Propostas de modelagem matemática para o problema de restauração de sistemas de distribuição de energia elétrica radiais

Pós-graduação em Engenharia Elétrica - FEIS

Algoritmo tabu search especializado para o problema de planejamento da expansao de sistemas de transmissão

Pós-graduação em Engenharia Elétrica - FEIS

Reconfiguração de sistemas de distribuição operando em vários níveis de demanda através de uma meta-heurística de busca em vizinhança variável

Pós-graduação em Engenharia Elétrica - FEIS

A comparison about evolutionary algorithms for optimum-path forest clustering optimization

In this paper we deal with the problem of boosting the Optimum-Path Forest (OPF) clustering approach using evolutionary-based optimization techniques. As the OPF classifier performs an exhaustive search to find out the size of sample's neighborhood that allows it to reach the minimum graph cut as a quality measure, we compared several optimization techniques that can obtain close graph cut values to the ones obtained by brute force. Experiments in two public datasets in the context of unsupervised network intrusion detection have showed the evolutionary optimization techniques can find suitable values for the neighborhood faster than the exhaustive search. Additionally, we have showed that it is not necessary to employ many agents for such task, since the neighborhood size is defined by discrete values, with constrain the set of possible solution to a few ones.

A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.

New Optimization Algorithms for Structural Reliability Analysis

Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.

Analog circuit synthesis performing fast Pareto frontier exploration and analysis through 3D graphs

This paper presents a technique for performing analog design synthesis at circuit level providing feedback to the designer through the exploration of the Pareto frontier. A modified simulated annealing which is able to perform crossover with past anchor points when a local minimum is found which is used as the optimization algorithm on the initial synthesis procedure. After all specifications are met, the algorithm searches for the extreme points of the Pareto frontier in order to obtain a non-exhaustive exploration of the Pareto front. Finally, multi-objective particle swarm optimization is used to spread the results and to find a more accurate frontier. Piecewise linear functions are used as single-objective cost functions to produce a smooth and equal convergence of all measurements to the desired specifications during the composition of the aggregate objective function. To verify the presented technique two circuits were designed, which are: a Miller amplifier with 96 dB Voltage gain, 15.48 MHz unity gain frequency, slew rate of 19.2 V/mu s with a current supply of 385.15 mu A, and a complementary folded cascode with 104.25 dB Voltage gain, 18.15 MHz of unity gain frequency and a slew rate of 13.370 MV/mu s. These circuits were synthesized using a 0.35 mu m technology. The results show that the method provides a fast approach for good solutions using the modified SA and further good Pareto front exploration through its connection to the particle swarm optimization algorithm.

Evaluation of a multi variated analysis for the selection of t-tbar multijet events in the current CMS implemented environment at LHC

In the present study we are using multi variate analysis techniques to discriminate signal from background in the fully hadronic decay channel of ttbar events. We give a brief introduction to the role of the Top quark in the standard model and a general description of the CMS Experiment at LHC. We have used the CMS experiment computing and software infrastructure to generate and prepare the data samples used in this analysis. We tested the performance of three different classifiers applied to our data samples and used the selection obtained with the Multi Layer Perceptron classifier to give an estimation of the statistical and systematical uncertainty on the cross section measurement.

Metodi di ottimizzazione morfologica nel progetto preliminare di propulsori aeronautici avanzati

