A busca de soluções para a mobilidade urbana que minimizem a agressão do setor de tráfego e transportes ao meio ambiente está cada vez maior. Os veículos elétricos se posicionam como uma alternativa interessante, pois reduzem a emissão de gases poluentes na atmosfera, a poluição sonora e o consumo de petróleo. No entanto, sua limitada autonomia e a escassez de postos de recarga intimidam sua adoção. Por conta disso, políticas governamentais de incentivo têm sido desenvolvidas para a oferta de benefícios a quem optar por um veículo elétrico. Estima-se que dentro de poucas décadas toda a frota urbana será substituída por veículos dessa natureza. Por isso, é importante entender as mudanças no tempo de viagem e no consumo de energia oriundos da inclusão de veículos elétricos em cenários de tráfego. Trabalhos anteriores estudaram as diferenças entre os mecanismos internos de veículos convencionais e elétricos na determinação destas mudanças. Porém, dadas as características destes últimos, motoristas de veículos elétricos se preocupam com a economia de energia e podem optar por rotas diferentes. Logo, uma análise completa destes impactos deve considerar uma nova distribuição de tráfego. Este trabalho propõe um método biobjetivo de alocação de tráfego que considera o tempo de viagem e o consumo de energia para determinar a distribuição de veículos elétricos em cenários de tráfego urbano. Duas estratégias de distribuição de fluxo são propostas como mecanismos de escolha de rotas. Como parte da alocação de tráfego, é proposto um algoritmo biobjetivo de caminhos mínimos para veículos elétricos. A abordagem apresentada foi aplicada a três cenários distintos, onde percebeu-se uma diminuição de até 80% no consumo total de energia. Em cenários com congestionamento, observou-se um aumento de 10% no tempo de viagem. Já em cenários sem congestionamento o tempo de viagem diminuiu cerca de 2%. A recuperação de energia representa quase 6% da economia total dos veículos elétricos. Além disso, experimentos mostraram que investimentos na eficiência dos veículos elétricos podem resultar em uma economia de até 15% de energia. / The search for urban mobility solutions that minimize the aggression to the environment is increasing. Electric vehicles are an attractive alternative because they reduce greenhouse gas emissions, noise pollution, and oil consumption. However, their limited autonomy and the lack of charging stations restrict their popularization. Therefore, government incentive policies have been developed in order to offer benefits to those who choose an electric vehicle. It is estimated that the entire urban fleet will be replaced by these vehicles in a few decades. Therefore, it is important to understand the changes in travel time and energy consumption from the inclusion of electric vehicles in traffic scenarios. Previous works determined these changes by studying the differences between the internal engine of conventional and electric vehicles. However, given the characteristics of the latter, drivers of electric vehicles care about saving energy and may want to choose different routes. Thus, a complete analysis of these impacts should consider a redistribution of traffic. This work proposes a bi-objective traffic assignment method that considers the travel time and the energy consumption to determine the distribution of electric vehicles in urban traffic scenarios. We introduce two strategies for flow distribution as models of route choice. As a procedure of the traffic assignment method, we propose a bi-objective shortest path algorithm for electric vehicles. Our approach was applied to three different scenarios, which resulted in a decrease of up to 80% in total energy consumption. In congested scenarios, we observe an increase of about 10% in average travel time. In uncongested scenarios, travel time decreases about 2%. Energy recovery is almost 6% of the total savings of electric vehicles. Moreover, experiments have shown that investments in the efficiency of electric vehicles can result in up to 15% of energy savings.

