A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions

In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities

Multi-Criterion Dynamic Traffic Assignment Models and Algorithms for Road Pricing Applications with Heterogeneous Users

This study develops a simulation-based dynamic traffic assignment, or dynamic user equilibrium (DUE), model for dynamic road pricing applications. This proposed model is considered as the bi-criterion DUE (BDUE) model, because it explicitly considers heterogeneous users with different values of time (VOT) choose paths that minimize the two path attributes: travel time and out-of-pocket cost. This study assumed trip-makers would select their respective least generalized cost paths, the generalized cost being the sum of travel cost and travel time weighted by the trip-maker's VOT. The VOT is modeled as a continuous random variable distributed across all users in a network. The BDUE problem is formulated as an infinite dimensional variational inequality (VI), and solved by a column generation-based algorithmic framework which embeds (i) a parametric analysis (PAM) to obtain the VOT breakpoints which determine multiple user classes, and find the set of extreme non-dominated paths, (ii) a simulator to determine experienced travel times, and (iii) a multi-class path flow equilibrating scheme to update path assignments. The idea of finding and assigning heterogeneous trips to the set of extreme non-dominated paths is based on the assumption that in the disutility minimization path choice model with convex utility functions, all trips would choose only among the set of extreme non-dominated paths. Moreover, to circumvent the difficulty of storing the grand path set and assignment results for large-scale network applications, a vehicle-based implementation technique is proposed. This BDUE model is generalized to the multi-criterion DUE (MDUE) model, in which heterogeneous users with different VOT and values of reliability (VOR) make path choices so as to minimize their path travel cost, travel time, and travel time variability. Another important extension of the BDUE model is the multi-criterion simultaneous route and departure time user equilibrium (MSRDUE) model, which considers heterogeneous trip-makers with different VOT and values of schedule delay (VOSD) making simultaneous route and departure time choices so as to minimize their respective trip costs, defined as the sum of travel cost, travel time weighted by VOT, and schedule delay weighted by VOSD. The MSRDUE problem is also solved by the column generation-based algorithmic framework. The Sequential Parametric Analysis Method (SPAM) is developed to find the VOT and VOSD breakpoints that define multiple user classes, and determine the least trip cost alternative (a combination of departure time and path) for each user class

