relations for its various cost components are developed. A total opportunity cost function was suggested for use as the comprehensive criterion of optimality in scheduling problems. Sensitivity analysis showed that none of the individual criteria gives optimal or near optimal results when compared to the total opportunity cost.
5

Integration of Hydrogen and CO2 Management within Refinery Planning

Alhajri, Ibrahim 01 December 2008 (has links)
The petroleum refining industry is considered to be one of the most important industries affecting daily life. However, this industry is facing many new and challenging situations, including such new trends as increased heavy crude markets, a shrinking market for fuel oils, clean-fuel legislation that encourages production of ultra low-sulfur (ULS) gasoline and diesel fuels, and strict green house gas (GHG) regulations to reduce CO2 emissions into the atmosphere. Refineries thus face a serious need to increase the capacity of their conversion units, such as the hydrocracker and fluid catalytic cracking units (FCCs), and to increase their consumption of hydrogen to meet the new requirements. These increases should be planned with reference to allowable CO2 emission limits. Refineries therefore need an appropriate tool for planning their operations and production. This research focuses on refinery planning under hydrogen and carbon management considerations. A systematic method that uses mathematical programming techniques to integrate the management of hydrogen and CO2 for refinery planning is proposed. Three different models for refinery planning, hydrogen management, and CO2 management, are prepared and then properly integrated. Firstly, a Nonlinear Programming (NLP) model that provides a more accurate representation of the refinery processes and which is able to optimize the operating variables such as the Crude Distillation Unit (CDU) cut-point temperatures and the conversion of the FCC unit is developed. The model is able to evaluate properties of the final products to meet market specifications as well as required product demands, thereby achieving maximum refinery profit. A systematic methodology for modeling the integration of hydrogen management and refinery planning was considered next. This resulted in a Mixed Integer Nonlinear Programming (MINLP) model that consists of two main building blocks: a set of nonlinear processing unit models and a hydrogen balance framework. The two blocks are integrated to produce a refinery-wide planning model with hydrogen management. The hydrogen alternatives considered in this research are hydrogen balancing, compressors, and purification processes. The model was illustrated on representative case studies and lead to an improvement in the hidden hydrogen unavailability that prevents refineries from achieving their maximum production and profit. It was found that an additional annual profit equivalent to $7 million could be achieved with a $13 million investment in a new purification unit. The consideration of CO2 management and the integration with refinery planning and the hydrogen network required the formulation of a CO2 management model. This model focused on the refinery emission sources and the mitigation options. The refinery emissions sources are the fuel system, hydrogen plant, and FCC unit, and the mitigation options considered are load shifting, fuel switching, and capturing technology. The model performance was tested on different case studies with various reduction targets. The optimization results showed that CO2 mitigation options worked successfully together to meet a given reduction target. The results show that load shifting can contribute up to a 3% reduction of CO2 emissions, and fuel switching can provide up to 20% reduction. To achieve greater than 30% reductions, a refinery must employ capturing technology solutions. The proposed model provides an efficient tool for assisting production planning in refineries and at the same time determines the optimum hydrogen and CO2 emissions strategies.
6

Production Scheduling Optimization of a Plastics Compounding Plant with Quality Constraints

Leung, Michelle January 2009 (has links)
Production scheduling is a common problem that occurs in multi-product manufacturing facilities where a wide range of products are produced in small quantities, resulting in frequent changeovers. A plastics compounding plant offering tailor-made resins is a representative case. This kind of scheduling problem has already been extensively researched and published in the past. However, the concept of incorporating quality of the finished product has never been visited previously. There are many different factors that may affect the quality of polymer resins produced by extrusion. One such factor is temperature. A production schedule cannot be related to the temperature or quality in any direct manner, and any other indirect relationships are not very apparent. The key to a correlation between the temperature of the processed material and the production schedule is the extruder flow rate. The flow rate affects the temperature of the molten plastic inside the extruder barrel, which means it also directly affects the quality of the final resin. Furthermore, the extruder is the critical machine in the extrusion process. Therefore, it determines the processing time of an order, serving as the basis for the scheduling problem. The extruded polymer resin must undergo quality control testing to ensure that quantitative quality measurements must meet specifications. This is formulated as a constraint, where the extruder flow rate is determined to generate an optimized production schedule while ensuring the quality is within range. The general scheduling problem at a plastics compounding plant is formulated as a mixed integer linear programming (MILP) model for a semi-continuous, multi-product plant with parallel production lines. The incorporation of quality considerations renders the problem a mixed integer nonlinear program (MINLP). Another objective of the proposed research deals with providing insight into the economic aspects of the scheduling process under consideration. The scheduling problem is analyzed and relations for its various cost components are developed. A total opportunity cost function was suggested for use as the comprehensive criterion of optimality in scheduling problems. Sensitivity analysis showed that none of the individual criteria gives optimal or near optimal results when compared to the total opportunity cost.
7