Les travaux effectués dans cette thèse industrielle concernent l'amélioration du calculateur d'itinéraire de Cityway, société spécialisée dans les technologies de l’information appliquées à la mobilité.Nous avons d'abord établi un état de l'art exhaustif, accompagné d'une mise en perspective de l'existant Cityway avec celui-ci. Cela nous a permis d'aider l'entreprise à prendre du recul sur son produit et de justifier les axes de recherche choisis pour nos travaux.Nous nous sommes ensuite intéressés à l'aspect multicritère du problème. En effet, le calculateur, basé sur l'algorithme de Dijkstra, permet de trouver des trajets minimisant une somme pondérée de critères. Nous avons développé un algorithme multilabel permettant de conserver et étendre plusieurs labels au même nœud. Malgré une légère augmentation des temps de calculs, des résultats satisfaisants ont été obtenus dans une application bicritère de ce nouvel algorithme.Nous avons également travaillé sur la génération et la sélection de trajets alternatifs. La génération s'appuie sur les algorithmes monolabel ou multilabel. La sélection s'appuie quant à elle sur la définition d'une distance entre les solutions et des méthodes de regroupement.Enfin, nous nous sommes intéressés à l'optimisation du calcul du critère lexicographique de durée minimale dans le cas bicritère. Pour qu'un trajet soit intéressant, il faut qu'il soit optimal sur les critères usuels, mais aussi qu'il dure le moins longtemps possible. L'utilisation de certaines propriétés sur ce critère permet de réduire des temps de calcul initialement trop longs. / The work carried out in this industrial PhD aims at improving the route planner of Cityway, a company specialized in information technologies applied to mobility. We first established an exhaustive state of the art, and compared it to the existing Cityway product. This allowed us to help the company take a step back from its urgent needs, and justify the research guidelines chosen for our work.We then looked at the multi-criteria aspect of the problem. Indeed, the trip planner, based on the Dijkstra algorithm, makes it possible to find paths minimizing a weighted sum of criteria. We have developed a multilabel algorithm to maintain and extend multiple labels at the same node. Despite a slight increase in computation time, satisfactory results were obtained in a bicriteria application of this new algorithm.We also worked on the generation and selection of alternative routes. The generation algorithm relies on the existing monolabel or newly developed multilabel algorithms. The selection algorithm is based on the definition of a distance between trips and adaptations of existing clustering algorithms to this specific case.Finally, we were interested in what we called the lexicographic criterion. For a trip to be interesting, it must be optimal on the usual criterion of earliest arrival, and, for trips arriving at the same time, on the latest departure criterion. The use of certain properties on this criterion makes it possible to reduce computation times on the bicriteria case.

A busca de soluções para a mobilidade urbana que minimizem a agressão do setor de tráfego e transportes ao meio ambiente está cada vez maior. Os veículos elétricos se posicionam como uma alternativa interessante, pois reduzem a emissão de gases poluentes na atmosfera, a poluição sonora e o consumo de petróleo. No entanto, sua limitada autonomia e a escassez de postos de recarga intimidam sua adoção. Por conta disso, políticas governamentais de incentivo têm sido desenvolvidas para a oferta de benefícios a quem optar por um veículo elétrico. Estima-se que dentro de poucas décadas toda a frota urbana será substituída por veículos dessa natureza. Por isso, é importante entender as mudanças no tempo de viagem e no consumo de energia oriundos da inclusão de veículos elétricos em cenários de tráfego. Trabalhos anteriores estudaram as diferenças entre os mecanismos internos de veículos convencionais e elétricos na determinação destas mudanças. Porém, dadas as características destes últimos, motoristas de veículos elétricos se preocupam com a economia de energia e podem optar por rotas diferentes. Logo, uma análise completa destes impactos deve considerar uma nova distribuição de tráfego. Este trabalho propõe um método biobjetivo de alocação de tráfego que considera o tempo de viagem e o consumo de energia para determinar a distribuição de veículos elétricos em cenários de tráfego urbano. Duas estratégias de distribuição de fluxo são propostas como mecanismos de escolha de rotas. Como parte da alocação de tráfego, é proposto um algoritmo biobjetivo de caminhos mínimos para veículos elétricos. A abordagem apresentada foi aplicada a três cenários distintos, onde percebeu-se uma diminuição de até 80% no consumo total de energia. Em cenários com congestionamento, observou-se um aumento de 10% no tempo de viagem. Já em cenários sem congestionamento o tempo de viagem diminuiu cerca de 2%. A recuperação de energia representa quase 6% da economia total dos veículos elétricos. Além disso, experimentos mostraram que investimentos na eficiência dos veículos elétricos podem resultar em uma economia de até 15% de energia. / The search for urban mobility solutions that minimize the aggression to the environment is increasing. Electric vehicles are an attractive alternative because they reduce greenhouse gas emissions, noise pollution, and oil consumption. However, their limited autonomy and the lack of charging stations restrict their popularization. Therefore, government incentive policies have been