[pt] Seja G= (V, E) um grafo não-orientado com custos não- negativos em suas arestas e D um conjunto de pares origem - destino. Um 2-caminho entre nós (s,t)é um caminho de s a t formado por , no máximo, 2 arestas. O problema de síntese de redes com 2-caminhos (2PNDP) consiste em encontrar um subconjunto de arestas com custo mínimo que contenha um 2- caminho entre as extremidades dea cada para origem- destino pertencente a D. Apicações deste problema encontram-se no projeto de redes de comunicação, onde caminhos com poucas arestas são desejáveis para garantir alta confiabilidade e pequenos atrasos. A metaheurística GRASP é um processo multipartida para resolver problemas combinatórios, cujas iterações consistem de duas fases, uma fase de construção e outra de busca local. O algoritmo retorna a melhor solução encontrada depois de um número determinado de iterações.Aplica-se a técnica de reconexão por caminhos ao final de cada iteração GRASP para melhorar a qualidade das soluções. Implementações paralelas de metaheurística são muito robustas. A maior parte das implementações paralelas da metaheurística GRASP segue uma estratégia do tipo independente , baseada na distribuição balanceada das iterações pelos processadores. No caso de estratégias colaboradtivas, os processadores trocam e compartilham informações coletadas ao longo da trajetória que cada um deles investiga. Neta tese são desenvolvidas heurísticas seqüenciais e paralelas para 2PNDP. São analisadas variantes e combinações de GRASP e reconexão por caminhos , comparando-se os resultados obtidos pelos algoritmos descritos na literatura. Heurísticas GRASP paralelas com reconexão por caminhos são avaliadas e comparadas para verificar qual o papel que a colaboração entre os processadores desempenha na qualidade das soluções e nos tempos de processamento. Procura-se também estudar a melhor maneira de desenvolver implementações paralelas , para se utilizar da melhor forma possível os recursos computacionais e reduzir conflitos de memória e comunicação. / [en] Let G = ( V, E) be a connected undirected graph , where V is the set of nodes and E denotes the set of edges. A 2- path between nodes (s,t)is a sequence of a most two edges connecting them. Given a non-negative weight function associated with edges of G and a set D of origin- destination pairs of nodes, the 2-path network design problem (2PNDP) consists in finding a minimum weighted subset of edges containing a 2-path between the extremities of every origin-destination pair in D. Applications can be found in the design of communication networks , in which paths with few edges are sought to enforce high reliability and small delays. The GRASP metaheuristic is a multistart process , in which each iteration consists of two phases : construction and local search. The best solution found after a fixed number of iterations is returned. Path- relinking is applied as an attempt to improve the solutions found at the of each GRASP iteration. Parallel implementations of metaheuistics ara very robust. Typical parallelizations of GRASP correspond to multiple-walk independent-thread strategies, based on the balanced distribuiton of the iterations over the processors. In the case of multiple-walk cooperative-thread strategies, the processors exchange and share information collected along the trajectories that they investigate. In this thesis, sequential and parallel heuristics are developed for 2PNDP. Variants and combinations of GRASP with path-relinking are analysed by comparing the results of the proposed algorithms with those obtained by others algoritms described in the literature. Parallel GRASP with pathrelinking heuristcs are compared to investigate the influence of the cooperation among processors in terms of solution quality and processing time. We also explore different strategies to optimize the parallel implementations, to make better use of the computational resources and to reduce communication and memory conflicts.

