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El brote actual de la enfermedad por coronavirus (COVID-19), que se informó por primera vez en Wuhan, China, el 31 de diciembre de 2019, ha dejado un saldo al 19 de abril de 2020 de más de 3500000 infectados y 160000 muertes en 185 países. En este trabajo utilizamos un modelo basado en el Método de Cadena Microscópica de Markov (MCMM, Markov Microscopic Chain Approach) para estimar la propagación del COVID-19 en la ciudad de Pereira (Risaralda-Colombia). Este modelo incorpora importantes aspectos de la población, relacionados con: ubicación espacial dentro de la ciudad discretizada por comunas, movilidad entre comunas, estratificación por grupos de edad y separación de individuos en siete compartimientos epidemiológicos. Este modelo se utiliza para predecir, en una línea de tiempo, la incidencia de epidemias en poblaciones geolocalizadas, lo que se traduce en una herramienta indicadora para tomar medidas de control. Así, el resultado de la metodología caracteriza la evolución en el tiempo y el espacio de la proporción de los individuos en cada uno de los compartimientos epidemiológicos y en cada grupo etario. Los datos que se refieren a COVID-19, desde la municipalidad de Pereira, hasta el 20 de abril de 2020, se utilizan para alimentar el modelo y obtener las proyecciones espacio-temporales. Los resultados presentados consideran múltiples escenarios de movilidad, de forma que el aplanamiento de las curvas de los diferentes compartimientos epidemiológicos pueda ser visualizados de acuerdo a diferentes estrategias de confinamiento. Por tratarse de un modelo espacio-temporal, los resultados del modelo pueden ser presentados fácilmente como mapas de calor sobre cada uno de los compartimientos epidemiológicos, a fin de facilitar los procesos de toma de decisiones.