The aim of this Doctoral Thesis is to develop a genetic algorithm based optimization methods to find the best conceptual design architecture of an aero-piston-engine, for given design specifications. Nowadays, the conceptual design of turbine airplanes starts with the aircraft specifications, then the most suited turbofan or turbo propeller for the specific application is chosen. In the aeronautical piston engines field, which has been dormant for several decades, as interest shifted towards turboaircraft, new materials with increased performance and properties have opened new possibilities for development. Moreover, the engine’s modularity given by the cylinder unit, makes it possible to design a specific engine for a given application. In many real engineering problems the amount of design variables may be very high, characterized by several non-linearities needed to describe the behaviour of the phenomena. In this case the objective function has many local extremes, but the designer is usually interested in the global one. The stochastic and the evolutionary optimization techniques, such as the genetic algorithms method, may offer reliable solutions to the design problems, within acceptable computational time. The optimization algorithm developed here can be employed in the first phase of the preliminary project of an aeronautical piston engine design. It’s a mono-objective genetic algorithm, which, starting from the given design specifications, finds the engine propulsive system configuration which possesses minimum mass while satisfying the geometrical, structural and performance constraints. The algorithm reads the project specifications as input data, namely the maximum values of crankshaft and propeller shaft speed and the maximal pressure value in the combustion chamber. The design variables bounds, that describe the solution domain from the geometrical point of view, are introduced too. In the Matlab® Optimization environment the objective function to be minimized is defined as the sum of the masses of the engine propulsive components. Each individual that is generated by the genetic algorithm is the assembly of the flywheel, the vibration damper and so many pistons, connecting rods, cranks, as the number of the cylinders. The fitness is evaluated for each individual of the population, then the rules of the genetic operators are applied, such as reproduction, mutation, selection, crossover. In the reproduction step the elitist method is applied, in order to save the fittest individuals from a contingent mutation and recombination disruption, making it undamaged survive until the next generation. Finally, as the best individual is found, the optimal dimensions values of the components are saved to an Excel® file, in order to build a CAD-automatic-3D-model for each component of the propulsive system, having a direct pre-visualization of the final product, still in the engine’s preliminary project design phase. With the purpose of showing the performance of the algorithm and validating this optimization method, an actual engine is taken, as a case study: it’s the 1900 JTD Fiat Avio, 4 cylinders, 4T, Diesel. Many verifications are made on the mechanical components of the engine, in order to test their feasibility and to decide their survival through generations. A system of inequalities is used to describe the non-linear relations between the design variables, and is used for components checking for static and dynamic loads configurations. The design variables geometrical boundaries are taken from actual engines data and similar design cases. Among the many simulations run for algorithm testing, twelve of them have been chosen as representative of the distribution of the individuals. Then, as an example, for each simulation, the corresponding 3D models of the crankshaft and the connecting rod, have been automatically built. In spite of morphological differences among the component the mass is almost the same. The results show a significant mass reduction (almost 20% for the crankshaft) in comparison to the original configuration, and an acceptable robustness of the method have been shown. The algorithm here developed is shown to be a valid method for an aeronautical-piston-engine preliminary project design optimization. In particular the procedure is able to analyze quite a wide range of design solutions, rejecting the ones that cannot fulfill the feasibility design specifications. This optimization algorithm could increase the aeronautical-piston-engine development, speeding up the production rate and joining modern computation performances and technological awareness to the long lasting traditional design experiences.

Models and Algorihtm for the Optimization of Real-World Routing and Logistics Problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.

Service level agreements-driven management of distributed applications in cloud computing environments

Advancements in cloud computing have enabled the proliferation of distributed applications, which require management and control of multiple services. However, without an efficient mechanism for scaling services in response to changing workload conditions, such as number of connected users, application performance might suffer, leading to violations of Service Level Agreements (SLA) and possible inefficient use of hardware resources. Combining dynamic application requirements with the increased use of virtualised computing resources creates a challenging resource Management context for application and cloud-infrastructure owners. In such complex environments, business entities use SLAs as a means for specifying quantitative and qualitative requirements of services. There are several challenges in running distributed enterprise applications in cloud environments, ranging from the instantiation of service VMs in the correct order using an adequate quantity of computing resources, to adapting the number of running services in response to varying external loads, such as number of users. The application owner is interested in finding the optimum amount of computing and network resources to use for ensuring that the performance requirements of all her/his applications are met. She/he is also interested in appropriately scaling the distributed services so that application performance guarantees are maintained even under dynamic workload conditions. Similarly, the infrastructure Providers are interested in optimally provisioning the virtual resources onto the available physical infrastructure so that her/his operational costs are minimized, while maximizing the performance of tenants’ applications. Motivated by the complexities associated with the management and scaling of distributed applications, while satisfying multiple objectives (related to both consumers and providers of cloud resources), this thesis proposes a cloud resource management platform able to dynamically provision and coordinate the various lifecycle actions on both virtual and physical cloud resources using semantically enriched SLAs. The system focuses on dynamic sizing (scaling) of virtual infrastructures composed of virtual machines (VM) bounded application services. We describe several algorithms for adapting the number of VMs allocated to the distributed application in response to changing workload conditions, based on SLA-defined performance guarantees. We also present a framework for dynamic composition of scaling rules for distributed service, which used benchmark-generated application Monitoring traces. We show how these scaling rules can be combined and included into semantic SLAs for controlling allocation of services. We also provide a detailed description of the multi-objective infrastructure resource allocation problem and various approaches to satisfying this problem. We present a resource management system based on a genetic algorithm, which performs allocation of virtual resources, while considering the optimization of multiple criteria. We prove that our approach significantly outperforms reactive VM-scaling algorithms as well as heuristic-based VM-allocation approaches.

