Polycrystalline diamond (PCD) is used as a cutting tool in many industries because of its superior wear resistance compared to single crystal diamond. Engineers who design new PCD materials must have an understanding of the tradeoffs between material properties in order to tailor a product for different applications. Two competing material properties that are often encountered in PCD are transverse rupture strength and thermal-resistance. Thermal-resistance is directly related to the cobalt content of PCD, and is the ability of the material to withstand thermally induced degradation. In this thesis, we characterize the tradeoff boundary between transverse rupture strength and cobalt content of PCD. We also characterize the tradeoff boundary between cost and cobalt content, and show how both of these tradeoff boundaries can be used to manage product development, which adds value for managers in both engineering and business. In order to characterize these tradeoffs, empirical models are developed for each material property in terms of the design variables of sintering pressure and diamond grain size, where the pressure ranges from 55 kbar to 77 kbar and the grain size ranges from 12 μm to 70 μm in diameter. Then the models are used as optimization objectives in the normal constraint method to generate the tradeoff boundary. Finally, the tradeoff boundary is validated through additional experiments. The tradeoff boundary shows that the relationship between transverse rupture strength and cobalt content is not linear. It also shows that the optimal PCD designs can occur over a wide range of pressures and grain sizes, but pressures above 66 kbar and grain sizes between 20 and 30 μm appear to offer the best compromise between these material properties. These results are compared to the wear rates of PCD compacts in rock cutting tests. The rock cutting test results confirm that the designs with the best compromise between transverse rupture strength and cobalt content also have the highest wear resistance. In general, the designs that offer the best compromise between the properties are also the most expensive to manufacture.

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For larger instances of multi-objective optimisation problems, the exact Pareto frontier can be both difficult and time-consuming to calculate. There is a wide range of methods to find feasible solutions to such problems, but techniques for finding good optimistic bounds to compare the feasible solutions with are missing. In this study, we investigate the use of Lagrangian relaxation to create optimistic bounds to bi-objective optimisation problems with complicating side constraints. The aim is to develop an effective method to produce optimistic bounds that are closer to the Pareto frontier than the commonly used linear programming bounds.  In order to use Lagrangian relaxation on the bi-objective problem, the objectives are combined using the weighted sum method. A Lagrangian dual function is then constructed by relaxing the complicating constraints and the subgradient method is used to optimise the dual problem in order to find an optimistic solution. By solving the single-objective problem for multiple weights, an optimistic bound to the Pareto frontier can be constructed. The subgradient method also includes a heuristic to find feasible solutions. The feasible solutions found by the heuristic form a pessimistic bound to the frontier. The method has been implemented and tested on several instances of a capacitated facility location problem with cost and CO2 emission as objectives. The results indicate that, by using Lagrangian relaxation, an optimistic bound close to the Pareto frontier can be found in a relatively short time. The heuristic used also manages to produce good pessimistic bounds, and hence the Pareto frontier can be tightly enclosed. The optimistic bounds found by Lagrangian relaxation are better and more consistent along the Pareto frontier than the bounds found by linear programming.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-08-09T15:35:44Z No. of bitstreams: 2 Dissertação - Fernando Aparecido Carvalho - 2015.pdf: 2908710 bytes, checksum: 4bf0d7b76218e028e53f5ebb2602a3a0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T12:11:09Z (GMT) No. of bitstreams: 2 Dissertação - Fernando Aparecido Carvalho - 2015.pdf: 2908710 bytes, checksum: 4bf0d7b76218e028e53f5ebb2602a3a0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-10T12:11:09Z (GMT). No. of bitstreams: 2 Dissertação - Fernando Aparecido Carvalho - 2015.pdf: 2908710 bytes, checksum: 4bf0d7b76218e028e53f5ebb2602a3a0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-10-30 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / By its modular feature a Distributed Generation project can be up to several generating units, which represents an alternative to better match supply and demand. This paper presents a multi-objective modeling to optimize the number of generating units from distributed generators considering minimizing electrical losses on the network and also CO2 emissions of distributed generators, considering renewable primary and non-renewable sources, as well as penetration of restrictions and maximum quantities generation units. The optimization model solution process employs genetic algorithms and weighting of the objectives of the method for obtaining a set of Pareto optimal solutions. Case studies with representative grids are presented for testing, analysis and validation of the proposed methodology. / Por sua característica modular, um empreendimento de Geração Distribuída pode constituir-se de diversas unidades geradoras, o que representa uma alternativa para melhor adequar oferta e demanda. Este trabalho apresenta uma modelagem multiobjetivo para otimizar o número de unidades geradoras provenientes de geradores distribuídos, considerando a minimização de perdas elétricas na rede e também emissões de CO2 dos geradores distribuídos, considerando fontes primárias renováveis e não renováveis, bem como, restrições de penetração e quantidades máximas de unidades de geração. O processo de solução do modelo de otimização emprega Algoritmos Genéticos e o Método da Ponderação dos Objetivos para obtenção de um conjunto de soluções Pareto-ótimas. Estudos de casos com redes elétricas representativas são apresentados para testes, análises e validação da metodologia proposta.

