Railroad is one of the primary modes for transporting hazardous materials (hazmat). Given the dangerous nature of the hazmat, risk mitigation in the railroad transportation is the need of the hour. Hence, we explore the idea of equitable distribution of risk in the railroad network. We propose the subsidy policy to be considered by government to induce favourable routings of the hazmat shipments. The government's objective is to achieve risk equity in the network, whereas, the carrier's cost effective approach leads to increased risk in low-cost service-legs. To model this, we formulate the problem as a bi-level mixed integer program. We derive the single level mixed integer linear program (MILP) and test it on the rail infrastructure in midwest United States using state-of-the-art solver CPLEX 12.8.0. The instances with upto 25 shipments on the network are solved efficiently on a local machine. We use high performance computing resource available at Graham cluster of Compute Canada facility to solve the large instances with 50 shipments on the network. We show the effectiveness of the subsidy policy as a risk mitigation tool for the railroad hazmat transportation, and review the efficiency of the solution methodology to solve the MILP for the network. Moreover, the results demonstrate the economic feasibility for the government to allocate the budget for the subsidy. / Thesis / Master of Science (MSc)

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an -- reliability criterion. This reliability criterion is a generalization of the well-known - criterion and dictates that at least fraction of the total system demand (for ) must be met following the failure of or fewer system components. We refer to this problem as the contingency-constrained unit commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network. These studies demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

In this study, a new selective and time-window routing problem is defined for the first time in the literature, which is called the campaign routing problem (CRP). The two special cases of the CRP correspond to the two real-life problems, namely political campaign routing problem (PCRP) and the experiments on wheels routing problem (EWRP). The PCRP is based on two main decision levels. In the first level, a set of campaign regions is selected according to a given criteria subject to the special time-window constraints. In the second level, a pair of selected regions or a single region is assigned to a campaign day. In the EWRP, a single selected region (school) is assigned to a campaign day. These two problems are modeled using classical mathematical programming and bi-level programming methods, and a two-step heuristic approach is developed for the solution of the problems. Implementation of the solution methods is done using the test instances that are compiled from the real-life data. Computational results show that the solution methods developed generate good solutions in reasonable time.

In recent decades, climate change has become one of the most crucial challenges for humanity. Climate change has a direct correlation with global warming, caused mainly by the green house gas emissions (GHG). The Environmental Protection Agency in the U.S. (EPA) attributes carbon dioxide to account for approximately 82\% of the GHG emissions. Unfortunately, the energy sector is the main producer of carbon dioxide, with China and the U.S. as the highest emitters. Therefore, there is a strong (positive) correlation between energy production, global warming, and climate change. Stringent carbon emissions reduction targets have been established in order to reduce the impacts of GHG. Achieving these emissions reduction goals will require implementation of policies like as cap-and-trade and carbon taxes, together with transformation of the electricity grid into a smarter system with high green energy penetration. However, the consideration of policies solely in view of carbon emissions reduction may adversely impact other market outcomes such as electricity prices and consumption. In this dissertation, a two-layer mathematical-statistical framework is presented, that serves to develop carbon policies to reduce emissions level while minimizing the negative impacts on other market outcomes. The bottom layer of the two layer model comprises a bi-level optimization problem. The top layer comprises a statistical model and a Pareto analysis. Two related but different problems are studied under this methodology. The first problem looks into the design of cap-and-trade policies for deregulated electricity markets that satisfy the interest of different market constituents. Via the second problem, it is demonstrated how the framework can be used to obtain levels of carbon emissions reduction while minimizing the negative impact on electricity demand and maximizing green penetration from microgrids. In the aforementioned studies, forecasts for electricity prices and production cost are considered. This, this dissertation also presents anew forecast model that can be easily integrated in the two-layer framework. It is demonstrated in this dissertation that the proposed framework can be utilized by policy-makers, power companies, consumers, and market regulators in developing emissions policy decisions, bidding strategies, market regulations, and electricity dispatch strategies.