El problema de programación de rutas en una empresa de transporte generalmente considera varios escenarios de distribución de bienes los cuales, a su vez, constituyen diferentes grados de complejidad en su programación. Un escenario común consiste en establecer la ruta más corta para la distribución de un conjunto de productos a través de un único vehículo. Sin embargo, existen escenarios mucho más complejos de modelar, en donde se consideran varios vehículos partiendo desde diferentes puntos a fin de distribuir los bienes a un conjunto amplio de clientes, ventanas de tiempo, entrega y recogida simultánea y entrega primero y recogida al regreso. En este libro se presenta un conjunto de problemáticas propias de la programación óptima de rutas, cuyos modelos han sido estudiados, definidos, propuestos y evaluados en el desarrollo del proyecto titulado: Herramienta computacional para la programación óptima de rutas en una empresa de transporte de carga, considerando diferentes estrategias de distribución de productos con código 6-19-5, realizado con el apoyo de la universidad Tecnológica de Pereira y su vicerrectoría de Investigaciones, Innovación y Extensión. Estos modelos son concatenados de forma pedagógica y gradual, con el objetivo de transitar fácilmente desde el modelo simple del TSP hasta el OLRP, pasando por el MTSP, CVRP y MCVRP. El aspecto pedagógico consiste en que la presentación de los problemas debe permitir apreciar el crecimiento gradual del modelo clásico del TSP, a través de restricciones, parámetros y variables adicionales, así como modificaciones a la función objetivo, hasta convertirse en los problemas subsecuentes. De esta forma, un estudiante de maestría, doctorado, o en general cualquier lector interesado, podría experimentar con la inclusión y exclusión de restricciones en el modelo para visualizar el impacto sobre los resultados obtenidos. The route scheduling problem in a transport company generally considers several goods distribution scenarios which, in turn, constitute different degrees of complexity in its programming. A common scenario is to establish the shortest route for the distribution of a set of products through a single vehicle. However, there are much more complex scenarios to model, where several vehicles departing from different points are considered in order to distribute the goods to a set of customers, time windows, simultaneous delivery and collection, and first delivery and return collection. This book presents a set of problems typical of optimal route scheduling, whose models have been studied, defined, proposed and evaluated in the development of the project entitled: Computational tool for optimal route scheduling in a freight transport company, considering different distribution strategies for products with code 6-19-5, carried out with the support of the Technological University of Pereira and its Vicerrectory for Research, Innovation and Extension. These models are concatenated in a pedagogical and gradual way, with the aim of moving easily from the simple model of the TSP to the OLRP, passing through the MTSP, CVRP and MCVRP. The pedagogical aspect is that the presentation of the problems should allow us to appreciate the gradual growth of the classic TSP model, through restrictions, parameters and additional variables, as well as modifications to the objective function, until it becomes the subsequent problems. In this way, a master's or doctoral student, or in general any interested reader, could experiment with the inclusion and exclusion of restrictions in the model to visualize the impact on the results obtained. CONTENIDO Introducción...................................................................................7 1 Problema del vendedor viajero...............................................15 1.1. Descripción formal del TSP...........................................17 1.2. Modelo con sub-tours ....................................................19 1.2.1. Implementación del TSP con sub-tours....................21 1.3. Modelos sin sub-tours....................................................28 1.3.1. TSP basado en flujo de vehículos...............................31 1.3.2. TSP basado en arborescencia .....................................35 1.3.3. TSP basado en flujo de mercancía .............................50 1.3.3.1. Abordaje de Miller, Tucker y Zemlin (MTZ) para representar el flujo de mercancía neta inyectada en el vértice i:...........51 1.3.3.2. Abordaje de Finke, Claus y Gunn (FCG) para representar el flujo de mercancía a trav´es del eje (i, j):......................................53 1.3.3.3. Abordaje de Baldacci, Hadjiconstantinou y Mingozzi (BHM) para representar los dos flujos en un mismo grafo orientado:......................................................................................56 2 Problema de múltiples vendedores viajeros..........................65 2.1. Descripción formal del MTSP.......................................66 2.2. MTSP basado en abordaje MTZ ...................................67 2.3. MTSP basado en arborescencia ....................................70 2.4. MTSP basado en el abordaje BHM...............................72 3 Problema de ruteo de vehículos con capacidad ...................79 3.1. Descripción formal del CVRP.......................................80 3.2. CVRP basado en arborescencia ....................................83 3.3. CVRP basado en el abordaje BHM...............................86 3.4. CVRP con ventanas de tiempo (abordaje BHM)........90 4 Problema de ruteo abierto considerando ubicación de depósitos.......................................................................................99 4.1. Descripción formal del OLRP.....................................101 4.2. OVRP multi-depósito...................................................109 4.3. MDOVRP con restricción de distancia......................109 5 Problema de ruteo de vehículos con recogida al regreso..119 5.1. Descripción formal del VRPB.....................................123 5.2. VRPB multi-depósito ...................................................132 5.3. Descripción formal del MDVRPB..............................134 6 Problema de ruteo de vehículos eléctricos con recogida al regreso.........................................................................................147 6.1. Formulación para el EVRPB........................................151 6.2. Metodología de inicialización para.............................161 obtener una soluci´on factible............................................161 6.2.1. Solución Básica Inicial...............................................163 6.2.2.1. Factibilidad de la ruta.............................................165 6.2.2.2. Construcción del grafo auxiliar ............................167 6.2.2.3. Factibilidad del SPP................................................169 6.2.3. Modelo matemático del SPP.....................................171 6.3. Búsqueda local Iterada .................................................171 6.3.1. Operadores de mejora ...............................................173 6.3.1.1. Operador de vecindad intra-ruta..........................174 6.3.1.2. Operador de vecindad inter-ruta..........................174 6.4. Resultados computacionales........................................175 Bibliografía .................................................................................179 Índice general.............................................................................184