[pt] Atualmente mais da metade da população mundial mora em cidades. O deslocamento na região urbana, mediante a utilização de transporte público se dificulta devido ao planejamento deficiente das rotas e redes de transporte, longos tempos de viagem, aumento do custo das passagens, dos tempos de espera, etc. Como consequência, a busca de operações mais eficientes no sistema de transporte público urbano tem aumentado visando atender as necessidades de transporte de forma mais sustentável. Após a revisão da literatura relacionada ao problema de desenho de rede de transporte público urbano, foi escolhido o método proposto por Aquino, (1980), aplicável para redes de ônibus urbanos. Por médio da modernização do programa do método escolhido e as melhorias nele, o número de rotas que define a rede conectada diminuiu. O número de transbordos na rede foi minimizado até zera-lo com um menor conjunto de rotas. Análise de indicadores e de rentabilidade das rotas que minimizam o número de transbordo na rede, permite ao planejador ter uma visão geral do comportamento dessas rotas possibilitando tomar decisões mantendo os requerimentos iniciais e o objetivo de estudo. O programa do método desenvolvido, adaptado a uma linguagem moderna, Cmais mais, oferece, tanto ao meio acadêmico quanto ao profissional, uma ferramenta de fácil aplicação para dar solução ao Problema de Desenho de Rede de Transporte Público Urbano. Contribuindo potencialmente ao incremento da eficiência do processo de planejamento e, portanto, à redução de não conformidades do serviço de transporte resultando em economia dos custos para as empresas prestadoras deste serviço. / [en] Nowadays, more than half of the world s population lives in cities. Displacement in the urban area through the use of public transportation is hampered by poor planning of transport routes and networks, long travel times, increased ticket costs and waiting times, etc. As a consequence, the search for more efficient operations in the urban public transport system has increased in order to meet the transport needs in a more sustainable way. After the literature review related to the urban public transport network design problem, the method proposed by Aquino (1980), applicable to urban bus networks, was chosen. By means of the program s modernization of the chosen method and the improvements in it, the number of routes defining the connected network has decreased. The overflow number on the network has been minimized to zero with a smaller set of routes. Analysis of indicators and profitability of the routes that minimize the number of transfer in the network, allows the planner to have an overview of the behavior of these routes allowing to make decisions keeping the initial requirements and the objective of study. The developed method program, adapted to a modern language, C plus plus, offers both an academic and a professional environment an easy application tool to solve the Urban Public Transport Network Design Problem. Potentially contributing to the increase of the efficiency of the planning process and, therefore, to the reduction of nonconformities of the transport service, resulting in cost savings for the companies that provide this service.

Esta dissertação trata do problema do projeto de redes de transporte público por ônibus, que consiste em estabelecer as linhas de ônibus a serem operadas e seus respectivos trajetos e frequências. Busca-se determinar uma rede de tal forma a minimizar custos de operadores e usuários, constituindo um problema multiobjetivo. O custo dos operadores é representado tanto pela frota como pela quilometragem total necessária para atender às frequências exigidas; já o custo dos usuários é representado pela soma dos tempos de espera, tempos de viagem dentro do veículo e eventuais penalidades de transferência. Dado tratar-se de um problema multiobjetivo, de natureza combinatória e complexo, é proposto um método de solução baseado na metaheurística Algoritmo Genético. O mesmo baseia-se na construção inicial de um banco de rotas viáveis, e cada solução proposta é formada selecionando-se um subconjunto de rotas deste banco para formar a rede. São aplicadas estratégias de busca por soluções viáveis nos operadores do Algoritmo Genético, devido à grande proporção de indivíduos inviáveis. O modelo é avaliado através de uma instância de teste da literatura e os resultados são comparados com os já obtidos em trabalhos anteriores. A melhor solução encontrada através do método descrito deste trabalho é superior às já reportadas na literatura. Uma análise de sensibilidade foi realizada para avaliar a influência de parâmetros de entrada do modelo na qualidade das soluções. Um Sistema de Visualização foi desenvolvido para representar graficamente as linhas de ônibus e demais variáveis das soluções. Sugere-se, ao final do trabalho, um conjunto de pesquisas futuras associadas à melhoria do modelo. / This dissertation addresses the public transport network design problem, which comprises determining the bus routes, their associated itineraries and frequencies. The network is designed as to minimize operators and users costs, creating a multiobjective problem. Operators costs are represented by the total fleet and mileage necessary to address required frequencies while user costs are represented by the sum of waiting times, in-vehicle travel times and possible transfer penalties. Given the complexity of this combinatorial and multiobjective problem, a solution method, based on the genetic algorithm metaheuristic, is proposed. Initially a database of feasible routes is built, and each proposed solution is formed by selecting a subset of routes from the database to form the network. Feasibility search strategies are applied inside genetic algorithms operators to make up for the large number of unfeasible individuals. The model is evaluated with a small network and the results are compared with those obtained in previous studies. The best solution attained with the present method is superior to previously published results. A sensitivity analysis was conducted to evaluate the influence of different model input parameters on solution quality. A Visualization System was developed to graphically represent the solutions bus lines and other variables. A set of future research ideas, related to the model improvement, are presented at the end of this study.