Transportation system is one of the key functioning components of the modern society and plays an important role in the circulation of commodity and growth of economy. Transportation system is not only the major influencing factor of the efficiency of large-scale complex industrial logistics, but also closely related to everyone’s daily life. The goals of an ideal transportation system are focused on improving mobility, accessibility, safety, enhancing the coordination of different transportation modals and reducing the impact on the environment, all these activities require sophisticated design and plan that consider different factors, balance tradeoffs and maintaining efficiency. Hence, the design and planning of transportation system are strongly considered to be the most critical problems in transportation research. Transportation system planning and design is a sequential procedure which generally contains two levels: strategic and operational. This dissertation conducts extensive research covering both levels, on the strategic planning level, two network design problems are studied and on the operational level, routing and scheduling problems are analyzed. The main objective of this study is utilizing operations research techniques to generate and provide managerial decision supports in designing reliable and efficient transportation system. Specifically, three practical problems in transportation system design and operations are explored. First, we collaborate with a public transit company to study the bus scheduling problem for a bus fleet with multiples types of vehicles. By considering different cost characteristics, we develop integer program and exact algorithm to efficiently solve the problem. Next, we examine the network design problem in emergency medical service and develop a novel two stage robust optimization framework to deal with uncertainty, then propose an approximate algorithm which is fast and efficient in solving practical instance. Finally, we investigate the major drawback of vehicle sharing program network design problem in previous research and provide a counterintuitive finding that could result in unrealistic solution. A new pessimistic model as well as a customized computational scheme are then introduced. We benchmark the performance of new model with existing model on several prototypical network structures. The results show that our proposed models and solution methods offer powerful decision support tools for decision makers to design, build and maintain efficient and reliable transportation systems.

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.

Major cyber attacks against the cyber networks of organizations has become a common phenomenon nowadays. Cyber attacks are carried out both through the spread of malware and also through multi-stage attacks known as hacking. A cyber network can be represented directly as a simple directed or undirected network (graph) of nodes and arcs. It can also be represented by a transformed network such as the attack graph which uses information about network topology, attacker profile, and existing vulnerabilities to represent all the potential attack paths from readily accesible vulnerabilities to valuable target nodes. Then, interdicting or hardening a subset of arcs in the network naturally maps into deploying security countermeasures on the associated devices or connections. In this dissertation, we develop network interdiction models and algorithms to optimally select a subset of arcs which upon interdiction minimizes the spread of infection or minimizes the loss from multi-stage attacks. In particular, we define four novel network connectivity-based metrics and develop interdiction models to optimize the metrics. Direct network representation of the physical cyber network is used as the underlying network in this case. Two of the interdiction models prove to be very effective arc removal methods for minimizing the spread of infection. We also develop multi-level network interdiction models that remove a subset of arcs to minimize the loss from multi-stage attacks. Our models capture the defenderattacker interaction in terms of stackelberg zero-sum games considering the attacker both as a complete rational and bounded rational agents. Our novel solution algorithms based on constraint and column generation and enhanced by heuristic methods efficiently solve the difficult multi-level mixed-integer programs with integer variables in all levels in reasonable times.

Le système étudié durant cette thèse est un véhicule électrique hybride avec deux sources d’énergies (Pile à combustible et Super-capacité). L’objectif fixé est de minimiser la consommation du carburant tout en satisfaisant la demande instantanée en puissance sous des contraintes de puissance et de capacité et de stockage. Le problème a été modélisé sous la forme d’un problème d’optimisation globale. Nous avons développé de nouvelles méthodes heuristiques pour le résoudre et proposé le calcul d’une borne inférieure de consommation, en apportant de meilleurs résultats que ceux trouvés dans la littérature. En plus, une étude de robustesse a été réalisée afin de minimiser la consommation de pire-cas suite à une perturbation ou du fait d’incertitudes sur les données d’entrée, précisément sur la puissance demandée. Le but de cette étude est de prendre en compte les perturbations dès la construction des solutions afin d’éviter l’infaisabilité des solutions non robustes en situation perturbée. Les heuristiques de résolution du problème robuste modélisé sous la forme d’un problème de Minimax ont fourni des solutions moins sensibles aux perturbations que les solutions classiques. / The system studied in this thesis is a hybrid electrical vehicle with two energy sources (fuel cell system and super-capacitor). The first goal is to minimize the fuel consumption whilst satisfying the requested power for each instant, taking into account constraints on the availability and the state of charge of the storage element. The system was modeled as a global optimization problem. The heuristics developped for obtaining the best power split between the two sources and the lower bound consumption computation proposed provide better results than those found in the literature. The second goal of the thesis is the study of the robustness of the solutions in order to minimize the worst-case consumption when perturbation happens or uncertainty is added to the input data. In this study the uncertainty concerns the power required for traction. The objective is to maintain the feasibility of solutions and limit the worst consumption that can happen due to a demand fluctuation. Dedicated heuristics are proposed for solving the identified robust variant of the problem, modeled as a Minimax problem. The solutions provided are less sensitive to the perturbations than the previous ones.