Network operators work constantly to maintain an appropriate level of reliability in their power supply and to preserve the integrity of the vegetation growing underneath overhead power distribution systems. Accordingly, this article proposes and adopts different approaches to optimally manage vegetation maintenance in such field. Mathematical modeling is used to represent the problem in terms of several aspects involved in vegetation management, based on the technical capacity of the utility company and the reliability goals established by governmental regulatory entities. The solution is a vegetation maintenance schedule in terms of when, where, and which crews must perform the pruning activities along the distribution network. As a result, the Non-Served Energy Level NSEL is minimized and the financial resources earmarked for this type of maintenance tasks are optimized. Resumen Los operadores de red están constantemente trabajando en mantener un nivel de confiabilidad apropiado en el suministro de energía y preservar la integridad de la vegetación que crece bajo las redes aéreas de distribución de energía. Por tal razón, en este artículo se proponen e implementan diferentes alternativas para gestionar de manera óptima el mantenimiento de la vegetación. El problema se representa a través de modelamiento matemático, en función de varios aspectos enmarcados en el manejo de la flora, basados en la capacidad técnica de la empresa y las metas de confiabilidad estipuladas por los organismos gubernamentales. En la solución del problema, se obtiene un programa de mantenimiento de la vegetación en términos de cuándo y dónde se debe realizar éste, además de la asignación de los grupos de trabajo destinados para las labores de poda a lo largo del sistema de distribución. De esta manera, se minimiza el nivel de energía no servida y se optimizan los recursos financieros necesarios para este tipo de tareas.

In this article, a hybrid algorithm is proposed to solve the Vehicle Scheduling Problem with Multiple Depots. The proposed methodology uses a genetic algorithm, initialized with three specialized constructive procedures. The solution generated by this first approach is then refined by means of a Set Partitioning (SP) model, whose variables (columns) correspond to the current itineraries of the final population. The SP approach possibly improves the incumbent solution which is then provided as an initial point to a well-known MDVSP model. Both the SP and MDVSP models are solved with the help of a mixed integer programming (MIP) solver. The algorithm is tested in benchmark instances consisting of 2, 3 and 5 depots, and a service load ranging from 100 to 500. The results obtained showed that the proposed algorithm was capable of finding the optimal solution in most cases when considering a time limit of 500 seconds. The methodology is also applied to solve a real-life instance that arises in the transportation system in Colombia (2 depots and 719 services), resulting in a decrease of the required fleet size and a balanced allocation of services, thus reducing deadhead trips.

The vehicle routing problem combined with loading of goods, considering the reduction of fuel consumption, aims at finding the set of routes that will serve the demands of the customers, arguing that the fuel consumption is directly related to the weight of the load in the paths that compose the routes. This study integrates the Fuel Consumption Heterogeneous Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-FHFVRP). To reduce fuel consumption taking the associated environmental impact into account is a classical VRP variant that has gained increasing attention in the last decade. The objective of this problem is to design the delivery routes to satisfy the customers’ demands with the lowest possible fuel consumption, which depends on the distances of the paths, the assigned vehicles, the loading/unloading pattern and the load weight. In the vehicle routing problem literature, the approximate algorithms have had great success, especially the evolutionary ones, which appear in previous works with quite a sophisticated structure, obtaining excellent results, but that are difficult to implement and adapt to other variants such as the one proposed here. In this study, we present a specialized genetic algorithm to solve the design of routes, keeping its main characteristic: the easy implementation. By contrast, the loading of goods restriction is validated by means of a GRASP algorithm, which has been widely employed for solving packing problems. With a view of confirming the performance of the proposed methodology, we provide a computational study that uses all the available benchmark instances, allowing to illustrate the savings achieved in fuel consumption. In addition, the methodology suggested can be adapted to the version of solely minimizing the total distance traveled for serving the customers (without the fuel consumption) and it is compared to the best works presented in the literature. The computational results show that the methodology manages to be adequately adapted to this version and it is capable of finding improved solutions for some benchmark instances. As for future work, we propose to adjust the methodology to consider the three-dimensional loading problem so that it adapts to more real-life conditions of the industry.