developed in order to offer benefits to those who choose an electric vehicle. It is estimated that the entire urban fleet will be replaced by these vehicles in a few decades. Therefore, it is important to understand the changes in travel time and energy consumption from the inclusion of electric vehicles in traffic scenarios. Previous works determined these changes by studying the differences between the internal engine of conventional and electric vehicles. However, given the characteristics of the latter, drivers of electric vehicles care about saving energy and may want to choose different routes. Thus, a complete analysis of these impacts should consider a redistribution of traffic. This work proposes a bi-objective traffic assignment method that considers the travel time and the energy consumption to determine the distribution of electric vehicles in urban traffic scenarios. We introduce two strategies for flow distribution as models of route choice. As a procedure of the traffic assignment method, we propose a bi-objective shortest path algorithm for electric vehicles. Our approach was applied to three different scenarios, which resulted in a decrease of up to 80% in total energy consumption. In congested scenarios, we observe an increase of about 10% in average travel time. In uncongested scenarios, travel time decreases about 2%. Energy recovery is almost 6% of the total savings of electric vehicles. Moreover, experiments have shown that investments in the efficiency of electric vehicles can result in up to 15% of energy savings.

Traffic congestion has been cited as the most conspicuous problem in traffic management. It has far-reaching economic,social and political effects. Intelligent Transportation Systems (ITS) research and development programs have been assigned the task of developing sophisticated techniques and counter-measures to reduce traffic congestion to manageable levels, and also achieve these objectives using area-wide traffic management methods. During times of traffic congestion, the traffic network in a transient, time-dynamic state, and resembles a dynamic network. In addition, in the context of ITS, the network can accurately detect such transient behavior using traffic sensors, and several other information gathering devices. In conjunction with Operations Research techniques, the time-varying traffic flows can be routed through the network in an optimal manner, based on the feedback from these information sources. Dynamic Traffic Assignment (DTA) methods have been proposed to perform this task. An important step in DTA is the calculation of user-optimal, system-optimal, and multiple optimal routes for assigning traffic. One would also require the calculation of user-optimal paths for vehicle scheduling and dispatching problems. The main objective of this research study is to analyze the effectiveness of time-dependent shortest path (TDSP) algorithms and k-shortest path (k-SP) algorithms as a practical routing tool in such intelligent transportation networks. Similar algorithms have been used to solve routing problems in computer networks. The similarities and differences between computer and ITS road networks are studied. An exhaustive review of TDSP and k-SP algorithms was conducted to classify and determine the best algorithms and implementation procedures available in the literature. A new (heuristic) algorithm (TD-kSP) that calculates multiple optimal paths for dynamic networks is proposed and developed. A complete object-oriented computer program in C++ was written using specialized network representations, node-renumbering schemes and efficient path processing data structures (classes) to implement this algorithm. A software environment where such optimization algorithms can be applied in practice was then developed using object-oriented design methodology. Extensive statistical and regression analysis tests for various random network sizes, densities and other parameters were conducted to determine the computational efficiency of the algorithm. Finally, the algorithm was incorporated within the GIS-based Wide-Area Incident Management Software System (WAIMSS) developed at the Center for Transportation Research, Virginia Tech. The results of these tests are used to obtain the empirical time-complexity of the algorithm. Results indicate that the performance of this algorithm is comparable to the best TDSP algorithms available in the literature, and strongly encourages its possible application in real-time applications. Complete testing of the algorithm requires the use of real-time link flow data. While the use of randomly generated data and delay functions in this study may not significantly affect its computational performance, other measures of effectiveness as a routing tool remains untested. This can be verified only if the algorithm itself becomes a part of the user-behavior feedback loop. A closed loop traffic simulation/ system-dynamics study would be required to perform this task. On the other hand, an open-loop simulation would suffice for vehicle scheduling/dispatching problems. / Master of Science