Les problèmes d’optimisation combinatoire sont généralement réputés NP-difficiles, donc il n’y a pas d’algorithmes efficaces pour les résoudre. Afin de trouver des solutions optimales locales ou réalisables, on utilise souvent des heuristiques ou des algorithmes approchés. Les dernières décennies ont vu naitre des méthodes approchées connues sous le nom de métaheuristiques, et qui permettent de trouver une solution approchées. Cette thèse propose de résoudre des problèmes d’optimisation déterministe et stochastique à l’aide de métaheuristiques. Nous avons particulièrement étudié la méthode de voisinage variable connue sous le nom de VNS. Nous avons choisi cet algorithme pour résoudre nos problèmes d’optimisation dans la mesure où VNS permet de trouver des solutions de bonne qualité dans un temps CPU raisonnable. Le premier problème que nous avons étudié dans le cadre de cette thèse est le problème déterministe de largeur de bande de matrices creuses. Il s’agit d’un problème combinatoire difficile, notre VNS a permis de trouver des solutions comparables à celles de la littérature en termes de qualité des résultats mais avec temps de calcul plus compétitif. Nous nous sommes intéressés dans un deuxième temps aux problèmes de réseaux mobiles appelés OFDMA-TDMA. Nous avons étudié le problème d’affectation de ressources dans ce type de réseaux, nous avons proposé deux modèles : Le premier modèle est un modèle déterministe qui permet de maximiser la bande passante du canal pour un réseau OFDMA à débit monodirectionnel appelé Uplink sous contraintes d’énergie utilisée par les utilisateurs et des contraintes d’affectation de porteuses. Pour ce problème, VNS donne de très bons résultats et des bornes de bonne qualité. Le deuxième modèle est un problème stochastique de réseaux OFDMA d’affectation de ressources multi-cellules. Pour résoudre ce problème, on utilise le problème déterministe équivalent auquel on applique la méthode VNS qui dans ce cas permet de trouver des solutions avec un saut de dualité très faible. Les problèmes d’allocation de ressources aussi bien dans les réseaux OFDMA ou dans d’autres domaines peuvent aussi être modélisés sous forme de problèmes d’optimisation bi-niveaux appelés aussi problèmes d’optimisation hiérarchique. Le dernier problème étudié dans le cadre de cette thèse porte sur les problèmes bi-niveaux stochastiques. Pour résoudre le problème lié à l’incertitude dans ce problème, nous avons utilisé l’optimisation robuste plus précisément l’approche appelée « distributionnellement robuste ». Cette approche donne de très bons résultats légèrement conservateurs notamment lorsque le nombre de variables du leader est très supérieur à celui du suiveur. Nos expérimentations ont confirmé l’efficacité de nos méthodes pour l’ensemble des problèmes étudiés. / Combinatorial optimization problems are generally NP-hard problems, so they can only rely on heuristic or approximation algorithms to find a local optimum or a feasible solution. During the last decades, more general solving techniques have been proposed, namely metaheuristics which can be applied to many types of combinatorial optimization problems. This PhD thesis proposed to solve the deterministic and stochastic optimization problems with metaheuristics. We studied especially Variable Neighborhood Search (VNS) and choose this algorithm to solve our optimization problems since it is able to find satisfying approximated optimal solutions within a reasonable computation time. Our thesis starts with a relatively simple deterministic combinatorial optimization problem: Bandwidth Minimization Problem. The proposed VNS procedure offers an advantage in terms of CPU time compared to the literature. Then, we focus on resource allocation problems in OFDMA systems, and present two models. The first model aims at maximizing the total bandwidth channel capacity of an uplink OFDMA-TDMA network subject to user power and subcarrier assignment constraints while simultaneously scheduling users in time. For this problem, VNS gives tight bounds. The second model is stochastic resource allocation model for uplink wireless multi-cell OFDMA Networks. After transforming the original model into a deterministic one, the proposed VNS is applied on the deterministic model, and find near optimal solutions. Subsequently, several problems either in OFDMA systems or in many other topics in resource allocation can be modeled as hierarchy problems, e.g., bi-level optimization problems. Thus, we also study stochastic bi-level optimization problems, and use robust optimization framework to deal with uncertainty. The distributionally robust approach can obtain slight conservative solutions when the number of binary variables in the upper level is larger than the number of variables in the lower level. Our numerical results for all the problems studied in this thesis show the performance of our approaches.

