Uma investigação do minos e sua aplicação ao problema de fluxo de potência ótimo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma proposta de sequência didática para o ensino de Programação Linear no Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Metodologia de otimização para o dimensionamento de reservatórios de águas pluviais

This work aimed to develop an optimization methodology for reservoir sizing in rainwater harvesting systems in order to increase the economic viability of projects in this area. For this, concepts of Operations Research were used so as to develop mathematical programming problems related to minimizing the life cycle cost and maximizing efficiency. The results obtained for different sizing methods were presented based on a case study, emphasizing the importance of tools that are able to provide a more accurate analysis and tend to significantly increase the economic viability of rainwater harvesting systems.

Integrated pulp and paper mill planning and scheduling

This article describes a real-world production planning and scheduling problem occurring at an integrated pulp and paper mill (P&P) which manufactures paper for cardboard out of produced pulp. During the cooking of wood chips in the digester, two by-products are produced: the pulp itself (virgin fibers) and the waste stream known as black liquor. The former is then mixed with recycled fibers and processed in a paper machine. Here, due to significant sequence-dependent setups in paper type changeovers, sizing and sequencing of lots have to be made simultaneously in order to efficiently use capacity. The latter is converted into electrical energy using a set of evaporators, recovery boilers and counter-pressure turbines. The planning challenge is then to synchronize the material flow as it moves through the pulp and paper mills, and energy plant, maximizing customer demand (as backlogging is allowed), and minimizing operation costs. Due to the intensive capital feature of P&P, the output of the digester must be maximized. As the production bottleneck is not fixed, to tackle this problem we propose a new model that integrates the critical production units associated to the pulp and paper mills, and energy plant for the first time. Simple stochastic mixed integer programming based local search heuristics are developed to obtain good feasible solutions for the problem. The benefits of integrating the three stages are discussed. The proposed approaches are tested on real-world data. Our work may help P&P companies to increase their competitiveness and reactiveness in dealing with demand pattern oscillations. (C) 2012 Elsevier Ltd. All rights reserved.

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Accelerating benders decomposition with heuristicmaster problem solutions

In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented. These cuts are based on feasible and infeasible master problem solutions generated by means of a heuristic. This article includes general guidelines and a case study with a fixed charge network design problem. Computational tests with instances of this problem show the efficiency of the strategy. The most important aspect of the proposed ideas is their generality, which allows them to be used in virtually any Benders decomposition implementation.

Decision Support Models for Composing and Navigating through e-Learning Objects

Libraries of learning objects may serve as basis for deriving course offerings that are customized to the needs of different learning communities or even individuals. Several ways of organizing this course composition process are discussed. Course composition needs a clear understanding of the dependencies between the learning objects. Therefore we discuss the metadata for object relationships proposed in different standardization projects and especially those suggested in the Dublin Core Metadata Initiative. Based on these metadata we construct adjacency matrices and graphs. We show how Gozinto-type computations can be used to determine direct and indirect prerequisites for certain learning objects. The metadata may also be used to define integer programming models which can be applied to support the instructor in formulating his specifications for selecting objects or which allow a computer agent to automatically select learning objects. Such decision models could also be helpful for a learner navigating through a library of learning objects. We also sketch a graph-based procedure for manual or automatic sequencing of the learning objects.