Robust aircraft trajectory optimization under meteorological uncertainty

Mención Internacional en el título de doctorThe Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems. One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories. To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning problem as it is now understood. The first contribution of this thesis addresses this challenge by introducing a framework for the solution of general nonlinear optimal control problems under parametric uncertainty. It is based on an ensemble trajectory scheme, where the trajectories of the system under multiple scenarios are considered simultaneously within the same dynamical system and the uncertain optimal control problem is turned into a large conventional optimal control problem that can be then solved by standard, well-studied direct methods in optimal control. We then employ this approach to solve the robust flight plan optimization problem at the planning horizon. In order to model uncertainty in the wind and estimating the probability of convective conditions, we employ Ensemble Prediction System (EPS) forecasts, which are composed by multiple predictions instead of a single deterministic one. The resulting method can be used to optimize flight plans for maximum expected efficiency according to the cost structure of the airline; additionally, predictability and exposure to convection can be incorporated as additional objectives. The inherent tradeoffs between these objectives can be assessed with this methodology. The second part of this thesis presents a solution for the rerouting of aircraft in uncertain convective weather scenarios at the tactical horizon. The uncertain motion of convective weather cells is represented with a stochastic model that has been developed from the output of a deterministic satellite-based nowcast product, Rapidly Developing Thunderstorms (RDT). A numerical optimal control framework, based on the pointmass model with the addition of turn dynamics, is employed for optimizing efficiency and predictability of the proposed trajectories in the presence of uncertainty about the future evolution of the storm. Finally, the optimization process is initialized by a randomized heuristic procedure that generates multiple starting points. The combined framework is able to explore and as exploit the space of solution trajectories in order to provide the pilot or the air traffic controller with a set of different suggested avoidance trajectories, as well as information about their expected cost and risk. The proposed methods are tested on example scenarios based on real data, showing how different user priorities lead to different flight plans and what tradeoffs are then present. These examples demonstrate that the solutions described in this thesis are adequate for the problems that have been formulated. In this way, the flight planning process can be enhanced to increase the efficiency and predictability of individual aircraft trajectories, which would lead to higher predictability levels of the ATM system and thus improvements in multiple performance indicators.El sistema de gestión del tráfico aéreo (Air Traffic Management, ATM) en los espacios aéreos más congestionados del mundo está siendo reformado para lidiar con múltiples desafíos socioeconómicos, medioambientales y de capacidad. Un pilar de este proceso es el gradual reemplazo de las estructuras rígidas de navegación, basadas en aerovías y waypoints, hacia las operaciones basadas en trayectorias. No obstante, la implementación exitosa de este concepto y la realización de las ganancias esperadas en rendimiento ATM requiere entender y gestionar apropiadamente la incertidumbre. Debido a su compleja estructura socio-técnica, el diseño y operaciones del sistema ATM se encuentran marcadamente influidos por la incertidumbre, que procede de múltiples fuentes y se propaga por las interacciones entre subsistemas y operadores humanos. Uno de los principales focos de incertidumbre en ATM es la meteorología. Debido a su naturaleza no-linear y caótica, muchos fenómenos de interés no pueden ser pronosticados con completa precisión en cualquier horizonte temporal, lo que crea disrupción en las operaciones en aire y tierra que se propaga a otros procesos de ATM. Por lo tanto, para lograr los objetivos de SESAR e iniciativas análogas, es imprescindible tener en cuenta la incertidumbre en múltiples escalas espaciotemporales, desde la predicción de trayectorias hasta la planificación de flujos y tráfico. Esta tesis aborda el problema de la planificación de vuelo de aeronaves individuales considerando dos fuentes importantes de incertidumbre meteorológica: el error en la predicción del viento y la actividad convectiva. Conforme la realización del viento se desvía de su previsión, la trayectoria real se desviará temporalmente de la planificada, lo que implica incertidumbre en tiempos de llegada a sectores y aeropuertos y en consumo de combustible. La actividad convectiva también tiene un impacto en la predictibilidad de las trayectorias, puesto que obliga a los pilotos a desviarse de sus planes de vuelo para evitarla, cambiado así la situación de tráfico. En este trabajo, buscamos desarrollar métodos y algoritmos para la optimización de trayectorias que puedan integrar información sobre la incertidumbre en estos fenómenos meteorológicos en el proceso de diseño de planes de vuelo en horizontes de planificación (antes del despegue) y tácticos (durante el vuelo), con el objetivo de generar trayectorias más eficientes y predecibles. Con este fin, formulamos la planificación de vuelo como un problema de control óptimo, modelando la dinámica del avión con un modelo de masa puntual y el modelo de rendimiento BADA. El control óptimo es un marco flexible y general con un largo historial de éxito en el campo de la ingeniería aeroespacial. Como método numérico, empleamos métodos directos, que son capaces de manejar sistemas dinámicos de alta dimensión con costes computacionales moderados. No obstante, si bien esta metodología es madura en contextos deterministas, la solución de problemas prácticas de control óptimo bajo incertidumbre en la literatura no está tan desarrollada, y los métodos propuestos en la literatura no son aplicables al problema de interés. La primera contribución de esta tesis hace frente a este reto mediante la introducción de un marco numérico para la resolución de problemas generales de control óptimo no-lineal bajo incertidumbre paramétrica. El núcleo de este método es un esquema de conjunto de trayectorias, en el que las trayectorias del sistema dinámico bajo múltiples escenarios son consideradas de forma simultánea, y el problema de control óptimo bajo incertidumbre es así transformado en un problema convencional que puede ser tratado mediante métodos existentes en control óptimo. A continuación, empleamos este método para resolver el problema de la planificación de vuelo robusta. La incertidumbre en el viento y la probabilidad de ocurrencia de condiciones convectivas son modeladas mediante el uso de previsiones de conjunto o ensemble, compuestas por múltiples predicciones en lugar de una única previsión determinista. Este método puede ser empleado para maximizar la eficiencia esperada de los planes de vuelo de acuerdo a la estructura de costes de la aerolínea; además, la predictibilidad de la trayectoria y la exposición a la convección pueden ser incorporadas como objetivos adicionales. El trade-off entre estos objetivos puede ser evaluado mediante la metodología propuesta. La segunda parte de la tesis presenta una solución para reconducir aviones en escenarios tormentosos en un horizonte táctico. La evolución de las células convectivas es representada con un modelo estocástico basado en las proyecciones de Rapidly Developing Thunderstorms (RDT), un sistema determinista basado en imágenes de satélite. Este modelo es empleado por un método de control óptimo numérico, basado en un modelo de masa puntual en el que se modela la dinámica de viraje, con el objetivo de maximizar la eficiencia y predictibilidad de la trayectoria en presencia de incertidumbre sobre la evolución futura de las tormentas. Finalmente, el proceso de optimizatión es inicializado por un método heurístico aleatorizado que genera múltiples puntos de inicio para las iteraciones del optimizador. Esta combinación permite explorar y explotar el espacio de trayectorias solución para proporcionar al piloto o al controlador un conjunto de trayectorias propuestas, así como información útil sobre su coste y el riesgo asociado. Los métodos propuestos son probados en escenarios de ejemplo basados en datos reales, ilustrando las diferentes opciones disponibles de acuerdo a las prioridades del planificador y demostrando que las soluciones descritas en esta tesis son adecuadas para los problemas que se han formulado. De este modo, es posible enriquecer el proceso de planificación de vuelo para incrementar la eficiencia y predictibilidad de las trayectorias individuales, lo que contribuiría a mejoras en el rendimiento del sistema ATM.These works have been financially supported by Universidad Carlos III de Madrid through a PIF scholarship; by Eurocontrol, through the HALA! Research Network grant 10-220210-C2; by the Spanish Ministry of Economy and Competitiveness (MINECO)'s R&D program, through the OptMet project (TRA2014-58413-C2-2-R); and by the European Commission's SESAR Horizon 2020 program, through the TBO-Met project (grant number 699294).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira iPresidente: Damián Rivas Rivas.- Secretario: Xavier Prats Menéndez.- Vocal: Benavar Sridha

