A t-design is a combinatorial structure consisting of a collection of blocks over a set of points satisfying certain properties. The existence of t-designs given a set of parameters can be reduced to finding nonnegative integer solutions to a given integer matrix equation. The matrix in this equation can be quite large, but by prescribing the automorphism group of the design, the matrix in the equation can be made more manageable so as to allow the equation to be solved via integer programming tools; this fact was developed by Kramer and Mesner. Algorithms to generate the matrix equation generally follow a simple template. In this thesis, a generic framework for generating the Kramer-Mesner matrix equation and solving it via integer programming is presented.

Influenza is a public health problem that causes serious illness and deaths all over the world. Vaccination has been shown to be the most effective mean to prevent infection. The primary component of influenza vaccine is the weakened strains. Vaccination triggers the immune system to develop antibodies against those strains whose viral surface glycoprotein hemagglutinin (HA) is similar to that of vaccine strains. However, influenza vaccine must be updated annually since the antigenic structure of HA is constantly mutation. Hemagglutination inhibition (HI) assay is a laboratory procedure frequently applied to evaluate the antigenic relationships of the influenza viruses. It enables the World Health Organization (WHO) to recommend appropriate updates on strains that will most likely be protective against the circulating influenza strains. However, HI assay is labour intensive and time-consuming since it requires several controls for standardization. We use two machine-learning methods, i.e. Artificial Neural Network (ANN) and Logistic Regression, and a Mixed-Integer Optimization Model to predict antigenic variety. The ANN generalizes the input data to patterns inherent in the data, and then uses these patterns to make predictions. The logistic regression model identifies and selects the amino acid positions, which contribute most significantly to antigenic difference. The output of the logistic regression model will be used to predict the antigenic variants based on the predicted probability. The Mixed-Integer Optimization Model is formulated to find hyperplanes that enable binary classification. The performances of our models are evaluated by cross validation.

Rail track operators have traditionally used manual methods to construct train timetables. Creating a timetable can take several weeks, and so the process usually stops once the first feasible timetable has been found. It is suspected that this timetable is often far from optimal. Existing methods schedule track maintenance once the best train timetable has been determined and allow little or no adjustments to the timetable. This approach almost certainly produces suboptimal integrated solutions since the track maintenance schedule is developed with the imposition of the previously constructed train timetable. The research in this thesis considers operationally feasible methods to produce integrated train timetables and track maintenance schedules so that, when evaluated according to key performance criteria, the overall schedule is the best possible. This research was carried out as part of the Cooperative Research Centre for Railway Engineering and Technologies. We developed a method that uses a local search meta-heuristic called 'problem space search'. A fast dispatch heuristic repeatedly selects and moves a track possessor (train or maintenance task) through the network; this results in a single integrated schedule. This technique generates a collection of alternative feasible schedules by applying the dispatch heuristic to different sets of randomly perturbed data. The quality of the schedules is then evaluated. Thousands of feasible solutions can be found within minutes. We also formulated an integer programming model that selects a path for each train and maintenance task from a set of alternatives. If all possible paths are considered, then the best schedule found is guaranteed to be optimal. To reduce the size of the model, we explored a reduction technique called 'branch and price'. The method works on small example problems where paths are selected from a predetermined set, but the computation time and memory requirements mean that the method is not suitable for realistic problems. The main advantages of the problem space search method are generality and speed. We are able to model the operations of a variety of rail networks due to the representation of the problem. The generated schedules can be ranked with a user-defined objective measure. The speed at which we produce a range of feasible integrated schedules allows the method to be used in an operational setting, both to create schedules and to test different scenarios. A comparison with simulated current practice on a range of test data sets reveals improvements in total delay of up to 22%.

Rail track operators have traditionally used manual methods to construct train timetables. Creating a timetable can take several weeks, and so the process usually stops once the first feasible timetable has been found. It is suspected that this timetable is often far from optimal. Existing methods schedule track maintenance once the best train timetable has been determined and allow little or no adjustments to the timetable. This approach almost certainly produces suboptimal integrated solutions since the track maintenance schedule is developed with the imposition of the previously constructed train timetable. The research in this thesis considers operationally feasible methods to produce integrated train timetables and track maintenance schedules so that, when evaluated according to key performance criteria, the overall schedule is the best possible. This research was carried out as part of the Cooperative Research Centre for Railway Engineering and Technologies. We developed a method that uses a local search meta-heuristic called 'problem space search'. A fast dispatch heuristic repeatedly selects and moves a track possessor (train or maintenance task) through the network; this results in a single integrated schedule. This technique generates a collection of alternative feasible schedules by applying the dispatch heuristic to different sets of randomly perturbed data. The quality of the schedules is then evaluated. Thousands of feasible solutions can be found within minutes. We also formulated an integer programming model that selects a path for each train and maintenance task from a set of alternatives. If all possible paths are considered, then the best schedule found is guaranteed to be optimal. To reduce the size of the model, we explored a reduction technique called 'branch and price'. The method works on small example problems where paths are selected from a predetermined set, but the computation time and memory requirements mean that the method is not suitable for realistic problems. The main advantages of the problem space search method are generality and speed. We are able to model the operations of a variety of rail networks due to the representation of the problem. The generated schedules can be ranked with a user-defined objective measure. The speed at which we produce a range of feasible integrated schedules allows the method to be used in an operational setting, both to create schedules and to test different scenarios. A comparison with simulated current practice on a range of test data sets reveals improvements in total delay of up to 22%.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 132-136).