From local to global and back : a closed walk in mathematical programming and its applications

Cafieri, Sonia 10 December 2012 (has links) (PDF)
Ce document propose un parcours de mes travaux de recherche en optimisation, en passant par l'optimisation mixte en variables entières, l'optimisation non-linéaire continue locale et le clustering dans les réseaux (graphes). Le premier chapitre traite de la programmation non linéaire mixte en variables entières et de l'optimisation globale déterministe. Il présente des contributions relatives à des investigations théoriques ainsi que des applications à des problèmes concrets. Nous discutons principalement de relaxations convexes et de reformulations automatiques de problèmes de programmation mathématique, dans le but d'améliorer l'efficacité des algorithmes de Branch-and-Bound. Dans le cadre de la programmation polynomiale, nous avons étudié des relaxations convexes pour les monômes multilinéaires et la génération de relaxations compactes de problèmes polynomiaux basés sur une technique spécifique de reformulation-linéarisation (RLT). Parmi les applications, une attention particulière est portée à des problèmes qui se posent dans la gestion du trafic aérien. Nous avons proposé de nouveaux modèles mathématiques et des approches de résolution basées d'une part sur l'optimisation mixte en variables entières et d'autre part sur le contrôle optimal. Deux thèmes de l'optimisation continue non-linéaire sont décrits au deuxième chapitre. Des méthodes de point intérieur pour la programmation quadratique et leurs noyaux d'algèbre linéaire (systèmes KKT) sont d'abord discutées. L'accent est mis sur les méthodes itératives pour les systèmes KKT et sur des questions connexes, telles que les techniques de préconditionnement et les propriétés de convergence. L'autre sujet discuté concerne, encore une fois, des problèmes de trafic aérien. Il porte sur les approches déjà mentionnées de contrôle optimal qui conduisent à des problèmes non-linéaires. Le troisième chapitre présente mes principaux résultats dans le domaine du clustering dans les réseaux. Le problème de l'identification de clusters dans les réseaux peut être formulé en utilisant la programmation mathématique et conduit généralement à un problème d'optimisation combinatoire. Mes contributions concernent les critères de classification et les méthodes de clustering correspondantes. Une attention particulière est portée aux méthodes exactes utilisées pour résoudre l'ensemble du problème d'optimisation ou, localement, les sous-problèmes survenant dans des heuristiques hiérarchiques, ou enfin dans le raffinement des solutions obtenues précédemment par d'autres méthodes.
8

Global Optimization Using Piecewise Linear Approximation

January 2020 (has links)
abstract: Global optimization (programming) has been attracting the attention of researchers for almost a century. Since linear programming (LP) and mixed integer linear programming (MILP) had been well studied in early stages, MILP methods and software tools had improved in their efficiency in the past few years. They are now fast and robust even for problems with millions of variables. Therefore, it is desirable to use MILP software to solve mixed integer nonlinear programming (MINLP) problems. For an MINLP problem to be solved by an MILP solver, its nonlinear functions must be transformed to linear ones. The most common method to do the transformation is the piecewise linear approximation (PLA). This dissertation will summarize the types of optimization and the most important tools and methods, and will discuss in depth the PLA tool. PLA will be done using nonuniform partitioning of the domain of the variables involved in the function that will be approximated. Also partial PLA models that approximate only parts of a complicated optimization problem will be introduced. Computational experiments will be done and the results will show that nonuniform partitioning and partial PLA can be beneficial. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2020
9

Producción de poli(hidroxialcanoato)s (PHA)s : estudios experimentales y diseño óptimo de biorrefinerías