Parameter inference and model selection for differential equation models

Includes bibliographical references.2015 Summer.Firstly, we consider the problem of estimating parameters of stochastic differential equations with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements of the new penalized simulated maximum likelihood method. The new procedure is designed for the challenging case when some state variables are unobserved and moreover, observed states are sparse over time, which commonly arises in ecological studies. We apply this new approach to two epidemics of chronic wasting disease in mule deer. Next, we consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on experience or subjective judgment. Due to the complex or intractable likelihood in most dynamical models, likelihood-based approaches for model selection are not suitable. We use approximate Bayesian computation for parameter estimation and model selection to gain further understanding of the dynamics of two epidemics of chronic wasting disease in mule deer. The main novel contribution of this work is that under a hierarchical model framework we compare three types of dynamical models: ordinary differential equation, continuous time Markov chain, and stochastic differential equation models. To our knowledge model selection between these types of models has not appeared previously. The practice of incorporating dynamical models into data models is becoming more common, the proposed approach may be useful in a variety of applications. Lastly, we consider estimation of parameters in nonlinear ordinary differential equation models with measurement error where closed-form solutions are not available. We propose a new numerical algorithm, the data driven adaptive mesh method, which is a combination of the Euler and 4th order Runge-Kutta methods with different step sizes based on the observation time points. Our results show that both the accuracy in parameter estimation and computational cost of the new algorithm improve over the most widely used numerical algorithm, the 4th Runge-Kutta method. Moreover, the generalized profiling procedure proposed by Ramsay et al. (2007) doesn't have good performance for sparse data in time as compared to the new approach. We illustrate our approach with both simulation studies and ecological data on intestinal microbiota

Optimization of a fed-batch bioreactor for 1,3-propanediol production using hybrid nonlinear optimal control

A nonlinear hybrid system was proposed to describe the fed-batch bioconversion of glycerol to 1,3-propanediol with substrate open loop inputs and pH logic control in previous work [47]. The current work concerns the optimal control of this fed-batch process. We slightly modify the hybrid system to provide a more convenient mathematical description for the optimal control of the fed-batch culture. Taking the feeding instants and the terminal time as decision variables, we formulate an optimal control model with the productivity of 1,3-propanediol as the performance index. Inequality path constraints involved in the optimal control problem are transformed into a group of end-point constraints by introducing an auxiliary hybrid system. The original optimal control problem is associated with a family of approximation problems. The gradients of the cost functional and the end-point constraint functions are derived from the parametric sensitivity system. On this basis, we construct a gradient-based algorithm to solve the approximation problems. Numerical results show that the productivity of 1,3-propanediol can be increased considerably by employing our optimal control policy

