No description available.

Page IV was not included in the thesis, and thus not included in the page count. / <p> Discretization is an important tool to transfer optimization problems that include differentiations and integrals into standard optimization problems with a finite number of variables and a finite number of constraints. Recently, Betts and Campbell proposed a heat-transfer optimization problem that includes the heat partial differential equation as one of its constraints, and the objective function includes integrals of the temperature function squared. Using discretization methods, this problem can be converted to a convex quadratic optimization problem, which can be solved by standard interior point method solvers in polynomial time.</p> <p> The discretized model of the one dimensional problem is further analyzed, and some of its variants are studied. Extensive numerical testing is performed to demonstrate the power of the "discretize then optimize". Then the heat transfer optimization problem is generalized to two dimensions, and the discretized model and computational comparisons for this variant are included.</p> <p> Flexibility of discretization methods allow us to apply the same "diseretize then optimize" methodology to solve optimization problems that include differential and integral functions as constraints or objectives.</p> / Thesis / Master of Science (MSc)

Session ID: TH-E1-4 / SCIS & ISIS 2010, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems. December 8-12, 2010, Okayama Convention Center, Okayama, Japan

Mixed integer programming (MIP) problems are highly parameterized, and finding parameter settings that achieve high performance for specific types of MIP instances is challenging. This paper presents a method to find the information about how CPLEX solver parameter settings perform for the different classes of mixed integer linear programs by using designed experiments and statistical models. Fitting a model through design of experiments helps in finding the optimal region across all combinations of parameter settings. The study involves recognizing the best parameter settings that results in the best performance for a specific class of instances. Choosing good setting has a large effect in minimizing the solution time and optimality gap.

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear convergence for strongly convex objectives. Second, we study distributed setting, in which the data describing the optimization problem does not fit into a single computing node. In this case, traditional methods are inefficient, as the communication costs inherent in distributed optimization become the bottleneck. We propose a communication-efficient framework which iteratively forms local subproblems that can be solved with arbitrary local optimization algorithms. Finally, we introduce the concept of Federated Optimization/Learning, where we try to solve the machine learning problems without having data stored in any centralized manner. The main motivation comes from industry when handling user-generated data. The current prevalent practice is that companies collect vast amounts of user data and store them in datacenters. An alternative we propose is not to collect the data in first place, and instead occasionally use the computational power of users' devices to solve the very same optimization problems, while alleviating privacy concerns at the same time. In such setting, minimization of communication rounds is the primary goal, and we demonstrate that solving the optimization problems in such circumstances is conceptually tractable.

The need for solving nonlinear optimization problems is pervasive in many fields. Particle swarm optimization, advantageous with the simple underlying implementation logic, and simultaneous perturbation stochastic approximation, which is famous for its saving in the computational power with the gradient-free attribute, are two solutions that deserve attention. Many researchers have exploited their merits in widely challenging applications. However, there is a known fact that both of them suffer from a severe drawback, non- effectively converging to the global best solution, because of the local “traps” spreading on the searching space. In this article, we propose two approaches to remedy this issue by combined their advantages. In the first algorithm, the gradient information helps optimize half of the particles at the initialization stage and then further updates the global best position. If the global best position is located in one of the local optima, the searching surface’s additional gradient estimation can help it jump out. The second algorithm expands the implementation of the gradient information to all the particles in the swarm to obtain the optimized personal best position. Both have to obey the rule created for updating the particle(s); that is, the solution found after employing the gradient information to the particle(s) has to perform more optimally. In this work, the experiments include five cases. The three previous methods with a similar theoretical basis and the two basic algorithms take participants in all five. The experimental results prove that the proposed two algorithms effectively improved the basic algorithms and even outperformed the previously designed three algorithms in some scenarios.

Em diversas indústrias de manufatura (por exemplo, papeleira, moveleira, metalúrgica, têxtil) as decisões do dimensionamento de lotes interagem com outras decisões do planejamento e programação da produção, tais como, a distribuição, o processo de corte, entre outros. Porém, usualmente, essas decisões são tratadas de forma isolada, reduzindo o espaço de soluções e a interdependência entre as decisões, elevando assim os custos totais. Nesta tese, estudamos o processo produtivo de indústrias de móveis de pequeno porte, que consiste em cortar placas grandes disponíveis em estoque para obter diversos tipos de peças que são processadas posteriormente em outros estágios e equipamentos com capacidades limitadas para, finalmente, comporem os produtos demandados. Os problemas de dimensionamento de lotes e corte de estoque são acoplados em um modelo de otimização linear inteiro cujo objetivo é minimizar os custos de produção, estoque de produtos, preparação de máquinas e perda de matéria-prima. Esse modelo mostra o compromisso existente entre antecipar ou não a fabricação de certos produtos aumentando os custos de estoque, mas reduzindo a perda de matéria-prima ao obter melhores combinações entre as peças. O impacto da incerteza da demanda (composta pela carteira de pedidos e mais uma quantidade extra estimada) foi amortizado pela estratégia de horizonte de planejamento rolante e por variáveis de decisão que representam uma produção extra para a demanda esperada no melhor momento, visando a minimização dos custos totais. Dois métodos heurísticos são desenvolvidos para resolver uma simplificação do modelo matemático proposto, o qual possui um alto grau de complexidade. Os experimentos computacionais realizados com exemplares gerados a partir de dados reais coletados em uma indústria de móveis de pequeno porte, uma análise dos resultados, as conclusões e perspectivas para este trabalho são apresentados / In the many manufacturing industries (e.g., paper industry, furniture, steel, textile), lot-sizing decisions generally arise together with other decisions of planning production, such as distribution, cutting, scheduling and others. However, usually, these decisions are dealt with separately, which reduce the solution space and break dependence on decisions, increasing the total costs. In this thesis, we study the production process that arises in small scale furniture industries, which consists basically of cutting large plates available in stock into several thicknesses to obtain different types of pieces required to manufacture lots of ordered products. The cutting and drilling machines are possibly bottlenecks and their capacities have to be taken into account. The lot-sizing and cutting stock problems are coupled with each other in a large scale linear integer optimization model, whose objective function consists in minimizing different costs simultaneously, production, inventory, raw material waste and setup costs. The proposed model captures the tradeoff between making inventory and reducing losses. The impact of the uncertainty of the demand, which is composed with ordered and forecasting products) was smoothed down by a rolling horizon strategy and by new decision variables that represent extra production to meet forecasting demands at the best moment, aiming at total cost minimization. Two heuristic methods are proposed to solve relaxation of the mathematical model. Randomly generated instances based on real world life data were used for the computational experiments for empirical analyses of the model and the proposed solution methods

