abstract: Given that more and more planned special events are hosted in urban areas, during which travel demand is considerably higher than usual, it is one of the most effective strategies opening public rapid transit lines and building park-and-ride facilities to allow visitors to park their cars and take buses to the event sites. In the meantime, special event workforce often needs to make balances among the limitations of construction budget, land use and targeted travel time budgets for visitors. As such, optimizing the park-and-ride locations and capacities is critical in this process of transportation management during planned special event. It is also known as park-and-ride facility design problem. This thesis formulates and solves the park-and-ride facility design problem for special events based on space-time network models. The general network design process with park-and-ride facilities location design is first elaborated and then mathematical programming formulation is established for special events. Meanwhile with the purpose of relax some certain hard constraints in this problem, a transformed network model which the hard park-and-ride constraints are pre-built into the new network is constructed and solved with the similar solution algorithm. In doing so, the number of hard constraints and level of complexity of the studied problem can be considerable reduced in some cases. Through two case studies, it is proven that the proposed formulation and solution algorithms can provide effective decision supports in selecting the locations and capabilities of park-and-ride facilities for special events. / Dissertation/Thesis / Masters Thesis Civil and Environmental Engineering 2016

Real-life transportation systems are subject to numerous uncertainties in their operation. Researchers have suggested various reliability measures to characterize their network-level performances. One of these measures is given by travel time reliability, defined as the probability that travel times remain below certain (acceptable) levels. Existing reliability assessment (and optimization) techniques tend to be computationally intensive. In this dissertation we develop computationally efficient alternatives. In particular, we make the following three contributions. In the first contribution, we present a novel reliability assessment methodology when the source of uncertainty is given by road capacities. More specifically, we present a method based on the theory of Fourier transforms to numerically approximate the probability density function of the (system-wide) travel time. The proposed methodology takes advantage of the established computational efficiency of the fast Fourier transform. In the second contribution, we relax the common assumption that probability distributions of the sources of uncertainties are known explicitly. In reality, this distribution may be unavailable (or inaccurate) as we may have no (or insufficient) data to calibrate the distributions. We present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is any positive integer) of the travel time to be known and that the travel times reside in a set of known and bounded intervals. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop analytical probability inequalities to quickly obtain upper bounds on the desired probability. Because of the computationally intensive nature of (virtually all) existing reliability assessment techniques, the optimization of the reliability of transportation systems has generally been computationally prohibitive. The third and final contribution of this dissertation is the introduction of a new transportation network design model in which the objective is to minimize the unreliability of travel time. The computational requirements are shown to be much lower due to the assessment techniques developed in this dissertation. Moreover, numerical results suggest that it has the potential to form a computationally efficient proxy for current simulation-based network design models. / text

In this dissertation, we examine specific network connectivity problems, and achieve improved approximation algorithm and integrality gap results for them. We introduce an important new, highly useful and applicable, network connectivity problem - the Vital Core Connectivity Problem (VCC). Despite its many practical uses, this problem has not been previously studied. We present the first constant factor approximation algorithm for VCC, and provide an upper bound on the integrality gap of its linear programming relaxation. We also introduce a new, useful, extension of the minimum spanning tree problem, called the Extended Minimum Spanning Tree Problem (EMST), that is based on a special case of VCC; and provide both a polynomial-time algorithm and a complete linear description for it. Furthermore, we show how to generalize this new problem to handle numerous disjoint vital cores, providing the first complete linear description of, and polynomial-time algorithm for, the generalized problem. We examine the Survivable Network Design Problem (SNDP) with multiple copies of edges allowed in the solution (multi-SNDP), and present a new approximation algorithm for which the approximation guarantee is better than that of the current best known for certain cases of multi-SNDP. With our method, we also obtain improved bounds on the integrality gap of the linear programming relaxation of the problem. Furthermore, we show the application of these results to variations of SNDP. We investigate cases where the optimal values of multi-SNDP and SNDP are equal; and we present an improvement on the previously best known integrality gap bound and approximation guarantee for the special case of SNDP with metric costs and low vertex connectivity requirements, as well as for the similar special case of the Vertex Connected Survivable Network Design Problem (VC-SNDP). The quality of the results that one can obtain for a given network design problem often depends on its integer linear programming formulation, and, in particular, on its linear programming relaxation. In this connection, we investigate formulations for the Steiner Tree Problem (ST). We propose two new formulations for ST, and investigate their strength in terms of their associated integrality gaps.