In this paper, an optimization model for the Charging Station Location Problem of Electric Vehicles for Freight Transportation CSLP-EVFT is presented. This model aims to determine an optimal location strategy of Electric Vehicle Charging Stations EVCSs and the routing plan of a fleet of electric vehicles under battery driving range limitation, in conjunction with the impact on the power distribution system. Freight transportation is modeled under the mobility patterns followed by the Capacitated Vehicle Routing Problem CVRP for contracted fleet, and Shortest Path SP problem for subcontracted fleet. A linear formulation of the power flow is used in order to consider the impact on the electric grid. Several costs are examined, i.e., EVs routing, installation and energy consumption of EVCSs, and energy losses. Although uncertainties related to temporal variation of some aspects (number of customers and their demands, fleet size, power network nodes and routes) are not addressed, the proposed model represents a useful approach to evaluate multiple scenarios or to be introduced within stochastic optimization. Instead, the mathematical model is studied under the variation of EVs travel range that accounts for the advance of battery technology and sensitivity analysis. Additionally, the problem is reduced to a mixed integer non-linear mathematical model, which is linearized by using multivariable Taylor’s series.

The separate delivery and collection services of goods through different routes is an issue of current interest for some transportation companies by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to give greater priority to the delivery customers. In the vehicle routing problem with backhauls (VRPB), the customers are partitioned into two subsets: linehaul (delivery) and backhaul (pickup) customers. Additionally, a precedence constraint is established: the backhaul customers in a route should be visited after all the linehaul customers. The VRPB is presented in the literature as an extension of the capacitated vehicle routing problem and is NP-hard in the strong sense. In this paper, we propose a mixed integer linear programming formulation for the VRPB, based on the generalization of the open vehicle routing problem; that eliminates the possibility of generating solutions formed by subtours using a set of new constraints focused on obtaining valid solutions formed by Hamiltonian paths and connected by tie-arcs. The proposed formulation is a general purpose model in the sense that it does not deserve specifically tailored algorithmic approaches for their effective solution. The computational results show that the proposed compact formulation is competitive against state-of-the-art exact methods for VRPB instances from the literature.

Electric Vehicles (EVs) represent an option that contributes substantively to improve mobility and decrease pollution, generating great expectations for the future of transportation sector, with pilot projects of companies using EVs for delivering products. In this work, a novel approach for optimal planning of EVs for cargo transportation is presented, considering battery swap stations (BSSs) location and the impact on the power distribution network (PDN). This integrated planning is formulated through a mixed integer linear programming mathematical model. To evaluate the model performance three test systems of different sizes are proposed (considering transportation network and PDN). The results show a tradeoff between EVs routing, energy losses of PDN and BSSs location.

This paper proposes a metaheuristic algorithm to solve the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDHFVRP). The problem consists of determining the customers and the vehicles to be assigned to each used depot and the routes to be performed to fulfill the demands of a set of customers. The objective is to minimize the sum of the fixed cost associated with the used vehicles and of the variable traveling costs related to the performed routes. The proposed approach is based on a modified genetic algorithm, which generates an initial population with heuristic solutions obtained from the well-known (LKH) heuristic algorithm for the TSP together with the solution of a mathematical model for the shortest path problem. In addition, two recombination methods and a mutation operator are considered. Computational experiments on benchmark instances show that the proposed algorithm can obtain high-quality solutions within short computing times.

In this paper, the Multi-Depot Electric Vehicle Location Routing Problem with Time Windows (MDVLRP) is addressed. This problem is an extension of the MDVLRP, where electric vehicles are used instead of internal combustion engine vehicles. The recent development of this model is explained by the advantages of this technology, such as the diminution of carbon dioxide emissions, and the support that they can provide to the design of the logistic and energy-support structure of electric vehicle fleets. There are many models that extend the classical VRP model to take electric vehicles into consideration, but the multi-depot case for location-routing models has not been worked out yet. Moreover, we consider the availability of two energy supply technologies: the “Plug-in” Conventional Charge technology, and Battery Swapping Stations; options in which the recharging time is a function of the amount of energy to charge and a fixed time, respectively. Three models are proposed: one for each of the technologies mentioned above, and another in which both options are taken in consideration. The models were solved for small scale instances using C++ and Cplex 12.5. The results show that the models can be used to design logistic and energy-support structures, and compare the performance of the different options of energy supply, as well as measure the impact of these decisions on the overall distance traveled or other optimization objectives that could be worked on in the future.