La représentation des temps de parcours est un enjeu influençant la qualité de l’information transmise aux usagers des réseaux de transport. En particulier, la congestion constitue un inconvénient majeur dont la prise en compte n’est pas toujours maîtrisée au sein des calculateurs d’itinéraires. De même, les évènements comme les réductions de capacité, les perturbations climatiques, ou encore les pics de fréquentation incitent à dépasser la définition statique des temps de parcours. Des travaux antérieurs se sont focalisés sur des temps dynamiques, i.e. dépendants de la date de départ, de manière à affiner le détail de la représentation, et à prendre notamment en compte le caractère périodique des congestions. La considération d’informations en temps réel est aussi une amélioration indéniable, que ce soit lors de la préparation du trajet, ou lorsqu’il s’agit de s’adapter à des perturbations rencontrées en cours de route. Ceci dit, aussi fines qu’elles soient dans les calculateurs disponibles, ces modélisations présentent un inconvénient majeur : elles ne prennent pas en compte toutes les facettes de la variabilité des temps de parcours. Cette variabilité est très importante, en particulier si l’on considère le niveau d’aversion au risque des usagers. En outre, dans un réseau multimodal, les correspondances éventuelles rendent encore plus critique l’incertitude associée aux temps de parcours. En réponse à ces enjeux, les présents travaux de thèse ont ainsi été consacrés à l’étude de temps de parcours stochastiques, i.e. vus comme des variables aléatoires distribuées.Dans une première étape, nous nous intéressons à la modélisation statistique des temps de parcours et à la quantification de leur variabilité. Nous proposons l’utilisation d’un système de lois développé dans le domaine de l’hydrologie, la famille des lois de Halphen. Ces lois présentent les caractéristiques typiques des distributions de temps de parcours, elles vérifient par ailleurs la propriété de fermeture par l’addition sous certaines hypothèses afférentes à leurs paramètres. En exploitant les ratios de moments associés aux définitions de ces lois de probabilité, nous mettons également au point de nouveaux indicateurs de fiabilité, que nous confrontons avec la palette d’indicateurs classiquement utilisés. Cette approche holistique de la variabilité des temps de parcours nous semble ainsi ouvrir de nouvelles perspectives quant au niveau de détail de l’information, notamment à destination des gestionnaires de réseaux.Par la suite, nous étendons le cadre d’analyse aux réseaux, en utilisant les résultats obtenus à l’étape précédente. Différentes lois de probabilité sont ainsi testées dans le cadre de la recherche du plus court chemin stochastique. Cette première étude nous permet de dresser un panorama des chemins identifiés en fonction du choix de modélisation. S’il est montré que le choix du modèle est important, il s’agit surtout d’affirmer que le cadre stochastique est pertinent. Ensuite, nous soulevons la relative inefficacité des algorithmes de recherche du plus court chemin stochastique, ceux-ci nécessitant des temps de calcul incompatibles avec un passage à l’échelle industrielle. Pour pallier cette difficulté, un nouvel algorithme mettant en oeuvre une technique d’accélération tirée du cadre déterministe est développé dans la dernière partie de la thèse. Les résultats obtenus soulignent la pertinence de l’intégration de modèles stochastiques au sein des calculateurs d’itinéraires. / The travel time representation has a major impact on user-oriented routing information. In particular, congestion detection is not perfect in current route planners. Moreover, the travel times cannot be considered as static because of events such as capacity drops, weather disturbances, or demand peaks. Former researches focused on dynamic travel times, i.e. that depend on departure times, in order to improve the representation details, for example concerning the periodicity of congestions. Real-time information is also a significant improvement for users aiming to prepare their travel or aiming to react to on-line events. However these kinds of model still have an important drawback : they do not take into account all the aspects of travel time variability. This dimension is of huge importance, in particular if the user risk aversion is considered. Additionally in a multimodal network, the eventual connections make the travel time uncertainty critical. In this way the current PhD thesis has been dedicated to the study of stochastic travel times, seen as distributed random variables.In a first step, we are interested in the travel time statistical modeling as well as in the travel time variability. In this goal, we propose to use the Halphen family, a probability law system previously developed in hydrology. The Halphen laws show the typical characteristics of travel time distributions, plus they are closed under addition under some parameter hypothesis. By using the distribution moment ratios, we design innovative reliability indexes, that we compare with classical metrics. This holistic approach appears to us as a promising way to produce travel time information, especially for infrastructure managers.Then we extend the analysis to transportation networks, by considering previous results. A set of probability laws is tested during the resolution of the stochastic shortest path problem. This research effort helps us to describe paths according to the different statistical models. We show that the model choice has an impact on the identified paths, and above all, that the stochastic framework is crucial. Furthermore we highlight the inefficiency of algorithms designed for the stochastic shortest path problem. They need long computation times and are consequently incompatible with industrial applications. An accelerated algorithm based on a deterministic state-of-the-art is provided to overcome this problem in the last part of this document. The obtained results let us think that route planners might include travel time stochastic models in a near future.