Network design decisions, especially those pertaining to urban infrastructure, are made by a central authority or network leader, and taking into consideration the network users or followers. These network decision problems are formulated as non-linear bi-level programming problems. In this work, a continuous network design problem (CNDP) and discrete network design problem (DNDP) bi-level optimization programs are proposed and solved in the context of transportation planning. The solution strategy involved reformulation and linearization as a single-level program by introducing the optimality conditions of the lower level problem into the upper level problem. For the CNDP, an alternative linearization algorithm (modified least squares partitioning, MLSPA) is proposed. MLSPA takes into consideration the current arc capacity and potential expansion to find a reduced set of planes to generalize the flow-capacity surface behavior. The concepts of flow capacity surface was introduced as a way to model of congested network and capture the effect of capacity on travel time/cost. It was found that the quality of the linear approximation depends on the goodness of fit the bottleneck arcs. The proposed approach was tested with well-known benchmark problems in transportation which yielded promising results in terms of efficiency, without sacrificing solution quality.

In this dissertation, we examine specific network connectivity problems, and achieve improved approximation algorithm and integrality gap results for them. We introduce an important new, highly useful and applicable, network connectivity problem - the Vital Core Connectivity Problem (VCC). Despite its many practical uses, this problem has not been previously studied. We present the first constant factor approximation algorithm for VCC, and provide an upper bound on the integrality gap of its linear programming relaxation. We also introduce a new, useful, extension of the minimum spanning tree problem, called the Extended Minimum Spanning Tree Problem (EMST), that is based on a special case of VCC; and provide both a polynomial-time algorithm and a complete linear description for it. Furthermore, we show how to generalize this new problem to handle numerous disjoint vital cores, providing the first complete linear description of, and polynomial-time algorithm for, the generalized problem. We examine the Survivable Network Design Problem (SNDP) with multiple copies of edges allowed in the solution (multi-SNDP), and present a new approximation algorithm for which the approximation guarantee is better than that of the current best known for certain cases of multi-SNDP. With our method, we also obtain improved bounds on the integrality gap of the linear programming relaxation of the problem. Furthermore, we show the application of these results to variations of SNDP. We investigate cases where the optimal values of multi-SNDP and SNDP are equal; and we present an improvement on the previously best known integrality gap bound and approximation guarantee for the special case of SNDP with metric costs and low vertex connectivity requirements, as well as for the similar special case of the Vertex Connected Survivable Network Design Problem (VC-SNDP). The quality of the results that one can obtain for a given network design problem often depends on its integer linear programming formulation, and, in particular, on its linear programming relaxation. In this connection, we investigate formulations for the Steiner Tree Problem (ST). We propose two new formulations for ST, and investigate their strength in terms of their associated integrality gaps.

In this dissertation, we examine specific network connectivity problems, and achieve improved approximation algorithm and integrality gap results for them. We introduce an important new, highly useful and applicable, network connectivity problem - the Vital Core Connectivity Problem (VCC). Despite its many practical uses, this problem has not been previously studied. We present the first constant factor approximation algorithm for VCC, and provide an upper bound on the integrality gap of its linear programming relaxation. We also introduce a new, useful, extension of the minimum spanning tree problem, called the Extended Minimum Spanning Tree Problem (EMST), that is based on a special case of VCC; and provide both a polynomial-time algorithm and a complete linear description for it. Furthermore, we show how to generalize this new problem to handle numerous disjoint vital cores, providing the first complete linear description of, and polynomial-time algorithm for, the generalized problem. We examine the Survivable Network Design Problem (SNDP) with multiple copies of edges allowed in the solution (multi-SNDP), and present a new approximation algorithm for which the approximation guarantee is better than that of the current best known for certain cases of multi-SNDP. With our method, we also obtain improved bounds on the integrality gap of the linear programming relaxation of the problem. Furthermore, we show the application of these results to variations of SNDP. We investigate cases where the optimal values of multi-SNDP and SNDP are equal; and we present an improvement on the previously best known integrality gap bound and approximation guarantee for the special case of SNDP with metric costs and low vertex connectivity requirements, as well as for the similar special case of the Vertex Connected Survivable Network Design Problem (VC-SNDP). The quality of the results that one can obtain for a given network design problem often depends on its integer linear programming formulation, and, in particular, on its linear programming relaxation. In this connection, we investigate formulations for the Steiner Tree Problem (ST). We propose two new formulations for ST, and investigate their strength in terms of their associated integrality gaps.