Many applications in engineering, computer science and economics involve mixed-integer optimal control problems. Solving these problems in real-time is a challenging task because of the explosion of integer combinations to evaluate. This thesis focuses on the development of new algorithms for mixed-integer programming with an emphasis on optimal control problems of fast dynamical systems with discrete controls. The first part proposes two reformulations to reduce the computational complexity. The first reformulation avoids integer variables altogether. By considering a sequence of switched dynamics, we analyze the switching time optimization problem. Even though it is a continuous smooth problem, it is non-convex and the cost function and derivatives are hard to compute. We develop a new efficient method to compute the cost function and its derivatives. Our technique brings up to two orders of magnitude speedups with respect to state-of-the-art tools. The second approach reduces the number of integer decisions. In hybrid model predictive control (MPC) the computational complexity grows exponentially with the horizon length. Using approximate dynamic programming (ADP) we reduce the horizon length while maintaining good control performance by approximating the tail cost offline. This approach allows, for the first time, the application of such control techniques to fast dynamical systems with sampling times of only a few microseconds. The second part investigates embedded branch-and-bound algorithms for mixed-integer quadratic programs (MIQPs). A core component of these methods is the solution of continuous quadratic programs (QPs). We develop OSQP, a new robust and efficient general-purpose QP solver based on the alternating direction method of multipliers (ADMM) and able, for the first time, to detect infeasible problems. We include OSQP into a custom branch-and-bound algorithm suitable for embedded systems. Our extension requires only a single matrix factorization and exploits warm-starting, thereby greatly reducing the number of ADMM iterations required. Numerical examples show that our algorithm solves small to medium scale MIQPs more quickly than commercial solvers.

Pessoas com deficiências possuem muitas dificuldades em participar do mercado de trabalho, possuindo uma taxa de desemprego bem maior do que a média populacional. Isso motiva o estudo de novos modos de produção que permitam incluir essas pessoas com baixo custo operacional. Neste trabalho é feito um estudo sobre a inclusão de pessoas com deficiências em flow shops com o objetivo de minimizar o makespan. Como flow shops normalmente possuem poucas máquinas, o foco do estudo é na inserção de um e dois trabalhadores. O problema é definido, são propostos modelos matemáticos e uma solução heurística para resolvê-lo, assim como instâncias de teste realistas. Nos testes computacionais a performance dos modelos e da heurística é avaliada e a utilidade prática deste modelo de inclusão é analisada. Nós concluímos que o problema pode ser resolvido de forma satisfatória e que a inclusão de trabalhadores com deficiêcia emn flow shops é economicamente viável. / Persons with disabilities have severe problems participating in the job market and their unemployment rate is usually much higher than the average of the population. This motivates the research of new modes of production which allow to include these persons at a low overhead. In this work we study the inclusion of persons with disabilities into flow shops with the objective of minimizing the makespan. Since flow shops usually have only a few machines, we focus on the inclusion of one and two workers. We define the problem, propose mathematical models and a heuristic solution, as well as realistic test instances. In computational tests we evaluate the performance of the models and the heuristic, and assess the utility of such a model of inclusion. We conclude that the problem can be solved satisfactorily, and that including workers with disabilities into flow shops is economically feasible.

In this paper we proposed 0-1 integer programming formulation to model single batch processing machine. This problem deals with a set of jobs with non-identical sizes and processing times that has to be grouped to form batches according to the limited capacity of the machine. The processing time of a batch is the longest processing time of all jobs in the batch. The performance measure is the total time required to process all jobs (makespan). The formulation presented strengthens the model, i.e., it is closer to the optimal formulation than those proposed in the literature. Computational experiments demonstrate that the model is consistent and adequately represents the problem addressed. / Neste trabalho é proposta uma formulação de programação inteira 0-1 para modelar o problema de programação e dimensionamento de lotes de produção em máquina única. Este problema considera um conjunto de tarefas com diferentes tamanhos e tempos de processamento que devem ser agrupadas em lotes de acordo com a capacidade limitada da máquina. O tempo de processamento de um lote é determinado pelo maior tempo de processamento dentre todas as tarefas que compõem o lote. A medida de desempenho é o tempo total necessário para processar todas as tarefas (makespan). A formulação apresentada é mais forte, ou seja, mais próxima da formulação ideal do que aquelas propostas na literatura. Experimentos computacionais demonstram que o modelo é consistente e representa adequadamente o problema tratado.