Orientador: Rubén Augusto Romero Lázaro / Banca: Jose Roberto Sanches Mantovani / Banca: Anna Diva Plasencia Lotufo / Banca: Marcos Julio Rider Flores / Banca: Eduardo Nobuhiro Asada / Resumo: Nessa pesquisa tem-se por objetivo a análise teórica e a implementação computacional de duas propostas de solução ao problema de planejamento da expansão de sistemas de transmissão de energia elétrica considerando diferentes fatores relacionados com a confiabilidade do sistema e a adoção dos novos modelos de mercados elétricos. É importante notar, que no planejamento básico não são levados em conta esses importantes aspectos. Dessa forma, uma primeira aproximação considera um critério de confiabilidade para expandir o sistema, de forma que ele opere adequadamente no horizonte de planejamento satisfazendo um nível de confiabilidade pré-definido. O índice de confiabilidade utilizado para exigir esse nível de confiabilidade é o LOLE, que corresponde ao número médio de horas/dias em um período dado (normalmente um ano) no qual o pico da carga horária/diária do sistema possivelmente exceder'a a capacidade de geração disponível. O problema de planejamento considerando a confiabilidade é, portanto, formulado como um problema de otimização que minimiza o investimento sujeito ao critério de confiabilidade. O índice de confiabilidade para o sistema de transmissão é calculado para cada configuração, subtraindo o índice de confiabilidade do sistema de geração do sistema composto geração-transmissão (bulk power system ). Para calcular o índice no sistema composto geração transmissão, utiliza-se uma curva de duração de carga efetiva para este sistema. Esta curva acumulada de carga é obtida de um processo de convolução de outras duas curvas que representam a função de distribuição de probabilidade (FDP) das saídas aleatórias dos componentes do sistema e a curva de duração de carga, respectivamente. A avaliação de confiabilidade no sistema de geração é feita usando um método que calcula o índice de confiabilidade por meio dos momentos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work aims to the theoretical analysis and computational implementation of two proposals for the transmission expansion planning problem considering several factors such as system reliability and new electricity market structures. It is important to observe, that the basic planning does not consider these issues. Therefore, one first approach considers a reliability criterion to expand the system, so that it operates in adequate conditions in the horizon planning while satisfying pre-defined limits in the reliability index. Transmission system reliability criterion regards to LOLE, which refers to the number of hours/days in a specified period of time (normally one year), in which the hourly/daily peak load possibly will exceed the available generation capacity. So, the planning problem considering reliability is formulated as an optimization problem that minimizes the investment subject to probabilistic reliability criterion. Reliability index for the transmission system is calculated for each configuration by subtraction of generation and bulk power reliability indexes. A composite power system effective load curve is used for reliability analysis of the bulk power system. This accumulate curve is obtained convolving two curves, one of them corresponding to a probability distribution function of the random outages of the system components, and the other one corresponding to the load duration curve. Reliability assessment in the generation system is done using a method that calculates the reliability index through the statistics moments of the frequency distribution of equivalents loads. This curve is obtained by convolving the generation units which are dispached in merit order. The proposed model is solved using the specialized genetic algorithm of Chu-Beasley (AGCB). Detailed results on two test systems are analyzed and discussed. A second approach to the transmission expansion... (Complete abstract click electronic access below) / Doutor