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.

Sistemas de gestión de puentes : optimización de estrategias de mantenimiento : implementación en redes locales de carreteras

En la actualidad, y en consonancia con la tendencia de “sostenibilidad” extendida a todos los campos y parcelas de la ciencia, nos encontramos con un área de estudio basado en la problemática del inevitable deterioro de las estructuras existentes, y la gestión de las acciones a realizar para mantener las condiciones de servicio de los puentes y prolongar su vida útil. Tal y como se comienza a ver en las inversiones en los países avanzados, con una larga tradición en el desarrollo de sus infraestructuras, se muestra claramente el nuevo marco al que nos dirigimos. Las nuevas tendencias van encaminadas cada vez más a la conservación y mantenimiento, reduciéndose las partidas presupuestarias destinadas a nuevas actuaciones, debido a la completa vertebración territorial que se ha ido instaurando en estos países, entre los que España se encuentra. Este nutrido patrimonio de infraestructuras viarias, que cuentan a su vez con un importante número de estructuras, hacen necesarias las labores de gestión y mantenimiento de los puentes integrantes en las mismas. Bajo estas premisas, la tesis aborda el estado de desarrollo de la implementación de los sistemas de gestión de puentes, las tendencias actuales e identificación de campos por desarrollar, así como la aplicación específica a redes de carreteras de escasos recursos, más allá de la Red Estatal. Además de analizar las diversas metodologías de formación de inventarios, realización de inspecciones y evaluación del estado de puentes, se ha enfocado, como principal objetivo, el desarrollo de un sistema específico de predicción del deterioro y ayuda a la toma de decisiones. Este sistema, adicionalmente a la configuración tradicional de criterios de formación de bases de datos de estructuras e inspecciones, plantea, de forma justificada, la clasificación relativa al conjunto de la red gestionada, según su estado de condición. Eso permite, mediante técnicas de optimización, la correcta toma de decisiones a los técnicos encargados de la gestión de la red. Dentro de los diversos métodos de evaluación de la predicción de evolución del deterioro de cada puente, se plantea la utilización de un método bilineal simplificado envolvente del ajuste empírico realizado y de los modelos markovianos como la solución más efectiva para abordar el análisis de la predicción de la propagación del daño. Todo ello explotando la campaña experimenta realizada que, a partir de una serie de “fotografías técnicas” del estado de la red de puentes gestionados obtenidas mediante las inspecciones realizadas, es capaz de mejorar el proceso habitual de toma de decisiones. Toda la base teórica reflejada en el documento, se ve complementada mediante la implementación de un Sistema de Gestión de Puentes (SGP) específico, adaptado según las necesidades y limitaciones de la administración a la que se ha aplicado, en concreto, la Dirección General de Carreteras de la Junta de Comunidades de Castilla-La Mancha, para una muestra representativa del conjunto de puentes de la red de la provincia de Albacete, partiendo de una situación en la que no existe, actualmente, un sistema formal de gestión de puentes. Tras un meditado análisis del estado del arte dentro de los Capítulos 2 y 3, se plantea un modelo de predicción del deterioro dentro del Capítulo 4 “Modelo de Predicción del Deterioro”. De la misma manera, para la resolución del problema de optimización, se justifica la utilización de un novedoso sistema de optimización secuencial elegido dentro del Capítulo 5, los “Algoritmos Evolutivos”, en sus diferentes variantes, como la herramienta matemática más correcta para distribuir adecuadamente los recursos económicos dedicados a mantenimiento y conservación de los que esta administración pueda disponer en sus partidas de presupuesto a medio plazo. En el Capítulo 6, y en diversos Anexos al presente documento, se muestran los datos y resultados obtenidos de la aplicación específica desarrollada para la red local analizada, utilizando el modelo de deterioro y optimización secuencial, que garantiza la correcta asignación de los escasos recursos de los que disponen las redes autonómicas en España. Se plantea con especial interés la implantación de estos sistemas en la red secundaria española, debido a que reciben en los últimos tiempos una mayor responsabilidad de gestión, con recursos cada vez más limitados. Finalmente, en el Capítulo 7, se plantean una serie de conclusiones que nos hacen reflexionar de la necesidad de comenzar a pasar, en materia de gestión de infraestructuras, de los estudios teóricos y los congresos, hacia la aplicación y la práctica, con un planteamiento que nos debe llevar a cambios importantes en la forma de concebir la labor del ingeniero y las enseñanzas que se imparten en las escuelas. También se enumeran las aportaciones originales que plantea el documento frente al actual estado del arte. Se plantean, de la misma manera, las líneas de investigación en materia de Sistemas de Gestión de Puentes que pueden ayudar a refinar y mejorar los actuales sistemas utilizados. In line with the development of "sustainability" extended to all fields of science, we are faced with the inevitable and ongoing deterioration of existing structures, leading nowadays to the necessary management of maintaining the service conditions and life time extension of bridges. As per the increased amounts of money that can be observed being spent in the countries with an extensive and strong tradition in the development of their infrastructure, the trend can be clearly recognized. The new tendencies turn more and more towards conservation and maintenance, reducing programmed expenses for new construction activities, in line with the already wellestablished territorial structures, as is the case for Spain. This significant heritage of established road infrastructure, consequently containing a vast number of structures, imminently lead to necessary management and maintenance of the including bridges. Under these conditions, this thesis focusses on the status of the development of the management implementation for bridges, current trends, and identifying areas for further development. This also includes the specific application to road networks with limited resources, beyond the national highways. In addition to analyzing the various training methodologies, inventory inspections and condition assessments of bridges, the main objective has been the development of a specific methodology. This methodology, in addition to the traditional system of structure and inspection database training criteria, sustains the classification for the entire road network, according to their condition. This allows, through optimization techniques, for the correct decision making by the technical managers of the network. Among the various methods for assessing the evolution forecast of deterioration of each bridge, a simplified bilinear envelope adjustment made empirical method and Markov models as the most effective solution to address the analysis of predicting the spread of damage, arising from a "technical snapshot" obtained through inspections of the condition of the bridges included in the investigated network. All theoretical basis reflected in the document, is completed by implementing a specific Bridges Management System (BMS), adapted according to the needs and limitations of the authorities for which it has been applied, being in this case particularly the General Highways Directorate of the autonomous region of Castilla-La Mancha, for a representative sample of all bridges in the network in the province of Albacete, starting from a situation where there is currently no formal bridge management system. After an analysis of the state of the art in Chapters 2 and 3, a new deterioration prediction model is developed in Chapter 4, "Deterioration Prediction Model". In the same way, to solve the optimization problem is proposed the use of a singular system of sequential optimization elected under Chapter 5, the "Evolutionary Algorithms", the most suitable mathematical tool to adequately distribute the economic resources for maintenance and conservation for mid-term budget planning. In Chapter 6, and in the various appendices, data and results are presented of the developed application for the analyzed local network, from the optimization model, which guarantees the correct allocation of scarce resources at the disposal of authorities responsible for the regional networks in Spain. The implementation of these systems is witnessed with particular interest for the Spanish secondary network, because of the increasing management responsibility, with decreasing resources. Chapter 7 presents a series of conclusions that triggers to reconsider shifting from theoretical studies and conferences towards a practical implementation, considering how to properly conceive the engineering input and the related education. The original contributions of the document are also listed. In the same way, the research on the Bridges Management System can help evaluating and improving the used systematics.