Ramos, Fernando Daniel 28 March 2019 (has links)
La gran versatilidad y amplia variedad de características que poseen los plásticos los hace materiales claves para el ser humano, ya que permiten mejorar la calidad de vida, al ser empleados en sectores como la construcción, el transporte, el envasado, la medicina y el deporte, entre otros. No obstante, los plásticos producidos a partir de petróleo tienen la gran desventaja de no ser biodegradables, por lo que esta preocupación ha creado un especial interés en el desarrollo de procesos alternativos para generar polímeros de origen biológico, amigables con el medio ambiente. A pesar de los esfuerzos destinados a la investigación de biopolímeros, éstos aún no resultan competitivos en términos económicos frente a los plásticos petroquímicos. El costo de los polímeros convencionales oscila entre 1 y 1,5 dólares por kilogramo y el de los biopolímeros puede variar entre 2,5 y 15 dólares por kilogramo. Por lo tanto, el objetivo que se propone en este trabajo de tesis es profundizar, tanto a nivel teórico como experimental, en el estudio de la producción de plásticos biodegradables (poli(hidroxialcanoato)s, PHAs) empleando fuentes de carbono alternativas para su biosíntesis. En la presente tesis se llevan a cabo experiencias in vivo con un microorganismo aislado del estuario de Bahía Blanca, Bacillus megaterium BBST4, en cultivos batch. A partir del biomaterial obtenido, se realizan ensayos que permiten caracterizar el polímero acumulado intracelularmente. Asimismo, se obtienen datos experimentales a nivel Erlenmeyer y biorreactor, que se emplean para ajustar un modelo cinético de crecimiento y biosíntesis de PHA. La estimación de parámetros se realiza mediante la formulación de un problema de optimización dinámico cuya función objetivo es de cuadrados mínimos, sujeto a un sistema de ecuaciones diferenciales y algebraicas. Por otro lado, con el objetivo de realizar aportes en el diseño de biorrefinerías, se propone la implementación de modelos detallados de los equipos de una planta de producción de PHA y también de una biorrefinería integrada, donde la síntesis de biopolímero brinda un valor agregado al objetivo económico de la misma. Para ello, las distintas configuraciones de operación de las plantas se incluyen en una superestructura y se formulan problemas de programación no lineal mixto entero (MINLP) en un entorno orientado a ecuaciones, con un criterio de optimización económico (maximización del valor presente neto del proceso productivo) sujeto a restricciones de balances de masa y energía, ecuaciones de diseño, condiciones operativas y correlaciones de costos. La metodología presentada en esta tesis junto con los resultados numéricos obtenidos, representan una progresión en el estudio biotecnológico de la síntesis de PHAs mediante la utilización de herramientas provistas por el modelado matemático. / Due to their great versatility and comprehensive features, plastics have become key materials to human beings. They allow improving the quality of human life in areas such as construction, transportation, packaging, medicine and sports, among others. Nevertheless, petroleum-based plastics are non-biodegradable. This issue has led to the development of alternative processes to produce bio- based polymers environmentally friendly. Despite efforts devoted to biopolymers research, they are still non-economically competitive with the petrochemical plastics. While synthetic polymers cost is between 1 to 1.5 dollars per kilogram, biopolymers prices vary between 2.5 to 15 dollars per kilogram. Therefore, the main objective of the work is to carry out theoretical and experimental studies of biodegradable biopolymer production (poly(hydroxyalkanoate)s, PHAs) using alternative carbon sources for their biosynthesis. In this thesis work, in vivo experiences in batch cultivations are performed by means of Bacillus megaterium BBST4, a microorganism isolated from Bahía Blanca estuary. With the obtained biomaterial, several tests were carried out in order to achieve a characterization of the intracellular accumulated polymer. Also, experimental data is obtained in Erlenmeyer and bioreactor cultures. This data is used to adjust a growth and PHA bio-synthesis kinetics model. Parameter estimation is performed within a dynamic optimization framework with a least squares objective function, subject to a differential algebraic equations system. Furthermore, in order to make a contribution to biorefineries design, we implemented two detailed equipment models: a PHA production plant and an integrated biorefinery, where biopolymer synthesis is a value- added co-product. Different plant configurations are embedded within a superstructure. Mixed integer nonlinear programming (MINLP) problems are formulated in an equation oriented approach. The economic objective function (net present value maximization of the productive process) is subjected to mass and energy balances, equipment design cost, operation conditions and cost correlations. The methodology presented in this thesis together with the obtained numerical results, provides useful insights on the biotechnological study of PHAs synthesis by means of mathematical modeling tools.
10

Optimisation of MSF Desalination Process for Fixed Water Demand using gPROMS

Sowgath, Md Tanvir, Mujtaba, Iqbal M. 21 February 2008 (has links)
Yes / Simultaneous optimisation of design and operating parameters of MSF desalination process is considered here using MINLP technique within gPROMS software. For a fixed fresh water demand throughout the year and with seasonal variation of seawater temperature, the external heat input (a measure of operating cost) to the process is minimised. It is observed that seasonal variation in seawater temperature results in significant variation in design with minimum variation in operating conditions in terms of process temperatures. The results also reveal the possibility of designing stand-alone flash stages which would offer flexible scheduling in terms of the connection of various units (to build up the process) and efficient maintenance of the units throughout the year as the weather condition changes. In addition, operation at low temperatures throughout the year will reduce design and operating costs in terms of low temperature materials of construction and reduced amount of antiscaling and anti-corrosion agents.

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