O problema de alocação de aeronaves a voos, ou tail assignment problem (TAP), consiste em determinar qual aeronave realizará cada voo da malha de uma empresa aérea, visando a minimizar o custo total da operação e respeitando diversas restrições de conectividade de voos, permanência de aeronaves no solo, serviços obrigatórios de manutenção, limitações técnicas e desempenho de aeronaves, conexões de passageiros e tripulantes e famílias com diversos modelos de aeronaves. Este trabalho apresenta um modelo matemático exato e um método heurístico para a solução do TAP considerando todas as restrições citadas, o que não ocorre com os modelos encontrados na literatura. Os modelos desenvolvidos, baseados em programação linear inteira e na meta-heurística Busca Tabu, foram aplicados a problemas reais, extraídos da malha de uma empresa aérea brasileira, operadora de 35 aeronaves e cerca de 210 voos diários. Os resultados obtidos são compatíveis com a operação da empresa e apresentam ganhos em relação ao método de alocação de aeronaves utilizado na operação diária. Os tempos de processamento para solução pelo método exato são excessivamente longos, indicando que o método heurístico é mais adequado para a utilização em empresas aéreas, com resultados adequados obtidos em tempos de processamento satisfatórios. / The problem known as Aircraft Assignment or Tail Assignment Problem (TAP) is the problem of assigning flights to each aircraft of an airline\'s fleet, aiming at minimizing the total operating cost while complying with several constraints, such as network connectivity, aircraft time on ground, mandatory maintenance services, aircraft technical restrictions, passengers and crew connections, aircraft performance and aircraft families with more than one type. This work presents a deterministic mathematical model and a heuristic method to solve the TAP considering all constraints listed above, what does not happen with the models found in the literature. The proposed methods, based on mathematical integer programming and on the Tabu Search metaheuristic, were applied to problems obtained from the network of a Brazilian airline, operating 35 aircraft and around 210 daily flights. The results show the models are suitable to solve the problem and savings are observed when compared to the current assignment method. The long processing times intrinsic to the deterministic method show the heuristic method is more suitable for use in airlines, with suitable results obtained at acceptable computational times.

O conteúdo deste trabalho trata da formulação para solução do problema de otimização estrutural com minimização de massa em estruturas unifilares, sujeitas a restrição de tensão, flambagem das barras isoladas e fadiga. São considerados três casos de otimização: paramétrica, de forma e dimensional. Os problemas de singularidades nas restrições de tensão e flambagem são evitados através de uma formulação que faz uso de programação inteira para solução do problema. Outra singularidade encontrada na otimização topológica é a singularidade na matriz de rigidez da estrutura. Este problema foi evitado através de uma formulação que considera a existência de matriz de rigidez regular como restrição do problema. O método de solução utilizado para resolver problema de otimização é o método dos algoritmos genéticos. As restrições do problema são impostas através da penalização da função objetivo. O método de solução mostrou-se adequado para solução dos problemas estudados. A formulação implementada é validada através da solução de problemas clássicos de otimização estrutural. Os resultados obtidos são comparados com a literatura onde verificou-se a coerência dos mesmos. Após realizar a validação, a formulação é utilizada em um estudo que tem como base uma estrutura real: uma torre de queima de gases (flare) oriundos do processo de extração e armazenagem de petróleo em uma unidade flutuante. Para o problema da torre as restrições foram determinadas com base em critérios de falha estabelecido na norma DNV. A otimização do flare permitiu minimizar a massa da estrutura sem que os critérios de falha fossem violados. Verificou-se que a metodologia proposta é adequada para solução com grande número de restrições e com diversos casos de carregamento. / The purpose of this work is the development of a methodology to solve the structural optimization problem of frame structures subject to stress, buckling of isolated members, and fatigue constraints. Three types of structural optimization problems are considered: sizing, shape and topological. The stress and buckling singularity problems are avoided by an integer design variable formulation, using integer programing to obtain the optimization problem solution. Another issue found in optimization problems is the stiffness matrix singularity. The proposed formulations include the linear system stability as a constraint in the optimization problem. A genetic algorithm is used to solve the general optimization problem. All constraints of the problem are included with a penalization equation. The results show that genetic algorithm is a good approach to solve the proposed formulation. The proposed formulation is tested for solving classical optimization problems. The obtained results are consistent with the literature. A real engineering problem is solved with proposed methodology: a gas burning tower (flare). In this problem, all constraints are based on failure criteria recommended by DNV standards. The structural optimization of this problem shows that structural mass minimization is possible without violating the failure criteria. It is observed that solution methodology deals successfully with problems with multiple constraints and load cases