In this paper, a heuristic algorithm based on Tabu Search Approach for solving the Vehicle Routing Problem with Backhauls (VRPB) is proposed. The problem considers a set of customers divided in two subsets: Linehaul and Backhaul customers. Each Linehaul customer requires the delivery of a given quantity of product from the depot, whereas a given quantity of product must be picked up from each Backhaul customer and transported to the depot. In the proposed algorithm, each route consists of one sub-route in which only the delivery task is done, and one sub-route in which only the collection process is performed. The search process allows obtaining a correct order to visit all the customers on each sub-route. In addition, the proposed algorithm determines the best connections among the sub-routes in order to obtain a global solution with the minimum traveling cost. The efficiency of the algorithm is evaluated on a set of benchmark instances taken from the literature. The results show that the computing times are greatly reduced with a high quality of solutions. Finally, conclusions and suggestions for future works are presented.

El sistema de suministro de energía eléctrica está conformado por varias etapas funcionales: generación, transmisión, subtransmisión y distribución de energía eléctrica. La generación transforma una forma de energía (hidráulica, térmica, solar, eólica, mareomotriz, etc.) en energía propiamente eléctrica. Esta es transportada a los centros de consumo a través de los sistemas de transmisión y subtransmisión; finalmente, los sistemas de distribución se encargan de llevar la energía eléctrica a todos los puntos de utilización con niveles de tensión adecuados. Las pérdidas técnicas en el sistema de distribución han representado históricamente un alto costo a los usuarios y a las empresas prestadoras del servicio. En general, el comercializador debe pagar al generador y al transmisor el total de la energía que ingresa a su sistema, aunque esta no sea facturada a los usuarios. No obstante, los usuarios pagan un valor adicional al asociado a su consumo, ya que la tarifa incluye costos de pérdidas reconocidas en generación, transmisión y distribución. Aunque los operadores de red tienen capacidad de gestión sobre las pérdidas técnicas, ya que son los encargados de la planeación y operación del sistema; no es económicamente viable diseñar un sistema con un porcentaje de pérdidas muy bajo, dado que eso implicaría niveles de inversión prohibitivos.

This paper introduces a new bi-objective vehicle routing problem that integrates the Open Location Routing Problem (OLRP), recently presented in the literature, coupled with the growing need for fuel consumption minimization, named Green OLRP (G-OLRP). Open routing problems (ORP) are known to be NP-hard problems, in which vehicles start from the set of existing depots and are not required to return to the starting depot after completing their service. The OLRP is a strategic-level problem involving the selection of one or many depots from a set of candidate locations and the planning of delivery radial routes from the selected depots to a set of customers. The concept of radial paths allows us to use a set of constraints focused on maintaining the radiality condition of the paths, which significantly simplifies the set of constraints associated with the connectivity and capacity requirements and provides a suitable alternative when compared with the elimination problem of sub-tours traditionally addressed in the literature. The emphasis in the paper will be placed on modeling rather than solution methods. The model proposed is formulated as a bi-objective problem, considering the minimization of operational costs and the minimization of environmental effects, and it is solved by using the epsilon constraint technique. The results illustrate that the proposed model is able to generate a set of trade-off solutions leading to interesting conclusions about the relationship between operational costs and environmental impact.

This paper presents a multiobjective ant colony algorithm for the Multi-Depot Vehicle Routing Problem with Backhauls (MDVRPB) where three objectives of traveled distance, traveling times and total consumption of energy are minimized. An ant colony algorithm is proposed to solve the MDVRPB. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. The effectiveness of the proposed approach is examined by considering a set of instances adapted from the literature. The computational results show high quality results within short computing times.