Towards description and optimization of abstract machines in an extension of prolog

Competitive abstract machines for Prolog are usually large, intricate, and incorpórate sophisticated optimizations. This makes them difñcult to code, optimize, and, especially, maintain and extend. This is partly due to the fact that efñciency considerations make it necessary to use low-level languages in their implementation. Writing the abstract machine (and ancillary code) in a higher-level language can help harness this inherent complexity. In this paper we show how the semantics of basic components of an efficient virtual machine for Prolog can be described using (a variant of) Prolog which retains much of its semantics. These descriptions are then compiled to C and assembled to build a complete bytecode emulator. Thanks to the high level of the language used and its closeness to Prolog the abstract machine descriptions can be manipulated using standard Prolog compilation and optimization techniques with relative ease. We also show how, by applying program transformations selectively, we obtain abstract machine implementations whose performance can match and even exceed that of highly-tuned, hand-crafted emulators.

Wavelet-based image fusion in multi-view three-dimensional microscopy

Multi-view microscopy techniques such as Light-Sheet Fluorescence Microscopy (LSFM) are powerful tools for 3D + time studies of live embryos in developmental biology. The sample is imaged from several points of view, acquiring a set of 3D views that are then combined or fused in order to overcome their individual limitations. Views fusion is still an open problem despite recent contributions in the field. We developed a wavelet-based multi-view fusion method that, due to wavelet decomposition properties, is able to combine the complementary directional information from all available views into a single volume. Our method is demonstrated on LSFM acquisitions from live sea urchin and zebrafish embryos. The fusion results show improved overall contrast and details when compared with any of the acquired volumes. The proposed method does not need knowledge of the system's point spread function (PSF) and performs better than other existing PSF independent fusion methods.