Optimización de la programación(scheduling) en Talleres de Mecanizado

Los problemas de programación de tareas son muy importantes en el mundo actual. Se puede decir que se presentan en todos los fundamentos de la industria moderna, de ahí la importancia de que estos sean óptimos, de forma que se puedan ahorrar recursos que estén asociados al problema. La programación adecuada de trabajos en procesos de manufactura, constituye un importante problema que se plantea dentro de la producción en muchas empresas. El orden en que estos son procesados, no resulta indiferente, sino que determinará algún parámetro de interés, cuyos valores convendrá optimizar en la medida de lo posible. Así podrá verse afectado el coste total de ejecución de los trabajos, el tiempo necesario para concluirlos o el stock de productos en curso que será generado. Esto conduce de forma directa al problema de determinar cuál será el orden más adecuado para llevar a cabo los trabajos con vista a optimizar algunos de los anteriores parámetros u otros similares. Debido a las limitaciones de las técnicas de optimización convencionales, en la presente tesis se presenta una metaheurística basada en un Algoritmo Genético Simple (Simple Genetic Algorithm, SGA), para resolver problemas de programación de tipo flujo general (Job Shop Scheduling, JSS) y flujo regular (Flow Shop Scheduling, FSS), que están presentes en un taller con tecnología de mecanizado con el objetivo de optimizar varias medidas de desempeño en un plan de trabajo. La aportación principal de esta tesis, es un modelo matemático para medir el consumo de energía, como criterio para la optimización, de las máquinas que intervienen en la ejecución de un plan de trabajo. Se propone además, un método para mejorar el rendimiento en la búsqueda de las soluciones encontradas, por parte del Algoritmo Genético Simple, basado en el aprovechamiento del tiempo ocioso. ABSTRACT The scheduling problems are very important in today's world. It can be said to be present in all the basics of modern industry, hence the importance that these are optimal, so that they can save resources that are associated with the problem. The appropriate programming jobs in manufacturing processes is an important problem that arises in production in many companies. The order in which they are processed, it is immaterial, but shall determine a parameter of interest, whose values agree optimize the possible. This may be affected the total cost of execution of work, the time needed to complete them or the stock of work in progress that will be generated. This leads directly to the problem of determining what the most appropriate order to carry out the work in order to maximize some of the above parameters or other similar. Due to the limitations of conventional optimization techniques, in this work present a metaheuristic based on a Simple Genetic Algorithm (Simple Genetic Algorithm, SGA) to solve programming problems overall flow rate (Job Shop Scheduling, JSS) and regular flow (Flow Shop Scheduling, FSS), which are present in a workshop with machining technology in order to optimize various performance measures in a plan. The main contribution of this thesis is a mathematical model to measure the energy consumption as a criterion for the optimization of the machines involved in the implementation of a work plan. It also proposes a method to improve performance in finding the solutions, by the simple genetic algorithm, based on the use of idle time.

Corporate social responsibility in portfolio selection: A "goal games" against nature approach

Nowadays, there is an uprising social pressure on big companies to incorporate into their decision-making process elements of the so-called social responsibility. Among the many implications of this fact, one relevant one is the need to include this new element in classic portfolio selection models. This paper meets this challenge by formulating a model that combines goal programming with "goal games" against nature in a scenario where the social responsibility is defined through the introduction of a battery of sustainability indicators amalgamated into a synthetic index. In this way, we have obtained an efficient model that only implies solving a small number of linear programming problems. The proposed approach has been tested and illustrated by using a case study related to the selection of securities in international markets.

A proposal for a modular and application-aware autonomic manager of private cloud infrastructures