Made available in DSpace on 2022-04-29T07:11:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-06-01 In this paper, an approach for probabilistic analysis of unbalanced three-phase weakly meshed distribution systems with dispersed generation is presented. The approach considers uncertainty in both load demand and the injected power of dispersed generators. In order to achieve high computational efficiency, the approach makes use of both an efficient method for probabilistic analysis and a radial power flow. The probabilistic strategy used is the well-known Three-Point Estimate Method. In the other hand, classical models based on the sequence impedance are implemented for modeling synchronous machines, asynchronous machines, and electronically interfaced sources. These models aim to consider the impact on the power flows from the installation of dispersed generators. A small-size test system, as well as the modified IEEE 123 bus system, is used to show the operation and effectiveness of the proposed approach. A Monte Carlo Simulations method is used to validate the results. © 2013 Brazilian Society for Automatics - SBA. Laboratório de Planejamento de Energia Elétrica Departamento de Engenharia Elétrica Universidade Estadual Paulista - Campus de Ilha Solteira, Ilha Solteira, SP Programa de Ingeniería Eléctrica Grupo de Planeamiento Eléctrico Universidad Tecnológica de Pereira, Pereira Risaralda Laboratório de Planejamento de Energia Elétrica Departamento de Engenharia Elétrica Universidade Estadual Paulista - Campus de Ilha Solteira, Ilha Solteira, SP

In this article a methodology to resolve the problem of optimal location of reclosers and fuses in power electric distribution systems is presented, to improve reliability indices associated to the periodicity of the transient and permanent failures in the distribution systems. To formulate the problem, two non-linear binary mathematical models are posed that consider the location of reclosers and fuses under two scenarios of coordination, denominated “fuse save scheme” and “fuse blow scheme”. The first model minimizes SAIFI index, and the second model minimizes MAIFI index. The set of constraints is the same for both models, which considers technical and operative characteristics. As solution strategy a methodology is proposed, which considers two different schemes of solution: the first scheme uses the commercial optimizer GAMS and the second scheme uses as solution technique a Chu & Beasley genetic algorithm (CBGA). In order to verify the validity of both strategies, these are executed in two tests systems from the specialized literature, comparing the results obtained. En este artículo se presenta una metodología para resolver el problema de localización óptima de reconectadores y fusibles en sistemas de distribución de energía, para mejorar indicadores de confiabilidad asociados a la frecuencia con la que inciden las fallas transitorias y permanentes en los sistemas de distribución. Para formular el problema se plantean dos modelos matemáticos no lineales de tipo binario que consideran la ubicación de reconectadores y fusibles bajo dos escenarios de coordinación, denominados fuse save scheme y fuse blow scheme. El primer modelo minimiza el índice SAIFI y el segundo minimiza el índice MAIFI. El conjunto de restricciones es el mismo para ambos modelos, el cual considera características técnicas y operativas. Como estrategia de solución se propone una metodología que considera dos esquemas diferentes de solución: la primera emplea el optimizador comercial GAMS y la segunda usa como técnica de solución un algoritmo genético de Chu & Beasley (AGCB). Con el fin de verificar la validez de ambas estrategias, estas son aplicadas a dos sistemas de prueba de la literatura especializada, comparando los resultados obtenidos.

Los sistemas de distribución operan de forma desbalanceada debido a sus características de configuración y naturaleza de sus cargas. Es aconsejable disminuir este desbalance ya que una operación en estas condiciones presenta un mayor nivel de pérdidas a las obtenidas en un sistema balanceado. En este documento, se presenta una aplicación de la metodología de colonia de hormigas al problema de balance de fases mostrando sus principales características y resolviendo un ejemplo de prueba.