Diversos problemas do mundo real estão relacionados ao projeto de redes, tais como projeto de circuitos de energia elétrica, roteamento de veículos, planejamento de redes de telecomunicações e reconstrução filogenética. Em geral, esses problemas podem ser modelados por meio de grafos, que manipulam milhares ou milhões de nós (correspondendo às variáveis de entrada), dificultando a obtenção de soluções em tempo real. O Projeto de uma Rede é um problema combinatório, em que se busca encontrar a rede mais adequada segundo um critério como, por exemplo, menor custo, menor caminho e tempo de percurso. A solução desses problemas é, em geral, computacionalmente complexa. Nesse sentido, metaheurísticas como Algoritmos Evolutivos têm sido amplamente investigadas. Diversas pesquisas mostram que o desempenho de Algoritmos Evolutivos para Problemas de Projetos de Redes pode ser aumentado significativamente por meio de representações mais apropriadas. Este trabalho investiga a paralelização da Representação Nó-Profundidade (RNP) em hardware, com o objetivo de encontrar melhores soluções para Problemas de Projetos de Redes. Para implementar a arquitetura de hardware, denominada de HP-RNP (Hardware Parallelized RNP), foi utilizada a tecnologia de FPGA para explorar o alto grau de paralelismo que essa plataforma pode proporcionar. Os resultados experimentais mostraram que o HP-RNP é capaz de gerar e avaliar novas redes em tempo médio limitado por uma constante (O(1)) / Many problems related to network design can be found in real world applications, such as design of electric circuits, vehicle routing, telecommunication network planning and phylogeny reconstruction. In general, these problems can be modelled using graphs that handle thousands or millions of nodes (input variables), making it hard to obtain solutions in real-time. The Network Design is the combinatorial problem of finding the most suitable network subject to a evaluation criterion as, for example, lower cost, minimal path and time to traverse the network. The solution of those problems is in general computationally complex. Metaheuristics as Evolutionary Algorithms have been widely investigated for such problems. Several researches have shown that the performance of Evolutionary Algorithms for the Network Design Problems can be significantly increased through more appropriated dynamic data structures (encodings). This work investigates the parallelization of Node-Depth Encoding (NDE) in hardware in order to find better solutions for Network Design Problems. To implement the proposed hardware architecture, called HP-NDE (Hardware Parallellized NDE), the FPGA technology was used to explore the high degree of parallelism that such platform can provide. The experimental results have shown that the HP-NDE can generate and evaluate new networks in average time constrained by a constant (O(1))