Recientemente, el paradigma de la computación en la nube ha recibido mucho interés por parte tanto de la industria como del mundo académico. Las infraestructuras cloud públicas están posibilitando nuevos modelos de negocio y ayudando a reducir costes. Sin embargo, una compañía podría desear ubicar sus datos y servicios en sus propias instalaciones, o tener que atenerse a leyes de protección de datos. Estas circunstancias hacen a las infraestructuras cloud privadas ciertamente deseables, ya sea para complementar a las públicas o para sustituirlas por completo. Por desgracia, las carencias en materia de estándares han impedido que las soluciones para la gestión de infraestructuras privadas se hayan desarrollado adecuadamente. Además, la multitud de opciones disponibles ha creado en los clientes el miedo a depender de una tecnología concreta (technology lock-in). Una de las causas de este problema es la falta de alineación entre la investigación académica y los productos comerciales, ya que aquella está centrada en el estudio de escenarios idealizados sin correspondencia con el mundo real, mientras que éstos consisten en soluciones desarrolladas sin tener en cuenta cómo van a encajar con los estándares más comunes o sin preocuparse de hacer públicos sus resultados. Con objeto de resolver este problema, propongo un sistema de gestión modular para infraestructuras cloud privadas enfocado en tratar con las aplicaciones en lugar de centrarse únicamente en los recursos hardware. Este sistema de gestión sigue el paradigma de la computación autónoma y está diseñado en torno a un modelo de información sencillo, desarrollado para ser compatible con los estándares más comunes. Este modelo divide el entorno en dos vistas, que sirven para separar aquello que debe preocupar a cada actor involucrado del resto de información, pero al mismo tiempo permitiendo relacionar el entorno físico con las máquinas virtuales que se despliegan encima de él. En dicho modelo, las aplicaciones cloud están divididas en tres tipos genéricos (Servicios, Trabajos de Big Data y Reservas de Instancias), para que así el sistema de gestión pueda sacar partido de las características propias de cada tipo. El modelo de información está complementado por un conjunto de acciones de gestión atómicas, reversibles e independientes, que determinan las operaciones que se pueden llevar a cabo sobre el entorno y que es usado para hacer posible la escalabilidad en el entorno. También describo un motor de gestión encargado de, a partir del estado del entorno y usando el ya mencionado conjunto de acciones, la colocación de recursos. Está dividido en dos niveles: la capa de Gestores de Aplicación, encargada de tratar sólo con las aplicaciones; y la capa del Gestor de Infraestructura, responsable de los recursos físicos. Dicho motor de gestión obedece un ciclo de vida con dos fases, para así modelar mejor el comportamiento de una infraestructura real. El problema de la colocación de recursos es atacado durante una de las fases (la de consolidación) por un resolutor de programación entera, y durante la otra (la online) por un heurístico hecho ex-profeso. Varias pruebas han demostrado que este acercamiento combinado es superior a otras estrategias. Para terminar, el sistema de gestión está acoplado a arquitecturas de monitorización y de actuadores. Aquella estando encargada de recolectar información del entorno, y ésta siendo modular en su diseño y capaz de conectarse con varias tecnologías y ofrecer varios modos de acceso. ABSTRACT The cloud computing paradigm has raised in popularity within the industry and the academia. Public cloud infrastructures are enabling new business models and helping to reduce costs. However, the desire to host company’s data and services on premises, and the need to abide to data protection laws, make private cloud infrastructures desirable, either to complement or even fully substitute public oferings. Unfortunately, a lack of standardization has precluded private infrastructure management solutions to be developed to a certain level, and a myriad of diferent options have induced the fear of lock-in in customers. One of the causes of this problem is the misalignment between academic research and industry ofering, with the former focusing in studying idealized scenarios dissimilar from real-world situations, and the latter developing solutions without taking care about how they f t with common standards, or even not disseminating their results. With the aim to solve this problem I propose a modular management system for private cloud infrastructures that is focused on the applications instead of just the hardware resources. This management system follows the autonomic system paradigm, and is designed around a simple information model developed to be compatible with common standards. This model splits the environment in two views that serve to separate the concerns of the stakeholders while at the same time enabling the traceability between the physical environment and the virtual machines deployed onto it. In it, cloud applications are classifed in three broad types (Services, Big Data Jobs and Instance Reservations), in order for the management system to take advantage of each type’s features. The information model is paired with a set of atomic, reversible and independent management actions which determine the operations that can be performed over the environment and is used to realize the cloud environment’s scalability. From the environment’s state and using the aforementioned set of actions, I also describe a management engine tasked with the resource placement. It is divided in two tiers: the Application Managers layer, concerned just with applications; and the Infrastructure Manager layer, responsible of the actual physical resources. This management engine follows a lifecycle with two phases, to better model the behavior of a real infrastructure. The placement problem is tackled during one phase (consolidation) by using an integer programming solver, and during the other (online) with a custom heuristic. Tests have demonstrated that this combined approach is superior to other strategies. Finally, the management system is paired with monitoring and actuators architectures. The former able to collect the necessary information from the environment, and the later modular in design and capable of interfacing with several technologies and ofering several access interfaces.