Desenvolvimento de estratégias de otimização contínua e discreta para problemas de fluxo de potência ótimo

O objetivo do presente trabalho é a investigação e o desenvolvimento de estratégias de otimização contínua e discreta para problemas de Fluxo de Potência Ótimo (FPO), onde existe a necessidade de se considerar as variáveis de controle associadas aos taps de transformadores em-fase e chaveamentos de bancos de capacitores e reatores shunt como variáveis discretas e existe a necessidade da limitação, e/ou até mesmo a minimização do número de ações de controle. Neste trabalho, o problema de FPO será abordado por meio de três estratégias. Na primeira proposta, o problema de FPO é modelado como um problema de Programação Não Linear com Variáveis Contínuas e Discretas (PNLCD) para a minimização de perdas ativas na transmissão; são propostas três abordagens utilizando funções de discretização para o tratamento das variáveis discretas. Na segunda proposta, considera-se que o problema de FPO, com os taps de transformadores discretos e bancos de capacitores e reatores shunts fixos, possui uma limitação no número de ações de controles; variáveis binárias associadas ao número de ações de controles são tratadas por uma função quadrática. Na terceira proposta, o problema de FPO é modelado como um problema de Otimização Multiobjetivo. O método da soma ponderada e o método ε-restrito são utilizados para modificar os problemas multiobjetivos propostos em problemas mono-objetivos. As variáveis binárias associadas às ações de controles são tratadas por duas funções, uma sigmoidal e uma polinomial. Para verificar a eficácia e a robustez dos modelos e algoritmos desenvolvidos serão realizados testes com os sistemas elétricos IEEE de 14, 30, 57, 118 e 300 barras. Todos os algoritmos e modelos foram implementados em General Algebraic Modeling System (GAMS) e os solvers CONOPT, IPOPT, KNITRO e DICOPT foram utilizados na resolução dos problemas. Os resultados obtidos confirmam que as estratégias de discretização são eficientes e as propostas de modelagem para variáveis binárias permitem encontrar soluções factíveis para os problemas envolvendo as ações de controles enquanto os solvers DICOPT e KNITRO utilizados para modelar variáveis binárias não encontram soluções.