Optimization-based methods for real-time generation of safe motions in mobile robots

Having robots operating in unstructured and dynamically changing environments is a challenging task that requires advanced motion generation approaches that are able to perform in real-time while maintaining the robot and environment safety. The progress in the field of numerical optimization, as well as the development of tailored algorithms, made Nonlinear Model Predictive Control (NMPC) an appealing candidate for real-time motion generation. By considering the robot model as prediction model and through appropriate constraints on the robot states and control inputs, NMPC can enforce safety to the resulting motion in a straightforward way. This thesis addresses the problem of real-time generation of safe motions for mobile robots and mobile manipulators. The different structure of the considered robots introduces different safety risks during the robot motion and so the motion generation problem for each robot is addressed in separate parts of this thesis. In the first part, the problem of motion generation for mobile robots navigating in environments populated by static and/or moving obstacles is considered. For the generation of the desired motion, real-time NMPC is used. We argue that, in order to tackle the risk of collision with the environment, traditional distance-based approaches are incapable of maintaining the robot safety when the NMPC uses relatively short prediction horizons. Instead, we propose two NMPC approaches that employ two alternative collision avoidance constraints. The first proposed NMPC approach is applied to a scenario of safe robot navigation in a human crowd. The NMPC serves as a motion generation module in a safe motion generation framework, complete with a crowd prediction module. The considered collision avoidance constraint is built upon an appropriate Control Barrier Function (CBF). The second NMPC approach is applied to a scenario of robot navigation among moving obstacles, where the dynamics of the considered robot are significant. The proposed collision avoidance constraint is built upon the notion of avoidable collision state, which considers not only the robot-obstacle distance but also their velocity as well as the robot actuation capabilities. The simulation results indicate that both methods are effective and able to maintain the robot safety even in cases where their purely distance-based counterparts fail. The second part of the thesis addresses the problem of safe motion generation for mobile manipulators, called to execute tasks that may require aggressive motions. Here, in addition to the risk of collision with its environment, the robot, consisting of multiple articulated bodies, is also susceptible to self-collisions. Moreover, fast motions can always result to loss of balance. To solve the problem, we propose a real-time NMPC scheme that uses the robot full dynamics, in order to enforce kinodynamic feasibility, while it also considers appropriate collision and self-collision avoidance constraints. To maintain the robot balance we enforce a constraint that restricts the feasible set of robot motions to those generating non-negative moments around the edges of the support polygon. This balance constraint, inherently nonlinear, is linearized using the NMPC solution of the previous iteration. In this way, we facilitate the solution of the NMPC in real-time, without compromising the robot safety. Although the proposed NMPC is effective when applied to MM with low degrees of freedom, when the robot becomes more complex the use of its full dynamic model as a prediction model in an NMPC can lead to unacceptably large computational times that are not compatible with the real-time requirement. However, the use of a simplified model of the robot in an NMPC can compromise the robot safety. For this reason, we propose an optimization-based controller equipped with balance constraints as well as CBF-based collision avoidance constraints. The proposed controller can serve as an intermediate between a motion generation module that does not consider the robot full dynamics and the robot itself in order to ensure that the resulting motion will be at least safe. Simulation results indicate the effectiveness of the proposed method