Arquitectura de supercomputación en la nube para la resolución de problemas de optimización combinatoria

La tesis está focalizada en la resolución de problemas de optimización combinatoria, haciendo uso de las opciones tecnológicas actuales que ofrecen las tecnologías de la información y las comunicaciones, y la investigación operativa. Los problemas de optimización combinatoria se resuelven en general mediante programación lineal y metaheurísticas. La aplicación de las técnicas de resolución de los problemas de optimización combinatoria requiere de una elevada carga computacional, y los algoritmos deben diseñarse, por un lado pensando en la efectividad para encontrar buenas soluciones del problema, y por otro lado, pensando en un uso adecuado de los recursos informáticos disponibles. La programación lineal y las metaheurísticas son técnicas de resolución genéricas, que se pueden aplicar a diferentes problemas, partiendo de una base común que se particulariza para cada problema concreto. En el campo del desarrollo de software, los frameworks cumplen esa función de comenzar un proyecto con el trabajo general ya disponible, con la opción de cambiar o extender ese comportamiento base o genérico, para construir el sistema concreto, lo que permite reducir el tiempo de desarrollo, y amplía las posibilidades de éxito del proyecto. En esta tesis se han desarrollado dos frameworks de desarrollo. El framework ILP permite modelar y resolver problemas de programación lineal, de forma independiente al software de resolución de programación lineal que se utilice. El framework LME permite resolver problemas de optimización combinatoria mediante metaheurísticas. Tradicionalmente, las aplicaciones de resolución de problemas de optimización combinatoria son aplicaciones de escritorio que permiten gestionar toda la información de entrada del problema y resuelven el problema en local, con los recursos hardware disponibles. Recientemente ha aparecido un nuevo paradigma de despliegue y uso de aplicaciones que permite compartir recursos informáticos especializados por Internet. Esta nueva forma de uso de recursos informáticos es la computación en la nube, que presenta el modelo de software como servicio (SaaS). En esta tesis se ha construido una plataforma SaaS, para la resolución de problemas de optimización combinatoria, que se despliega sobre arquitecturas compuestas por procesadores multi-núcleo y tarjetas gráficas, y dispone de algoritmos de resolución basados en frameworks de programación lineal y metaheurísticas. Toda la infraestructura es independiente del problema de optimización combinatoria a resolver, y se han desarrollado tres problemas que están totalmente integrados en la plataforma SaaS. Estos problemas se han seleccionado por su importancia práctica. Uno de los problemas tratados en la tesis, es el problema de rutas de vehículos (VRP), que consiste en calcular las rutas de menor coste de una flota de vehículos, que reparte mercancías a todos los clientes. Se ha partido de la versión más clásica del problema y se han hecho estudios en dos direcciones. Por un lado se ha cuantificado el aumento en la velocidad de ejecución de la resolución del problema en tarjetas gráficas. Por otro lado, se ha estudiado el impacto en la velocidad de ejecución y en la calidad de soluciones, en la resolución por la metaheurística de colonias de hormigas (ACO), cuando se introduce la programación lineal para optimizar las rutas individuales de cada vehículo. Este problema se ha desarrollado con los frameworks ILP y LME, y está disponible en la plataforma SaaS. Otro de los problemas tratados en la tesis, es el problema de asignación de flotas (FAP), que consiste en crear las rutas de menor coste para la flota de vehículos de una empresa de transporte de viajeros. Se ha definido un nuevo modelo de problema, que engloba características de problemas presentados en la literatura, y añade nuevas características, lo que permite modelar los requerimientos de las empresas de transporte de viajeros actuales. Este nuevo modelo resuelve de forma integrada el problema de definir los horarios de los trayectos, el problema de asignación del tipo de vehículo, y el problema de crear las rotaciones de los vehículos. Se ha creado un modelo de programación lineal para el problema, y se ha resuelto por programación lineal y por colonias de hormigas (ACO). Este problema se ha desarrollado con los frameworks ILP y LME, y está disponible en la plataforma SaaS. El último problema tratado en la tesis es el problema de planificación táctica de personal (TWFP), que consiste en definir la configuración de una plantilla de trabajadores de menor coste, para cubrir una demanda de carga de trabajo variable. Se ha definido un modelo de problema muy flexible en la definición de contratos, que permite el uso del modelo en diversos sectores productivos. Se ha definido un modelo