Hybrid simulation-optimization based approach for the optimal design of single-product biotechnological processes

In this work, we present a systematic method for the optimal development of bioprocesses that relies on the combined use of simulation packages and optimization tools. One of the main advantages of our method is that it allows for the simultaneous optimization of all the individual components of a bioprocess, including the main upstream and downstream units. The design task is mathematically formulated as a mixed-integer dynamic optimization (MIDO) problem, which is solved by a decomposition method that iterates between primal and master sub-problems. The primal dynamic optimization problem optimizes the operating conditions, bioreactor kinetics and equipment sizes, whereas the master levels entails the solution of a tailored mixed-integer linear programming (MILP) model that decides on the values of the integer variables (i.e., number of equipments in parallel and topological decisions). The dynamic optimization primal sub-problems are solved via a sequential approach that integrates the process simulator SuperPro Designer® with an external NLP solver implemented in Matlab®. The capabilities of the proposed methodology are illustrated through its application to a typical fermentation process and to the production of the amino acid L-lysine.

Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.

Primal Attainment in Convex Infinite Optimization Duality

This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.

Comparative study of RPSALG algorithm for convex semi-infinite programming

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.

Geometry and Optimization of Relative Arbitrage

Thesis (Ph.D.)--University of Washington, 2016-06

Optimising profitability and environmental trade-offs in managing cropping systems using differential evolution

Whilst traditional optimisation techniques based on mathematical programming techniques are in common use, they suffer from their inability to explore the complexity of decision problems addressed using agricultural system models. In these models, the full decision space is usually very large while the solution space is characterized by many local optima. Methods to search such large decision spaces rely on effective sampling of the problem domain. Nevertheless, problem reduction based on insight into agronomic relations and farming practice is necessary to safeguard computational feasibility. Here, we present a global search approach based on an Evolutionary Algorithm (EA). We introduce a multi-objective evaluation technique within this EA framework, linking the optimisation procedure to the APSIM cropping systems model. The approach addresses the issue of system management when faced with a trade-off between economic and ecological consequences.

Optimal design of a regenerative dynamic dynamometer using genetic algorithms

This paper presents an approach for optimal design of a fully regenerative dynamic dynamometer using genetic algorithms. The proposed dynamometer system includes an energy storage mechanism to adaptively absorb the energy variations following the dynamometer transients. This allows the minimum power electronics requirement at the mains power supply grid to compensate for the losses. The overall dynamometer system is a dynamic complex system and design of the system is a multi-objective problem, which requires advanced optimisation techniques such as genetic algorithms. The case study of designing and simulation of the dynamometer system indicates that the genetic algorithm based approach is able to locate a best available solution in view of system performance and computational costs.

A Bayesian formulation of search, control and the exploration/exploitation trade-off

A new approach to optimisation is introduced based on a precise probabilistic statement of what is ideally required of an optimisation method. It is convenient to express the formalism in terms of the control of a stationary environment. This leads to an objective function for the controller which unifies the objectives of exploration and exploitation, thereby providing a quantitative principle for managing this trade-off. This is demonstrated using a variant of the multi-armed bandit problem. This approach opens new possibilities for optimisation algorithms, particularly by using neural network or other adaptive methods for the adaptive controller. It also opens possibilities for deepening understanding of existing methods. The realisation of these possibilities requires research into practical approximations of the exact formalism.

Experimental optimization of triangular pulse generation in normal dispersion fiber for all optical processing applications

We experimentally investigate a multi-parameter optimization of conditions for generation of triangular pulses in normal dispersion fiber. We find that triangular pulses suitable for all optical processing applications can be generated for a wide range of input pulse chirps but that triangular pulse quality and stability is improved with increased input pulse chirp.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

A bi-objective weighted model for improving the discrimination power in MCDEA

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach. © 2013 Elsevier B.V. All rights reserved.