Este artículo propone un Método de Optimización por Colonia de Hormigas para resolver el sub-problema de inversión existente dentro del Problema de Planeamiento de la Expansión de la Transmisión de Sistemas Eléctricos de Potencia. El problema operativo de Programación Lineal es resuelto mediante un Método de Puntos Interiores de Alto Orden. Adicionalmente, se implementa otro Método de Puntos Interiores para Programación No Lineal cuya solución relajada es usada como índice de sensibilidad asociado a la escogencia de una línea candidata. Estos índices de sensibilidad son calculados una única vez durante todo el proceso iterativo. Adicionalmente, dentro del Algoritmo de Optimización por Colonia de Hormigas, se propone un método de dos etapas para la construcción de una alternativa de solución. La metodología propuesta se valida con los sistemas de prueba IEEE de 24 y 6 nodos./This paper proposes an Ant Colony Optimization method to solve the investment problem for the Transmission Expansion Planning Problem for Electrical Power Systems. Operative problem of Linear Programming is solved trough a High Order Interior Point Method. Moreover, the solution of a Non Linear Interior Point Method is used as a sensitivity index to initialize pheromone matrix used in the Ant Colony Algorithm, where is proposed a method with two stages to obtain a solution. The methodology is tested on the 24 and 6 Bus IEEE systems.

This paper presents a hybrid algorithm for solving the Capacitated Vehicle Routing Problem with practical three-dimensional loading constraint. This problem is known as 3L-CVRP (Three-dimensional Loading Capacitated Vehicle Routing Problem). The proposed methodology consists of two phases. The first phase uses an optimization procedure based on cuts to obtain solutions for the well-known Capacitated Vehicle Routing Problem (CVRP). The second phase validates the results of the first phase of a GRASP algorithm (Greedy Randomized Adaptive Search Procedure). In particular, the GRASP approach evaluates the packing constraints for each performed route of the CVRP. The proposed hybrid algorithm uses a relaxation of the classical model of two sub-indices for the vehicle routing problem. Specifically different types of cuts are added: subtour elimination, capacity-cut constraints, and packing-cut constrains. The proposed algorithm is compared with the most efficient approaches for the 3L-CVRP on the set of benchmark instances considered in the literature. The computational results indicate that the proposed approach is able to obtain good solutions, improving some of the best-known solutions from the literature.

Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-27T11:26:24Z No. of bitstreams: 0Bitstream added on 2014-05-27T14:42:09Z : No. of bitstreams: 1 2-s2.0-84863461361.pdf: 579888 bytes, checksum: 37e18b612ffbf0c9c03741dcf6fed876 (MD5) Made available in DSpace on 2014-05-27T11:26:24Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-03-01 In this paper the point estimation method is applied to solve the probabilistic power flow problem for unbalanced three-phase distribution systems. Through the implementation of this method the probability distribution functions of voltages (magnitude and angle) as well as the active and reactive power flows in the branches of the distribution system are determined. Two different approaches of the point estimation method are presented (2m and 2m+1 point schemes). In order to test the proposed methodology, the IEEE 34 and 123 bus test systems are used. The results obtained with both schemes are compared with the ones obtained by a Monte Carlo Simulation (MCS). Universidade Estadual Paulista Departamento de Engenharia Elétrica Laboratório de Planejamento de Energia Elétrica, Campus de Ilha Solteira, Ilha Solteira, SP Universidad Tecnológica de Pereira Programa de Ingeniería Eléctrica Grupo de Planeamiento Eléctrico, Pereira, Risaralda Universidade Estadual Paulista Departamento de Engenharia Elétrica Laboratório de Planejamento de Energia Elétrica, Campus de Ilha Solteira, Ilha Solteira, SP

La operacíon segura del sistema de potencia es una tarea difícil para el operador del sistema, el cual es responsable por la coordinación, control y monitoreo de este. En la mayoría de los sistemas de potencia, la seguridad es manejada mediante una metodología multi–etapa. En este caso, los criterios de seguridad son incorporados mediante restricciones adicionales que modifican el cálculo de despacho inicial. En este artículo se presenta un modelo de despacho de generación para mercados eléctricos competitivos considerando restricciones de seguridad. La metodología propuesta combina el despacho de generación de mercados pool y contratos bilaterales con flujos de potencia óptimos post–contingencia acoplados en un solo modelo de despacho, lo cual evita ineficiencias económicas que aparecen en los despachos convencionales multi–etapa. El modelo propuesto es lineal, y como tal, se basa en el modelo DC de la red. Un sistema didáctico de seis barras y el sistema IEEE RTS–24 son utilizados para ilustrar la operación y efectividad de la metodología propuesta y para compararlo con el despacho pool/bilateral básico sin restricciones de seguridad. Los resultados muestran que la inclusión de restricciones de seguridad lleva a un despacho más costoso. Por otra parte, se encontró que la ejecución de contratos bilaterales firmes puede llevar a problemas de congestión en el sistema. PACS. 88.80.H-, 88.50.Mp, 88.05.Lg