Inference of Gaussian graphical models and ordinary differential equations

Netwerken vormen een handig instrument bij het visualiseren van systemen bestaand uit elementen die onderling interactie aangaan. Genregulatienetwerken, bijvoorbeeld, zijn complexe systemen die bestaan uit genen, eiwitten en andere moleculen. De elementen van een dergelijk systeem worden weergegeven door knooppunten, die door lijnen worden verbonden op het moment dat de bijbehorende elementen met elkaar in interactie zijn.In veel wetenschappelijke disciplines vormt het blootleggen van de structuur van een netwerk een belangrijk en ingewikkeld probleem. Vaak is er weinig bekend over een systeem en moet men uitgaan van meetgegevens uit knooppunten om een inschatting te kunnen maken van de structuur van het bijbehorende netwerk. Deze meetgegevens zijn echter aan ruis onderhevig. Wanneer de structuur van de interacties bekend is, staan we voor een andere uitdaging: of het nou gaat om het beschrijving van bruggen die een hevige wind moeten weerstaan of om de verspreiding van een infectieziekte, de vraag is hoe we op basis van dezelfde aan ruis onderhevige data kunnen bepalen hoe de fijne dynamica van het systeem in elkaar zit.In dit proefschrift stellen we enkele aanpassingen voor op bestaande methodes, om het schatten van de structuur van en interacties binnen netwerken en dynamische systemen te verbeteren.Enkele toepassingen van de methodes die we ontwikkelen zijn: het voorspellen van het aantal individuen dat tijdens de kindertijd mazelen krijgt, en inferentie van de interactie tussen genen en eiwitten in de E. colibacterie.Networks provide a simple way to visualize a system of interacting elements. For example, gene regulatory networks are complex systems whose elements are genes, proteins and other molecules. The elements of this system are represented by nodes and lines are drawn between them if they interact with each other. In many sciences uncovering the network structure is an important and difficult problem. With a limited knowledge about the system noisy measurements on the nodes should be used to estimate the network. When we know the structure of the interactions, another major obstacle is to learn the fine dynamics of the system using the same noisy data, from describing bridges subject to strong winds to the spread of an infectious disease.In this thesis we propose modifications of existing methods to improve the estimation of networks and dynamical systems.Some applications of methods we develop include: predicting the number of individuals that get infected by childhood disease measles, reconstructing transcription factor activities in streptomyces coelicolor bacterium, and inferring the interaction between genes and proteins in Escherichia coli bacterium

Hybrid multi-objective trajectory optimization of low-thrust space mission design