matemático de programación lineal para representar el problema. Se han definido una serie de casos de uso, que muestran la versatilidad del modelo de problema, y permiten simular el proceso de toma de decisiones de la configuración de una plantilla de trabajadores, cuantificando económicamente cada decisión que se toma. Este problema se ha desarrollado con el framework ILP, y está disponible en la plataforma SaaS. ABSTRACT The thesis is focused on solving combinatorial optimization problems, using current technology options offered by information technology and communications, and operations research. Combinatorial optimization problems are solved in general by linear programming and metaheuristics. The application of these techniques for solving combinatorial optimization problems requires a high computational load, and algorithms are designed, on the one hand thinking to find good solutions to the problem, and on the other hand, thinking about proper use of the available computing resources. Linear programming and metaheuristic are generic resolution techniques, which can be applied to different problems, beginning with a common base that is particularized for each specific problem. In the field of software development, frameworks fulfill this function that allows you to start a project with the overall work already available, with the option to change or extend the behavior or generic basis, to build the concrete system, thus reducing the time development, and expanding the possibilities of success of the project. In this thesis, two development frameworks have been designed and developed. The ILP framework allows to modeling and solving linear programming problems, regardless of the linear programming solver used. The LME framework is designed for solving combinatorial optimization problems using metaheuristics. Traditionally, applications for solving combinatorial optimization problems are desktop applications that allow the user to manage all the information input of the problem and solve the problem locally, using the available hardware resources. Recently, a new deployment paradigm has appeared, that lets to share hardware and software resources by the Internet. This new use of computer resources is cloud computing, which presents the model of software as a service (SaaS). In this thesis, a SaaS platform has been built for solving combinatorial optimization problems, which is deployed on architectures, composed of multi-core processors and graphics cards, and has algorithms based on metaheuristics and linear programming frameworks. The SaaS infrastructure is independent of the combinatorial optimization problem to solve, and three problems are fully integrated into the SaaS platform. These problems have been selected for their practical importance. One of the problems discussed in the thesis, is the vehicle routing problem (VRP), which goal is to calculate the least cost of a fleet of vehicles, which distributes goods to all customers. The VRP has been studied in two directions. On one hand, it has been quantified the increase in execution speed when the problem is solved on graphics cards. On the other hand, it has been studied the impact on execution speed and quality of solutions, when the problem is solved by ant colony optimization (ACO) metaheuristic, and linear programming is introduced to optimize the individual routes of each vehicle. This problem has been developed with the ILP and LME frameworks, and is available in the SaaS platform. Another problem addressed in the thesis, is the fleet assignment problem (FAP), which goal is to create lower cost routes for a fleet of a passenger transport company. It has been defined a new model of problem, which includes features of problems presented in the literature, and adds new features, allowing modeling the business requirements of today's transport companies. This new integrated model solves the problem of defining the flights timetable, the problem of assigning the type of vehicle, and the problem of creating aircraft rotations. The problem has been solved by linear programming and ACO. This problem has been developed with the ILP and LME frameworks, and is available in the SaaS platform. The last problem discussed in the thesis is the tactical planning staff problem (TWFP), which is to define the staff of lower cost, to cover a given work load. It has been defined a very rich problem model in the definition of contracts, allowing the use of the model in various productive sectors. It has been defined a linear programming mathematical model to represent the problem. Some use cases has been defined, to show the versatility of the model problem, and to simulate the decision making process of setting up a staff, economically quantifying every decision that is made. This problem has been developed with the ILP framework, and is available in the SaaS platform.