This paper presents a hybrid algorithm for solving the Capacitated Vehicle Routing Problem with practical three-dimensional loading constraint. This problem is known as 3L-CVRP (Three-dimensional Loading Capacitated Vehicle Routing Problem). The proposed methodology consists of two phases. The first phase uses an optimization procedure based on cuts to obtain solutions for the well-known Capacitated Vehicle Routing Problem (CVRP). The second phase validates the results of the first phase of a GRASP algorithm (Greedy Randomized Adaptive Search Procedure). In particular, the GRASP approach evaluates the packing constraints for each performed route of the CVRP. The proposed hybrid algorithm uses a relaxation of the classical model of two sub-indices for the vehicle routing problem. Specifically different types of cuts are added: subtour elimination, capacity-cut constraints, and packing-cut constrains. The proposed algorithm is compared with the most efficient approaches for the 3L-CVRP on the set of benchmark instances considered in the literature. The computational results indicate that the proposed approach is able to obtain good solutions, improving some of the best-known solutions from the literature.

Nesta dissertação apresenta-se um novo modelo de programação linear inteira mista, para avaliar as estratégias de planejamento no sistema de distribuição de energia elétrica (SDEE). Estas estratégias envolvem o recondutoramento e seleção de condutores nos ramos, instalação e alocação de geradores distribuídos (GDs), capacitoresfixos e/ou chaveados. O objetivo é minimizar os custos de investimento e operação relacionados com o SDEE, tais como: custo de aquisição dos tipos de condutores, GDs, capacitores fixos e chaveados, além dos custos de operação advindos da energia gerada pelos GDs e pelas perdas de energia nos condutores ao longo do SDEE durante um determinado horizonte de períodos. No modelo proposto, o cálculo do ponto de operação em regime permanente é formulado através de um conjunto de restrições lineares relacionadas com o balanço de potência ativa, reativa, queda de tensão, e limites de corrente e tensão. Um conjunto de técnicas de linearização é empregada para desenvolver este modelo linear. Os resultados obtidos pela formulação matemática indicam redução das perdas de potência ativa, e incremento dos níveis de tensão. O modelo é solucionado através de ferramentas de otimização clássicas, garantindo a convergência para a solução ótima. O modelo proposto foi implementado no AMPL (A Modeling Language for Mathematical Programming) e resolvido utilizando o solver comercial CPLEX. Na validação da metodologia, os sistemas 27 e 136 nós foram testados. In this dissertation, a new mixed integer linear programming model is presented to evaluate planning strategies in the electric distribution system (EDS). These strategies involve the reconductoring and selection of conductors in the branches, installation and allocation of distributed generators (DGs), fixed and/or switched capacitors. The objective is to minimize investment and operating costs related to EDS, such as: cost of acquisition types of conductors, DGs, fixed and switched capacitors, as well as the operating costs arising from the energy generated by the DGs and the energy losses in the conductors throughout the EDS for one horizon of periods. In the proposed model, the calculation of the operating point in steady state is formulated through a set of linear constraints related to the active, reactive power balance, voltage drop, and current and voltage limits. A set of linearization techniques is employed to develop this linear model. The results obtained by the mathematical formulation indicate reduction of the losses of active power, and increase of the voltage levels. The model is solved through classic optimization tools, guaranteeing convergence to the optimal solution. The proposed model was implemented in AMPL (A Modeling Language for Mathematical Programming) and solved using the CPLEX commercial solver. In the validation of the methodology, the systems 27 and 136 nodes were tested.