The aim of the research project that is the subject of this thesis is to apply mathematical techniques, especially those in the area of operations research, to the problem of maritime minefield transit. We develop several minefield models applicable to different aspects of the minefield problem. These include optimal mine clearance, shortest time traversal and time constrained traversal. We hope the suite of models and tools developed will help make mine field clearance and traversal both safer and more efficient and that exposition of the models will bring a clearer understanding of the mine problem from a mathematical perspective. In developing the solutions to mine field models, extensive use is made of network path planning algorithms, particularly the Weight Constrained Shortest Path Problem (WCSPP) for which the current state-of-the-art algorithm is extended. This is done by closer integration of Lagrangean relaxation and preprocessing to reduce the size of the network. This is then integrated with gap-closing algorithms based on enumeration to provide optimal or near optimal solutions to the path planning problem. We provide extensive computational evidence on the performance of our algorithm and compare it to other algorithms found in the literature. This tool then became fundamental in solving various separate minefield models. Our models can be broadly separated into obstacle models in which mine affected regions are treated as obstacles to be avoided and continuous threat in which each point of space has an associated risk. In the later case, we wish to find a path that minimizes the integral of the risk along the path while constraining the length of the path. We call this the Continuous Euclidean Length Constrained Minimum Cost Path Problem (C-LCMCPP), for which we present a novel network approach to solving this continuous problem. This approach results in being able to calculate a global lower bound on a non-convex optimization problem.

In this thesis, we use integer programming techniques to solve the resource constrained shortest path problem (RCSPP) which seeks a minimum cost path between two nodes in a directed graph subject to a finite set of resource constraints. Although NP-hard, the RCSPP is extremely useful in practice and often appears as a subproblem in many decomposition schemes for difficult optimization problems. We begin with a study of the RCSPP polytope for the single resource case and obtain several new valid inequality classes. Separation routines are provided, along with a polynomial time algorithm for constructing an auxiliary conflict graph which can be used to separate well known valid inequalities for the node packing polytope. We establish some facet defining conditions when the underlying graph is acyclic and develop a polynomial time sequential lifting algorithm which can be used to strengthen one of the inequality classes. Next, we outline a branch-and-cut algorithm for the RCSPP. We present preprocessing techniques and branching schemes which lead to strengthened linear programming relaxations and balanced search trees, and the majority of the new inequality classes are generalized to consider multiple resources. We describe a primal heuristic scheme that uses fractional solutions, along with the current incumbent, to search for new feasible solutions throughout the branch-and-bound tree. A computational study is conducted to evaluate several implementation choices, and the results demonstrate that our algorithm outperforms the default branch-and-cut algorithm of a leading integer programming software package. Finally, we consider the dial-a-flight problem (DAFP), a new vehicle routing problem that arises in the context of on-demand air transportation and is concerned with the scheduling of a set of travel requests for a single day of operations. The DAFP can be formulated as an integer multicommodity network flow model consisting of several RCSPPs linked together by set partitioning constraints which guarantee that all travel requests are satisfied. Therefore, we extend our branch-and-cut algorithm for the RCSPP to solve the DAFP. Computational experiments with practical instances provided by the DayJet Corporation verify that the extended algorithm also outperforms the default branch-and-cut algorithm of a leading integer programming software package.

O Problema dos K Menores Caminhos é uma generalização do Problema do Menor Caminho, em que desejamos encontrar os K caminhos de menor custo entre dois vértices de um grafo. Estudamos e implementamos algoritmos que resolvem esse problema em grafos dirigidos, com peso nos arcos e que permitem apenas caminhos sem repetição de vértices na resposta. Comparamos seus desempenhos utilizando grafos do 9th DIMACS Implementation Challenge. Identificamos os pontos fortes e fracos de cada algoritmo, e propusemos uma variante híbrida dos algoritmos de Feng e de Pascoal. Essa variante proposta obteve desempenho superior aos algoritmos base em alguns grafos, e resultado superior a pelo menos um deles na grande maioria dos testes. / The K-Shortest Path Problem is a generalization of the Shortest Path Problem, in which we must find the K paths between two vertices in a graph that have the lowest costs. We study some K-Shortest Path Problem algorithms applied to weighted directed graphs, allowing only paths with no repeated vertices. We compare empirically implementation of some algorithms, using instance graphs from the 9th DIMACS Implementation Challenge. We identify the strengths and weaknesses of each algorithm, and we propose a hybrid version of Feng\'s and Pascoal\'s algorithms. This proposed variant achieve better perfomance compared to both base algorithms in some graphs, and it is better than at least one of them in most cases.

Les graphes sont des objets couramment utilisés pour modéliser de nombreuses situations réelles comme des réseaux routiers, informatiques ou encore électriques. Ils permettent de résoudre des problèmes sur ces réseaux comme le routage (aller d'un sommet à un autre en suivant les arêtes du graphe) ou encore leur exploration (obtenir une carte du graphe étudié). Les réseaux étudiés, et donc les graphes qui les modélisent, peuvent être grands, c'est-à-dire avoir un très grand nombre de sommets. Dans ce cas, comme dans le cas de l'étude de grandes données en général, nous pouvons utiliser le paradigme << Diviser pour mieux régner >> pour répondre aux questions posées. En effet, en travaillant sur des petites parties du graphe et en fusionnant les résultats obtenus sur ces petites parties, on peut obtenir le résultat sur le graphe global. Dans ce document, nous présenterons une manière de décomposer les graphes en utilisant des plus courts chemins comme séparateurs. Cette décomposition permet d'obtenir, par exemple, un routage efficace, un étiquetage compacte pour pouvoir estimer les distances entre les sommets d'un graphe ou encore une navigation efficace dans les graphes<< petit monde >>. Cette méthode va nous permettre de définir de nouvelles classes de graphes. / Graphs are widely used to MODELISER a lot of real situations like road networks, computers networks or electricity ones. Using them, we can solve problems on these networks like routing (go from a vertex ti another one) or explore them (to have a map of studied graph).Studied networks, and so graphs which MODELISER them, can be large (i.e. have a lot of vertices). In this case, we can use the paradigm "Divide and conquer" to answer the questions. Indeed, working on small parts of graphs and merging the results on these small parts, we can obtain the result on the whole graph.In this document, we present a way to separate graphs using shortest paths like separators. This decomposition let to obtain a compact routing, a compact labeling to estimate the distance between vertices of the graph. This method let us to define new class of graphs.

O Problema dos K Menores Caminhos é uma generalização do Problema do Menor Caminho, em que desejamos encontrar os K caminhos de menor custo entre dois vértices de um grafo. Estudamos e implementamos algoritmos que resolvem esse problema em grafos dirigidos, com peso nos arcos e que permitem apenas caminhos sem repetição de vértices na resposta. Comparamos seus desempenhos utilizando grafos do 9th DIMACS Implementation Challenge. Identificamos os pontos fortes e fracos de cada algoritmo, e propusemos uma variante híbrida dos algoritmos de Feng e de Pascoal. Essa variante proposta obteve desempenho superior aos algoritmos base em alguns grafos, e resultado superior a pelo menos um deles na grande maioria dos testes. / The K-Shortest Path Problem is a generalization of the Shortest Path Problem, in which we must find the K paths between two vertices in a graph that have the lowest costs. We study some K-Shortest Path Problem algorithms applied to weighted directed graphs, allowing only paths with no repeated vertices. We compare empirically implementation of some algorithms, using instance graphs from the 9th DIMACS Implementation Challenge. We identify the strengths and weaknesses of each algorithm, and we propose a hybrid version of Feng\'s and Pascoal\'s algorithms. This proposed variant achieve better perfomance compared to both base algorithms in some graphs, and it is better than at least one of them in most cases.