Optical systems design using the SMS method and optimizations

Resumen El diseño de sistemas ópticos, entendido como un arte por algunos, como una ciencia por otros, se ha realizado durante siglos. Desde los egipcios hasta nuestros días los sistemas de formación de imagen han ido evolucionando así como las técnicas de diseño asociadas. Sin embargo ha sido en los últimos 50 años cuando las técnicas de diseño han experimentado su mayor desarrollo y evolución, debido, en parte, a la aparición de nuevas técnicas de fabricación y al desarrollo de ordenadores cada vez más potentes que han permitido el cálculo y análisis del trazado de rayos a través de los sistemas ópticos de forma rápida y eficiente. Esto ha propiciado que el diseño de sistemas ópticos evolucione desde los diseños desarrollados únicamente a partir de la óptica paraxial hasta lo modernos diseños realizados mediante la utilización de diferentes técnicas de optimización multiparamétrica. El principal problema con el que se encuentra el diseñador es que las diferentes técnicas de optimización necesitan partir de un diseño inicial el cual puede fijar las posibles soluciones. Dicho de otra forma, si el punto de inicio está lejos del mínimo global, o diseño óptimo para las condiciones establecidas, el diseño final puede ser un mínimo local cerca del punto de inicio y lejos del mínimo global. Este tipo de problemática ha llevado al desarrollo de sistemas globales de optimización que cada vez sean menos sensibles al punto de inicio de la optimización. Aunque si bien es cierto que es posible obtener buenos diseños a partir de este tipo de técnicas, se requiere de muchos intentos hasta llegar a la solución deseada, habiendo un entorno de incertidumbre durante todo el proceso, puesto que no está asegurado el que se llegue a la solución óptima. El método de las Superficies Múltiples Simultaneas (SMS), que nació como una herramienta de cálculo de concentradores anidólicos, se ha demostrado como una herramienta también capaz utilizarse para el diseño de sistemas ópticos formadores de imagen, aunque hasta la fecha se ha utilizado para el diseño puntual de sistemas de formación de imagen. Esta tesis tiene por objeto presentar el SMS como un método que puede ser utilizado de forma general para el diseño de cualquier sistema óptico de focal fija o v afocal con un aumento definido así como una herramienta que puede industrializarse para ayudar al diseñador a afrontar de forma sencilla el diseño de sistemas ópticos complejos. Esta tesis está estructurada en cinco capítulos: El capítulo 1, es un capítulo de fundamentos donde se presentan los conceptos fundamentales necesarios para que el lector, aunque no posea una gran base en óptica formadora de imagen, pueda entender los planteamientos y resultados que se presentan en el resto de capítulos El capitulo 2 aborda el problema de la optimización de sistemas ópticos, donde se presenta el método SMS como una herramienta idónea para obtener un punto de partida para el proceso de optimización. Mediante un ejemplo aplicado se demuestra la importancia del punto de partida utilizado en la solución final encontrada. Además en este capítulo se presentan diferentes técnicas que permiten la interpolación y optimización de las superficies obtenidas a partir de la aplicación del SMS. Aunque en esta tesis se trabajará únicamente utilizando el SMS2D, se presenta además un método para la interpolación y optimización de las nubes de puntos obtenidas a partir del SMS3D basado en funciones de base radial (RBF). En el capítulo 3 se presenta el diseño, fabricación y medidas de un objetivo catadióptrico panorámico diseñado para trabajar en la banda del infrarrojo lejano (8-12 μm) para aplicaciones de vigilancia perimetral. El objetivo presentado se diseña utilizando el método SMS para tres frentes de onda de entrada utilizando cuatro superficies. La potencia del método de diseño utilizado se hace evidente en la sencillez con la que este complejo sistema se diseña. Las imágenes presentadas demuestran cómo el prototipo desarrollado cumple a la perfección su propósito. El capítulo 4 aborda el problema del diseño de sistemas ópticos ultra compactos, se introduce el concepto de sistemas multicanal, como aquellos sistemas ópticos compuestos por una serie de canales que trabajan en paralelo. Este tipo de sistemas resultan particularmente idóneos para él diseño de sistemas afocales. Se presentan estrategias de diseño para sistemas multicanal tanto monocromáticos como policromáticos. Utilizando la novedosa técnica de diseño que en este capítulo se presenta el diseño de un telescopio de seis aumentos y medio. En el capítulo 5 se presenta una generalización del método SMS para rayos meridianos. En este capítulo se presenta el algoritmo que debe utilizarse para el diseño de cualquier sistema óptico de focal fija. La denominada optimización fase 1 se vi introduce en el algoritmo presentado de forma que mediante el cambio de las condiciones iníciales del diseño SMS que, aunque el diseño se realice para rayos meridianos, los rayos skew tengan un comportamiento similar. Para probar la potencia del algoritmo desarrollado se presenta un conjunto de diseños con diferente número de superficies. La estabilidad y potencia del algoritmo se hace evidente al conseguirse por primera vez el diseño de un sistema de seis superficies diseñado por SMS. vii Abstract The design of optical systems, considered an art by some and a science by others, has been developed for centuries. Imaging optical systems have been evolving since Ancient Egyptian times, as have design techniques. Nevertheless, the most important developments in design techniques have taken place over the past 50 years, in part due to the advances in manufacturing techniques and the development of increasingly powerful computers, which have enabled the fast and efficient calculation and analysis of ray tracing through optical systems. This has led to the design of optical systems evolving from designs developed solely from paraxial optics to modern designs created by using different multiparametric optimization techniques. The main problem the designer faces is that the different optimization techniques require an initial design which can set possible solutions as a starting point. In other words, if the starting point is far from the global minimum or optimal design for the set conditions, the final design may be a local minimum close to the starting point and far from the global minimum. This type of problem has led to the development of global optimization systems which are increasingly less sensitive to the starting point of the optimization process. Even though it is possible to obtain good designs from these types of techniques, many attempts are necessary to reach the desired solution. This is because of the uncertain environment due to the fact that there is no guarantee that the optimal solution will be obtained. The Simultaneous Multiple Surfaces (SMS) method, designed as a tool to calculate anidolic concentrators, has also proved useful for the design of image-forming optical systems, although until now it has occasionally been used for the design of imaging systems. This thesis aims to present the SMS method as a technique that can be used in general for the design of any optical system, whether with a fixed focal or an afocal with a defined magnification, and also as a tool that can be commercialized to help designers in the design of complex optical systems. The thesis is divided into five chapters. Chapter 1 establishes the basics by presenting the fundamental concepts which the reader needs to acquire, even if he/she doesn‟t have extensive knowledge in the field viii of image-forming optics, in order to understand the steps taken and the results obtained in the following chapters. Chapter 2 addresses the problem of optimizing optical systems. Here the SMS method is presented as an ideal tool to obtain a starting point for the optimization process. The importance of the starting point for the final solution is demonstrated through an example. Additionally, this chapter introduces various techniques for the interpolation and optimization of the surfaces obtained through the application of the SMS method. Even though in this thesis only the SMS2D method is used, we present a method for the interpolation and optimization of clouds of points obtained though the SMS3D method, based on radial basis functions (RBF). Chapter 3 presents the design, manufacturing and measurement processes of a catadioptric panoramic lens designed to work in the Long Wavelength Infrared (LWIR) (8-12 microns) for perimeter surveillance applications. The lens presented is designed by using the SMS method for three input wavefronts using four surfaces. The powerfulness of the design method used is revealed through the ease with which this complex system is designed. The images presented show how the prototype perfectly fulfills its purpose. Chapter 4 addresses the problem of designing ultra-compact optical systems. The concept of multi-channel systems, such as optical systems composed of a series of channels that work in parallel, is introduced. Such systems are especially suitable for the design of afocal systems. We present design strategies for multichannel systems, both monochromatic and polychromatic. A telescope designed with a magnification of six-and-a-half through the innovative technique exposed in this chapter is presented. Chapter 5 presents a generalization of the SMS method for meridian rays. The algorithm to be used for the design of any fixed focal optics is revealed. The optimization known as phase 1 optimization is inserted into the algorithm so that, by changing the initial conditions of the SMS design, the skew rays have a similar behavior, despite the design being carried out for meridian rays. To test the power of the developed algorithm, a set of designs with a different number of surfaces is presented. The stability and strength of the algorithm become apparent when the first design of a system with six surfaces if obtained through the SMS method.