Em diversas indústrias de manufatura (por exemplo, papeleira, moveleira, metalúrgica, têxtil) as decisões do dimensionamento de lotes interagem com outras decisões do planejamento e programação da produção, tais como, a distribuição, o processo de corte, entre outros. Porém, usualmente, essas decisões são tratadas de forma isolada, reduzindo o espaço de soluções e a interdependência entre as decisões, elevando assim os custos totais. Nesta tese, estudamos o processo produtivo de indústrias de móveis de pequeno porte, que consiste em cortar placas grandes disponíveis em estoque para obter diversos tipos de peças que são processadas posteriormente em outros estágios e equipamentos com capacidades limitadas para, finalmente, comporem os produtos demandados. Os problemas de dimensionamento de lotes e corte de estoque são acoplados em um modelo de otimização linear inteiro cujo objetivo é minimizar os custos de produção, estoque de produtos, preparação de máquinas e perda de matéria-prima. Esse modelo mostra o compromisso existente entre antecipar ou não a fabricação de certos produtos aumentando os custos de estoque, mas reduzindo a perda de matéria-prima ao obter melhores combinações entre as peças. O impacto da incerteza da demanda (composta pela carteira de pedidos e mais uma quantidade extra estimada) foi amortizado pela estratégia de horizonte de planejamento rolante e por variáveis de decisão que representam uma produção extra para a demanda esperada no melhor momento, visando a minimização dos custos totais. Dois métodos heurísticos são desenvolvidos para resolver uma simplificação do modelo matemático proposto, o qual possui um alto grau de complexidade. Os experimentos computacionais realizados com exemplares gerados a partir de dados reais coletados em uma indústria de móveis de pequeno porte, uma análise dos resultados, as conclusões e perspectivas para este trabalho são apresentados / In the many manufacturing industries (e.g., paper industry, furniture, steel, textile), lot-sizing decisions generally arise together with other decisions of planning production, such as distribution, cutting, scheduling and others. However, usually, these decisions are dealt with separately, which reduce the solution space and break dependence on decisions, increasing the total costs. In this thesis, we study the production process that arises in small scale furniture industries, which consists basically of cutting large plates available in stock into several thicknesses to obtain different types of pieces required to manufacture lots of ordered products. The cutting and drilling machines are possibly bottlenecks and their capacities have to be taken into account. The lot-sizing and cutting stock problems are coupled with each other in a large scale linear integer optimization model, whose objective function consists in minimizing different costs simultaneously, production, inventory, raw material waste and setup costs. The proposed model captures the tradeoff between making inventory and reducing losses. The impact of the uncertainty of the demand, which is composed with ordered and forecasting products) was smoothed down by a rolling horizon strategy and by new decision variables that represent extra production to meet forecasting demands at the best moment, aiming at total cost minimization. Two heuristic methods are proposed to solve relaxation of the mathematical model. Randomly generated instances based on real world life data were used for the computational experiments for empirical analyses of the model and the proposed solution methods

This thesis discusses the operational coordination of electrical appliances and devices in a smart home. At present, the diminishing volume of fossil fuels and the increasing pressure to use renewable sources of energy necessitate the integration of such volatile sources into electrical grids. This process, however, results in higher energy costs, and the consumers are thus more willing to change their behaviour to either reduce the expenses or maintain them at a reasonable level. One of the relatively few customer-oriented options to optimise energy costs consists in the demand – response principle, which utilises external information to minimise energy consumption during high price periods. Assuming the constantly changing conditions in electrical grids, and thus also the varying demands, it is vital to provide for automatic optimisation excluding the need of user intervention. The thesis presents a method which, after being implemented into the control member, will facilitate the optimal use of appliances and devices within a smart home. As the behaviour considered optimal from the perspective of demand - response is often inconsistent with the consumer‘s requirements for comfortable use of the appliances, the proposed technique offers a compromise through enabling the consumer to select the appropriate strategy. Five universal optimisation models are designed within the thesis; these models facilitate description of common home appliances and local electricity sources. The core of the method lies in formulating and optimising a mixed integer quadratic problem (MIQP). The optimisation task yields an operational schedule for the individual appliances, and this scheme considers the energy costs, the working cycle of the appliance, the user’s demands, the system restrictions and/or other input data. Furthermore, the author extends the above-discussed general technique, enabling it to adopt robust behaviour. The method then secures the preset strategy even during a marked change of the input conditions, and its robustness is a viable precondition for the overall applicability of the technique in the real control member.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19123号 / 情博第569号 / 新制||情||100(附属図書館) / 32074 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 中村 佳正, 教授 田中 利幸 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM