CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / No problema do Caminho MÃnimo com RestriÃÃo ProbabilÃstica de Atraso MÃximo visamos considerar o fator tempo no projeto de rotas de transporte de cargas em malhas viÃrias a custo mÃnimo, atentando à crescente incerteza nos tempos de percurso dessas rotas em malhas reais, e observÃ-lo tendo em mente estratÃgias de qualidade de serviÃo, de forma a obtermos um compromisso entre o custo de percurso e a conformidade ao prazo de chegada ao destino. Realizamos um estudo de problemas relacionados na literatura da Ãrea de otimizaÃÃo em redes de transporte, de forma a tentarmos conhecer melhor o problema a ser estudado, sobre o qual nÃo tomamos conhecimento de trabalhos existentes. Desenvolvemos um esquema para enumeraÃÃo de partiÃÃes do espaÃo de soluÃÃes do problema, que utiliza uma decomposiÃÃo em L para selecionar partiÃÃes de forma inteligente, e que à auxiliado por soluÃÃes de relaxaÃÃes do problema de forma a obter cotas para o custo Ãtimo. AlÃm disso, desenvolvemos algumas estratÃgias de ramificaÃÃo e de poda para um esquema de Branch-and-Bound, com uma fase de prÃ-processamento, de forma a tentar resolver o problema diretamente. Os resultados computacionais obtidos demonstram que somos competitivos com a ferramenta comercial utilizada para comparaÃÃo em instÃncias de menor porte para o problema. Para as demais instÃncias, essa ferramenta se mostrou mais eficiente quanto ao tempo necessÃrio para a resoluÃÃo. / In the Probabilistic Delay Constrained Shortest Path problem we aim to consider the time factor in the design of cargo routing paths in road networks at minimum cost, considering the increasing uncertainty in travel times of these routes in real networks, and keeping in mind strategies of quality of service, in order to obtain a compromise between the travel costs and the compliance of the arrival time at the destination. We conducted a study of related problems in the literature of transport networks optimization, in order to better understand the problem to be addressed, about which we are not aware of existing works. We developed a scheme for enumerating partitions of the solution space of this problem, which uses an L decomposition to select these partitions wisely, and is aided by solutions to relaxations of the problem to obtain bounds for the optimal cost. In addition, we developed some branching and pruning strategies for a Branch-and-Bound scheme, with a pre-processing phase, in order to try and solve the problem directly. The computational results show that we are competitive with the commercial tool used for comparison in the smaller instances. For the remaining instances, this tool is more efficient in the time required for solving the problem.

O problema de caminhos mínimos (SP shortest path problem) é frequentemente colo- cado em prática em uma grande variedade de aplicações em diversas áreas. Nessas aplicações geralmente se deseja realizar algum tipo de deslocamento ou transporte entre dois ou mais pontos específicos em uma rede. Tal ação deve ser executada de forma ótima em relação a algum critério, por exemplo o menor custo possível, ou o menor gasto de tempo ou o máximo de confiabilidade/segurança. Na prática, muitas vezes não desejamos apenas o menor custo ou o menor tempo, mas desejamos otimizar uma combinação de diferentes critérios, por exemplo, um caminho que seja rápido e barato. Como não é possível otimizar sobre todos os critérios de uma só vez, nós escolhemos um dos critérios para representar a função custo, que será minimizada, e para os demais critérios representamos como recursos e definimos os limites que julgamos aceitáveis para o consumo de cada um desses recursos. Esta variação é cha- mada de problema de caminhos mínimos com restrições por recursos, ou como preferimos chamar, problema de caminhos mínimos com recursos limitados (RCSP resource constrained shortest path problem), o qual será o objeto de estudo neste trabalho. A adição de restrições por recursos no SP, infelizmente torna o problema NP-difícil, mesmo em grafos acíclicos, com restrições sobre um único recurso, e com todos os consu- mos de recursos positivos. Temos reduções dos famosos problemas N P-difíceis Mochila e Partição para o nosso problema. Em contextos diversos são encontrados problemas de cunho teórico e prático que po- dem ser formulados como problemas de caminhos mínimos com recursos limitados, o que nos motivou a estudá-lo a fim de desenvolver um trabalho que resumisse informações sufi- cientes para auxiliar pesquisadores ou desenvolvedores que tenham interesse no problema. Nós apresentamos aqui, uma detalhada revisão bibliográfica do RCSP, tendo como foco o desenvolvimento de algoritmos exatos para o caso onde possuímos um único recurso e a im- plementação e comparação dos principais algoritmos conhecidos, observando-os em situações práticas. / The problem of choosing a route to a trip, where we want minimize the distance of the path is a major problem in computing. In this basic form, this is the shortest path problem. But sometimes, besides the length we need to consider more parameters for selecting a good path. A common parameters to consider is the consumption of resources in a limited budget. A shortest path with these additional constraints is called resource constrained shortest path - RCSP. This paper has two main objectives: to present a literature review of the problem RCSP, focusing on exact algorithms for the case where we have a single resource, and implement and compare some algorithms, observing them in practical situations. The Shortest Path (SP) problem is among the fundamental problems of computer sci- ence. Its been deeply studied and subject of many publications. Also, many efficient solutions (polynomial time algorithms) are known for this problem. The SP is widely applied in many fields of science, not only computer science. These situations usually need to transport a load between two or more specific spots of a network. This action must be taken optimally regarding to some criterion, for instance the least cost, or the least time or maximum relia- bility. While new solutions for SP were presented, new demands were issued too, with new variations for the problem. One of these variations comes from the fact that, in a real scenario, a combination of many criteria must be optimized, for instance a path with least cost and least time. This problem is known as Multiobjective Shortest Path. Since its not possible to optimize all criteria at once, one of them is chosen to represent the cost function to be minimized and the others to represent resources with defined boundary. This variation, known as Resource Constrained Shortest Path (RCSP), was the object of the present study. By adding resource constraints, the SPbecomes N P-hard, even in acyclic graphs with only one resource constrained and all resource consumption being positive. There are reduc- tions from the famous NP-hard problems Knapsack and Partition to our problem. In many fields, are found theoretical and practical problems that may be expressed as a Resource Constrained Shortest Path Problem, which motivated us to study this problem in order to summarize enough information to researchers and developers involved with this problem. This paper presents a detailed bibliographic revision to RCSP, focusing on the development of exact algorithms for the case when there is only only one resource and on the implementation and comparison of the main known algorithms in practical situations.

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.

This thesis presents a comparison between a basic shortest path routing policy of the Destination-Sequence Distance Vector (DSDV) protocol and two power-aware policy variations of it. In the two modified versions, the routes are selected based on the energy available on the nodes and not only the shortest path distance to the destination. Simulations are conducted for a given situation of nodes and the energy efficiency of the three aforementioned policies are evaluated for example scenarios. First, a brief overview of the theory behind the study is presented. It consists of an description of ad hoc networking, DSDV, and our energy-aware modifications to DSDV. After the fundamental theory, the method is presented. It consists of a description of how the simulated scenarios relates to a real-world scenario and the simplifications made in the model. We present an overview of the model used for simulation and the operation of the program. This section ends with an explanation of the three simulated policies: shortest path, simple weighted and doubled weighted. When the theory behind the thesis are completed, the simulations are conducted. The results are examined and a summary of their meaning is discussed. It is explained how the assumptions effect the reliability of the study and an estimation of the accuracy of the results are presented. We find that the power-aware policy variations (simple weighted and double weighted) both achieve better network lifetime than the basic shortest path policy, at the cost of slightly longer per-packet paths. These results are encouraging and show that very simple modifications to DSDV can achieve significant gains in the network lifetime, helping users get the most out of their networks. Future investigation could try to optimize these gains.

Cerný, em 1964, conjecturou que um autômato sincronizado com n estados possui uma palavra sincronizadora mínima de tamanho no máximo (n-1)². Esta conjectura permanece em aberto. Neste trabalho são apresentados algoritmos para obter palavras sincronizadoras e é feito um experimento comparativo entre os resultados obtidos por estes algoritmos em relação a algumas séries infinitas de autômatos. Por fim, é feito um breve histórico sobre os resultados parciais obtidos até a presente data e alguns destes trabalhos são apresentados em mais detalhes. / Cerný, on 1964, conjectured that a synchronizing automata with n states has a synchronizing word of size at most (n-1)². The conjecture remains open. We show some algorithms for obtaining synchronizing sequences and a comparative experiment between these algorithms with respect to some infinite series of automata. Furthermore, we briefly survey some of the partial results obtained until the present day.

Threat modeling for information technology infrastructure can be done using shortest path algorithms in stochastic graphs. By modeling the infrastructure as a graph, potential vulnerabilities may be presented by computing what paths an attacker might take. This thesis project presents and compares two memory efficient algorithms that can be used to solve this problem approximately, the online k-means and sampled k-shortest path algorithm. By computing paths for several different graph types, the two algorithms were compared against a naive algorithm. The online k-means algorithm uses approximately 77 times less memory, executes in the same amount of time, and produces similar path lengths. In our experiments, the sampled k-shortest path algorithm uses approximately 154 times less memory, execution time is seen to be lowered by a factor of 5 to 20 depending on the graph type, but path distances computed are longer.

This paper deals with the analysis of the collected GPS data and the possibility of the prediction of most advantageous route on its basis, by the application written in the PHP scripting language. The suitability of the route is considered by the distance, driving time, or elevation. The thesis also describes a GPS system, the format of the source data and their storing in an appropriate database. There is also a description of the search of the shortest path in the graph and some famous algorithms for finding it. The paper includes information about implementation of new data integration and path finding within this data in PHP scripting language. In conclusion it is evaluated what are the benefits of this application and design saying how this application can be improved in the future.

This project seeks to demonstrate routing optimization that would allow pedestrian and micromobility user groups to select and prioritize different route features according to their preferences. Through the creation of a routing demonstrator that considers both static and dynamic parameters in the form of pavement quality, elevation climb, travel time, and air quality, along with user-specified weights for their prioritization of each of these parameters, a number of routes were created and mapped to qualitatively compare against routes representing only a shortest path. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

A stochastic shortest path (SSP) problem is an undiscounted Markov decision process with an absorbing and zero-cost target state, where the objective is to reach the target state with minimum expected cost. This problem provides a foundation for algorithms for decision-theoretic planning and probabilistic model checking, among other applications. This thesis describes an implementation and evaluation of recently developed error bounds for SSP problems. The bounds can be used in a test for convergence of iterative dynamic programming algorithms for solving SSP problems, as well as in action elimination procedures that can accelerate convergence by excluding provably suboptimal actions that do not need to be re-evaluated each iteration. The techniques are shown to be effective for both decision-theoretic planning and probabilistic model checking.

A major factor that negatively impacts flight operations globally is adverse weather. To reduce the impact of adverse weather, avoidance procedures such as finding an alternative flight path can usually be carried out. However, such procedures usually introduce extra costs such as flight delay. Hence, there exists a need for alternative flight paths that efficiently avoid adverse weather regions while minimising costs. Existing weather avoidance methods used techniques, such as Dijkstra’s and artificial potential field algorithms that do not scale adequately and have poor real time performance. They do not adequately consider the impact of weather and its avoidance on passengers. The contributions of this work include a new development of an improved integrated model for weather avoidance, that addressed the impact of weather on passengers by defining a corresponding cost metric. The model simultaneously considered other costs such as flight delay and fuel burn costs. A genetic algorithm (GA)-based rerouting technique that generates optimised alternative flight paths was proposed. The technique used a modified mutation strategy to improve global search. A discrete firefly algorithm-based rerouting method was also developed to improve rerouting efficiency. A data framework and simulation platform that integrated aeronautical, weather and flight data into the avoidance process was developed. Results show that the developed algorithms and model produced flight paths that had lower total costs compared with existing techniques. The proposed algorithms had adequate rerouting performance in complex airspace scenarios. The developed system also adequately avoided the paths of multiple aircraft in the considered airspace.