Mención Internacional en el título de doctorThe overall goal of this dissertation is to develop multi-objective optimization algorithms for computing low-thrust trajectories. The thesis is motivated by the increasing number of space projects that will benefit from low-thrust propulsion technologies to gain unprecedented scientific, economic and social return. The low-cost design of such missions and the inclusion of concurrent engineering practices during the preliminary design phase demand advanced tools to rapidly explore different solutions and to benchmark them with respect to multiple conicting criteria. However, the determination of optimal low-thrust transfers is a challenging task and remains an active research field that seeks performance improvements. This work contributes to increase the efficiency of searching wide design spaces, reduce the amount of necessary human involvement, and enhance the capabilities to include complex operational constraints. To that end, the general low-thrust trajectory optimization problem is stated as a multi-objective Hybrid Optimal Control Problem. This formulation allows to simultaneously optimize discrete decisionmaking processes, discrete dynamics, and the continuous low-thrust steering law. Within this framework, a sequential two-step solution approach is devised for two different scenarios. The first problem considers the optimization of low-thrust multi-gravity assist trajectories. The proposed solution procedure starts by assuming a planar shape-based model for the interplanetary trajectory. A multi-objective heuristic algorithm combined with a gradient-based solver optimize the parameters de_ning the shape of the trajectory, the number and sequence of the gravity assists, the departure and arrival dates, and the launch excess velocity. In the second step, candidate solutions are deemed as initial guesses to solve the Nonlinear Programming Problem resulting from applying a direct collocation transcription scheme. In this step, the sequence of planetary gravity assists is known and provided by the heuristic search, dynamics is three-dimensional, and the steering law is not predefined. Operational constraints to comply with launch asymptote declination limits and fixed reorientation times during the transfer apply. The presented approach is tested on a rendezvous mission to Ceres, on a yby mission to Jupiter, and on a rendezvous mission to Pluto. Pareto-optimal solutions in terms of time of ight and propellant mass consumed (or alternatively delivered mass) are obtained. Results outperform those found in the literature in terms of optimality while showing the effectiveness of the proposed methodology to generate quick performance estimates. The second problem considers the simultaneous optimization of fully electric, fully chemical and combined chemical-electric orbit raising transfers between Earth's orbits is considered. In the first step of the solution approach, the control law of the electric engine is parameterized by a Lyapunov function. A multi-objective heuristic algorithm selects the optimal propulsion system, the transfer type, the low-thrust control history, as well as the number, orientation, and magnitude of the chemical firings. Earth's shadow, oblateness and Van-Allen radiation effects are included. In the second step, candidate solutions are deemed as initial guesses to solve the Nonlinear Programming Problem resulting from applying a direct collocation scheme. Operational constraints to avoid the GEO ring in combination to slew rate limits and slot phasing constraints are included. The proposed approach is applied to two transfer scenarios to GEO orbit. Pareto-optimal solutions trading of propellant mass, time of ight and solar-cell degradation are obtained. It is identified that the application of operational restrictions causes minor penalties in the objective function. Additionally, the analysis highlights the benefits that combined chemical-electric platforms may provide for future GEO satellites.El objetivo principal de esta trabajo es desarrollar algoritmos de optimización multi-objetivo para la obtención de trayectorias espaciales con motores de bajo empuje. La tesis está motivada por el creciente número de misiones que se van a beneficiar del uso de estas tecnologías para conseguir beneficios científicos, económicos y sociales sin precedentes. El diseño de bajo coste de dichas misiones ligado a los principios de ingeniería concurrente requieren herramientas computacionales avanzadas que exploren rápidamente distintas soluciones y las comparen entre sí respecto a varios criterios. Sin embargo, esta tarea permanece como un campo de investigación activo que busca continuamente mejoras de rendimiento durante el proceso. Este trabajo contribuye a aumentar la eficiencia cuando espacio de diseño es amplio, a reducir la participación humana requerida y a mejorar las capacidades para incluir restricciones operacionales complejas. Para este fin, el problema general de optimización de trayectorias de bajo empuje se presenta como un problema híbrido de control óptimo. Esta formulación permite optimizar al mismo tiempo procesos de toma de decisiones, dinámica discreta y la ley de control del motor. Dentro de este marco, se idea un algoritmo secuencial de dos pasos para dos escenarios diferentes. El primer problema considera la optimización de trayectorias de bajo empuje con múltiples y-bys. El proceso de solución propuesto comienza asumiendo un modelo plano y shape-based para la trayectoria interplanetaria. Un algoritmo de optimización heurístico y multi-objetivo combinado con un resolvedor basado en gradiente optimizan los parámetros de la espiral que definen la forma de la trayectoria, el número y la secuencia de las maniobras gravitacionales, las fechas de salida y llegada, y la velocidad de lanzamiento. En el segundo paso, las soluciones candidatas se usan como estimación inicial para resolver el problema de optimización no lineal que resulta de aplicar un método de transcripción directa. En este paso, las secuencia de y-bys es conocida y determinada por el paso anterior, la dinámica es tridimensional, y la ley de control no está prefinida. Además, se pueden aplicar restricciones operacionales relacionadas con las declinación de la asíntota de salida e imponer tiempos de reorientación fijos. Este enfoque es probado en misiones a Ceres, a Júpiter y a Plutón. Se obtienen soluciones óptimas de Pareto en función del tiempo de vuelo y la masa de combustible consumida (o la masa entregada). Los resultados obtenidos mejoran los disponibles en la literatura en términos de optimalidad, a la vez que reflejan la efectividad de la metodología a propuesta para generar estimaciones rápidas. El segundo problema considera la optimización simultanea de transferencias entre órbitas terrestres que usan propulsión eléctrica, química o una combinación de ambas. En el primer paso del método de solución, la ley de control del motor eléctrico se parametriza por una función de Lyapunov. Un algoritmo de optimización heurístico y multi-objetivo selecciona el sistema propulsivo óptimo, el tipo de transferencia, la ley de control del motor de bajo empuje, así como el número, la orientación y la magnitud de los impulsos químicos. Se incluyen los efectos de la sombra y de la no esfericidad de la Tierra, además de la radiación de Van-Allen. En el segundo paso, las soluciones candidatas se usan como estimación inicial para resolver el problema de optimización no lineal que resulta de aplicar un método de transcripción directa. El método de solución propuesto se aplica a dos transferencias a GEO diferentes. Se obtienen soluciones óptimas de Pareto con respecto a la masa de combustible, el tiempo de vuelo y la degradación de las células solares. Se identifican que la aplicación de las restricciones operacionales penaliza mínimamente la función objetivo. Además, los análisis presentados destacan los beneficios que la propulsión química y eléctrica combinada proporcionarían a los satélites en GEO.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i Virgili.Presidente: Rafael Vázquez Valenzuela.- Secretario: Claudio Bombardelli.- Vocal: Bruce A. Conwa