Robustness and Recoverability in Transport Logistics

Abstract Transport is the foundation of any economy: it boosts economic growth, creates wealth, enhances trade, geographical accessibility and the mobility of people. Transport is also a key ingredient for a high quality of life, making places accessible and bringing people together. The future prosperity of our world will depend on the ability of all of its regions to remain fully and competitively integrated in the world economy. Efficient transport is vital in making this happen. Operations research can help in efficiently planning the design and operating transport systems. Planning and operational processes are fields that are rich in combinatorial optimization problems. These problems can be analyzed and solved through the application of mathematical models and optimization techniques, which may lead to an improvement in the performance of the transport system, as well as to a reduction in the time required for solving these problems. The latter aspect is important, because it increases the flexibility of the system: the system can adapt in a faster way to changes in the environment (i.e.: weather conditions, crew illness, failures, etc.). These disturbing changes (called disruptions) often enforce the schedule to be adapted. The direct consequences are delays and cancellations, implying many schedule adjustments and huge costs. Consequently, robust schedules and recovery plans must be developed in order to fight against disruptions. This dissertation makes contributions to two different fields: rail and air applications. Robust planning and recovery methods are presented. In the field of railway transport we develop several mathematical models which answer to RENFE’s (the major railway operator in Spain) needs: 1. We study the rolling stock assignment problem: here, we introduce some robust aspects in order to ameliorate some operations which are likely to fail. Once the rolling stock assignment is known, we propose a robust routing model which aims at identifying the train units’ sequences while minimizing the expected delays and human resources needed to perform the sequences. 2. It is widely accepted that the sequential solving approach produces solutions that are not global optima. Therefore, we develop an integrated and robust model to determine the train schedule and rolling stock assignment. We also propose an integrated model to study the rolling stock circulations. Circulations are determined by the rolling stock assignment and routing of the train units. 3. Although our aim is to develop robust plans, disruptions will be likely to occur and recovery methods will be needed. Therefore, we propose a recovery method which aims to recover the train schedule and rolling stock assignment in an integrated fashion all while considering the passenger demand. In the field of air transport we develop several mathematical models which answer to IBERIA’s (the major airline in Spain) needs: 1. We look at the airline-scheduling problem and develop an integrated approach that optimizes schedule design, fleet assignment and passenger use so as to reduce costs and create fewer incompatibilities between decisions. Robust itineraries are created to ameliorate misconnected passengers. 2. Air transport operators are continuously facing competition from other air operators and different modes of transport (e.g., High Speed Rail). Consequently, airline profitability is critically influenced by the airline’s ability to estimate passenger demands and construct profitable flight schedules. We consider multi-modal competition including airline and rail, and develop a new approach that estimates the demand associated with a given schedule; and generates airline schedules and fleet assignments using an integrated schedule design and fleet assignment optimization model that captures the impacts of schedule decisions on passenger demand.