The public transport system in South Africa is in a precarious state, capturing no more than 50% of the passenger market. The three public transport modes that are currently utilized—train, bus, and minibus-taxi—are competing for market share instead of complementing one another. Furthermore, most public transport networks have not been properly redesigned over the past three decades. Improvements were initiated reactively in the past: transit stops and routes were added or removed from the network when demand fluctuated. This reactive process has diminished the confidence of commuters in the public transport networks, forcing commuters to use private transport. A proactive redesign method is needed—one that includes all the modes of public transport, and anticipates an increase in demand and rapid development in geographic areas, while ensuring good accessibility to the network. Current network design models do not include multiple modes of public transport, and are based on the geographical layout of developed cities and their particularities, which makes them unsuitable for the South African environment with its unique land use disparities. This dissertation proposes a multimodal network design model that is capable of designing real world and large scale networks for the South African metropolitan areas. The City of Tshwane Metropolitan Municipality (CTMM) transport network area was used to develop and test the model, which consists of four components. The Geographic Information System (GIS) component has a central role in storing, manipulating, and exchanging the geographic data within the model. For the GIS the appropriate input data is identified, and a design for the geo-database is proposed. The Population Generation Algorithm (PGA) component translates the demographic data into point data representing the transit demand in the study area. The Bus Stop Placement Algorithm (BSPA) component is a metaheuristic that searches for near-optimal solutions for the placement of bus stops in the study area. A novel solution approach proposed in this dissertation uses geographic data of commuters to evaluate the bus stop placement in the study area. The Multimodal Network Design Algorithm (MNDA) component also employs a metaheuristic, enabling the design of near-optimal multimodal networks. The addition of multiple modes to the Transit Network Design Problem (TNDP) is also a novel and significant contribution. The two metaheuristic components are first tested on a test network, and subjected to a comprehensive sensitivity analysis. After identifying suitable parameter values and algorithm settings, the components are applied to the entire CTMM. / Dissertation (MSc)--University of Pretoria, 2009. / Industrial and Systems Engineering / unrestricted

No description available.

De nombreux problèmes en transport et en logistique peuvent être formulés comme des modèles de conception de réseau. Ils requièrent généralement de transporter des produits, des passagers ou encore des données dans un réseau afin de satisfaire une certaine demande tout en minimisant les coûts. Dans ce mémoire, nous nous intéressons au problème de conception de réseau avec coûts fixes et capacités. Ce problème consiste à ouvrir un sous-ensemble des liens dans un réseau afin de satisfaire la demande, tout en respectant les contraintes de capacités sur les liens. L'objectif est de minimiser les coûts fixes associés à l'ouverture des liens et les coûts de transport des produits. Nous présentons une méthode exacte pour résoudre ce problème basée sur des techniques utilisées en programmation linéaire en nombres entiers. Notre méthode est une variante de l'algorithme de branch-and-bound, appelée branch-and-price-and-cut, dans laquelle nous exploitons à la fois la génération de colonnes et de coupes pour la résolution d'instances de grande taille, en particulier, celles ayant un grand nombre de produits. En nous comparant à CPLEX, actuellement l'un des meilleurs logiciels d'optimisation mathématique, notre méthode est compétitive sur les instances de taille moyenne et supérieure sur les instances de grande taille ayant un grand nombre de produits, et ce, même si elle n'utilise qu'un seul type d'inégalités valides. / Many problems in transportation and logistics can be formulated as network design models. They usually require to transport commodities, passengers or data in a network to satisfy a certain demand while minimizing the costs. In this work, we focus on the multicommodity capacited fixed-charge network design problem which consists of opening a subset of the links in the network to satisfy the demand. Each link has a capacity and a fixed cost that is paid if it is opened. The objective is to minimize the fixed costs of the opened links and the transportation costs of the commodities. We present an exact method to solve this problem based on mixed integer programming techniques. Our method is a specialization of the branch-and-bound algorithm, called branch-and-price-and-cut, in which we use column generation and cutting-plane method to solve large-scale instances. We compare our method with CPLEX, currently one of the best solver. Numerical results show that our method is competitive on medium-scale instances and better on large-scale instances.