As the the number of cores on a single chip continue to grow, communication increasingly becomes the bottleneck to performance. Networks on Chips (NoC) is an interconnection paradigm showing promise to allow system size to increase while maintaining acceptable performance. One of the challenges of this paradigm is in constructing the network of inter-core connections. Using the traditional wire interconnect as long range links is proving insufficient due to the increase in relative delay as miniaturization progresses. Novel link types are capable of delivering single-hop long-range communication. We investigate the potential benefits of constructing networks with many link types applied to heterogeneous NoCs and hypothesize that a network with many link types available can achieve a higher performance at a given cost than its homogeneous network counterpart. To investigate NoCs with heterogeneous links, a multiobjective evolutionary algorithm is given a heterogeneous set of links and optimizes the number and placement of those links in an NoC using objectives of cost, throughput, and energy as a representative set of a NoC's quality. The types of links used and the topology of those links is explored as a consequence of the properties of available links and preference set on the objectives. As the platform of experimentation, the Complex Network Evolutionary Algorithm (CNEA) and the associated Complex Network Framework (CNF) are developed. CNEA is a multiobjective evolutionary algorithm built from the ParadisEO framework to facilitate the construction of optimized networks. CNF is designed and used to model and evaluate networks according to: cost of a given topology; performance in terms of a network's throughput and energy consumption; and graph-theory based metrics including average distance, degree-, length-, and link-distributions. It is shown that optimizing complex networks to cost as a function of total link length and average distance creates a power-law link-length distribution. This offers a way to decrease the average distance of a network for a given cost when compared to random networks or the standard mesh network. We then explore the use of several types of constrained-length links in the same optimization problem and find that, when given access to all link types, we obtain networks that have the same or smaller average distance for a given cost than any network that is produced when given access to only one link type. We then introduce traffic on the networks with an interconnect-based packet-level shortest-path-routed traffic model. We find heterogeneous networks can achieve a throughput as good or better than the homogeneous network counterpart using the same amount of link. Finally, these results are confirmed by augmenting a wire-based mesh network with non-traditional link types and finding significant increases the overall performance of that network.

Dynamic Traffic Assignment (DTA) is gaining wider acceptance among agencies and practitioners because it serves as a more realistic representation of real-world traffic phenomena than static traffic assignment. Many metropolitan planning organizations and transportation departments are beginning to utilize DTA to predict traffic flows within their networks when conducting traffic analysis or evaluating management measures. To analyze DTA-based optimization applications, it is critical to obtain the dual (or gradient) information as dual information can typically be employed as a search direction in algorithmic design. However, very limited number of approaches can be used to estimate network-wide dual information while maintaining the potential to scale. This dissertation investigates the theoretical/practical aspects of DTA-based dual approximation techniques and explores DTA applications in the context of various transportation models, such as transportation network design, off-line DTA capacity calibration and dynamic congestion pricing. Each of the later entities is formulated as bi-level programs. Transportation Network Design Problem (NDP) aims to determine the optimal network expansion policy under a given budget constraint. NDP is bi-level by nature and can be considered a static case of a Stackelberg game, in which transportation planners (leaders) attempt to optimize the overall transportation system while road users (followers) attempt to achieve their own maximal benefit. The first part of this dissertation attempts to study NDP by combining a decomposition-based algorithmic structure with dual variable approximation techniques derived from linear programming theory. One of the critical elements in considering any real-time traffic management strategy requires assessing network traffic dynamics. Traffic is inherently dynamic, since it features congestion patterns that evolve over time and queues that form and dissipate over a planning horizon. It is therefore imperative to calibrate the DTA model such that it can accurately reproduce field observations and avoid erroneous flow predictions when evaluating traffic management strategies. Satisfactory calibration of the DTA model is an onerous task due to the large number of variables that can be modified and the intensive computational resources required. In this dissertation, the off-line DTA capacity calibration problem is studied in an attempt to devise a systematic approach for effective model calibration. Congestion pricing has increasingly been seen as a powerful tool for both managing congestion and generating revenue for infrastructure maintenance and sustainable development. By carefully levying tolls on roadways, a more efficient and optimal network flow pattern can be generated. Furthermore, congestion pricing acts as an effective travel demand management strategy that reduces peak period vehicle trips by encouraging people to shift to more efficient modes such as transit. Recently, with the increase in the number of highway Build-Operate-Transfer (B-O-T) projects, tolling has been interpreted as an effective way to generate revenue to offset the construction and maintenance costs of infrastructure. To maximize the benefits of congestion pricing, a careful analysis based on dynamic traffic conditions has to be conducted before determining tolls, since sub-optimal tolls can significantly worsen the system performance. Combining a network-wide time-varying toll analysis together with an efficient solution-building approach will be one of the main contributions of this dissertation. The problems mentioned above are typically framed as bi-level programs, which pose considerable challenges in theory and as well as in application. Due to the non-convex solution space and inherent NP-complete complexity, a majority of recent research efforts have focused on tackling bi-level programs using meta-heuristics. These approaches allow for the efficient exploration of complex solution spaces and the identification of potential global optima. Accordingly, this dissertation also attempts to present and compare several meta-heuristics through extensive numerical experiments to determine the most effective and efficient meta-heuristic, as a means of better investigating realistic network scenarios. / text

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))