Le problème de conception de réseaux est un problème qui a été beaucoup étudié dans le domaine de la recherche opérationnelle pour ses caractéristiques, et ses applications dans des nombreux domaines tels que le transport, les communications, et la logistique. Nous nous intéressons en particulier dans ce mémoire à résoudre le problème de conception de réseaux avec coûts fixes et sans capacité, en satisfaisant les demandes de tous les produits tout en minimisant la somme des coûts de transport de ces produits et des coûts fixes de conception du réseau. Ce problème se modélise généralement sous la forme d’un programme linéaire en nombres entiers incluant des variables continues. Pour le résoudre, nous avons appliqué la méthode exacte de Branch-and-Bound basée sur une relaxation linéaire du problème avec un critère d’arrêt, tout en exploitant les méthodes de génération de colonnes et de génération de coupes. Nous avons testé la méthode de Branch-and-Price-and-Cut sur 156 instances divisées en cinq groupes de différentes tailles, et nous l’avons comparée à Cplex, l’un des meilleurs solveurs d’optimisation mathématique, ainsi qu’à la méthode de Branch-and- Cut. Notre méthode est compétitive et plus performante sur les instances de grande taille ayant un grand nombre de produits. / The network design problem has been studied extensively in the field of operational research given its characteristics and applications in many areas such as transportation, communications, and logistics. We are particularly interested in solving the multicommodity uncapacitated fixed-charge network design problem, with the aim of meeting the demands of all the products while minimizing the total cost of transporting commodities and designing the network. This problem is typically modeled as a linear integer program including continuous variables. To solve it, we applied the exact method of Branch-and-bound based on linear relaxation with a stopping criterion, while exploiting the column generation and cutting-plane methods. We tested our Branch-and-Price-and-Cut algorithm on 156 instances divided into five groups of different sizes, and we compared it with Cplex, one of the best mathematical optimization solvers. We compare it also with the Branch-and-Cut method. Numerical results show that our method is competitive and perform better especially on large-scale instances with many commodities.

De nombreux problèmes en transport et en logistique peuvent être formulés comme des modèles de conception de réseau. Ils requièrent généralement de transporter des produits, des passagers ou encore des données dans un réseau afin de satisfaire une certaine demande tout en minimisant les coûts. Dans ce mémoire, nous nous intéressons au problème de conception de réseau avec coûts fixes et capacités. Ce problème consiste à ouvrir un sous-ensemble des liens dans un réseau afin de satisfaire la demande, tout en respectant les contraintes de capacités sur les liens. L'objectif est de minimiser les coûts fixes associés à l'ouverture des liens et les coûts de transport des produits. Nous présentons une méthode exacte pour résoudre ce problème basée sur des techniques utilisées en programmation linéaire en nombres entiers. Notre méthode est une variante de l'algorithme de branch-and-bound, appelée branch-and-price-and-cut, dans laquelle nous exploitons à la fois la génération de colonnes et de coupes pour la résolution d'instances de grande taille, en particulier, celles ayant un grand nombre de produits. En nous comparant à CPLEX, actuellement l'un des meilleurs logiciels d'optimisation mathématique, notre méthode est compétitive sur les instances de taille moyenne et supérieure sur les instances de grande taille ayant un grand nombre de produits, et ce, même si elle n'utilise qu'un seul type d'inégalités valides. / Many problems in transportation and logistics can be formulated as network design models. They usually require to transport commodities, passengers or data in a network to satisfy a certain demand while minimizing the costs. In this work, we focus on the multicommodity capacited fixed-charge network design problem which consists of opening a subset of the links in the network to satisfy the demand. Each link has a capacity and a fixed cost that is paid if it is opened. The objective is to minimize the fixed costs of the opened links and the transportation costs of the commodities. We present an exact method to solve this problem based on mixed integer programming techniques. Our method is a specialization of the branch-and-bound algorithm, called branch-and-price-and-cut, in which we use column generation and cutting-plane method to solve large-scale instances. We compare our method with CPLEX, currently one of the best solver. Numerical results show that our method is competitive on medium-scale instances and better on large-scale instances.

No description available.