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New helicopter rotor designs are desired that offer increased efficiency, reduced vibration, and reduced noise. This problem is multidisciplinary, requiring knowledge of structural dynamics, aerodynamics, and aeroacoustics. Rotor optimization requires achieving multiple, often conflicting objectives. There is no longer a single optimum but rather an optimal trade-off space, the Pareto Frontier. Rotor Designers in industry need methods that allow the most accurate simulation tools available to search for Pareto designs. Computer simulation and optimization of rotors have been advanced by the development of "comprehensive" rotorcraft analysis tools. These tools perform aeroelastic analysis using Computational Structural Dynamics (CSD). Though useful in optimization, these tools lack built-in high fidelity aerodynamic models. The most accurate rotor simulations utilize Computational Fluid Dynamics (CFD) coupled to the CSD of a comprehensive code, but are generally considered too time consuming where numerous simulations are required like rotor optimization. An approach is needed where high fidelity CFD/CSD simulation can be routinely used in design optimization. This thesis documents the development of physics based rotor simulation frameworks. A low fidelity model uses a comprehensive code with simplified aerodynamics. A high fidelity model uses a parallel processor capable CFD/CSD methodology. Both frameworks include an aeroacoustic simulation for prediction of noise. A synergistic process is developed that uses both frameworks together to build approximate models of important high fidelity metrics as functions of certain design variables. To test this process, a 4-bladed hingeless rotor model is used as a baseline. The design variables investigated include tip geometry and spanwise twist. Approximation models are built for high fidelity metrics related to rotor efficiency and vibration. Optimization using the approximation models found the designs having maximum rotor efficiency and minimum vibration. Various Pareto generation methods are used to find frontier designs between these two anchor designs. The Pareto anchors are tested in the high fidelity simulation and shown to be good designs, providing evidence that the process has merit. Ultimately, this process can be utilized by industry rotor designers with their existing tools to bring high fidelity analysis into the preliminary design stage of rotors.

The research objective of this dissertation is to create and demonstrate methods for parameterizing the Pareto frontiers of continuous multi-attribute design problems using barycentric coordinates, and in doing so, to enable intuitive exploration of optimal trade spaces. This work is enabled by two observations about Pareto frontiers that have not been previously addressed in the engineering design literature. First, the observation that the mapping between non-dominated designs and Pareto efficient response vectors is a bijection almost everywhere suggests that points on the Pareto frontier can be inverted to find their corresponding design variable vectors. Second, the observation that certain common classes of Pareto frontiers are topologically equivalent to simplices suggests that a barycentric coordinate system will be more useful for parameterizing the frontier than the Cartesian coordinate systems typically used to parameterize the design and objective spaces. By defining such a coordinate system, the design problem may be reformulated from y = f(x) to (y,x) = g(p) where x is a vector of design variables, y is a vector of attributes and p is a vector of barycentric coordinates. Exploration of the design problem using p as the independent variables has the following desirable properties: 1) Every vector p corresponds to a particular Pareto efficient design, and every Pareto efficient design corresponds to a particular vector p. 2) The number of p-coordinates is equal to the number of attributes regardless of the number of design variables. 3) Each attribute y_i has a corresponding coordinate p_i such that increasing the value of p_i corresponds to a motion along the Pareto frontier that improves y_i monotonically. The primary contribution of this work is the development of three methods for forming a barycentric coordinate system on the Pareto frontier, two of which are entirely original. The first method, named "non-domination level coordinates," constructs a coordinate system based on the (k-1)-attribute non-domination levels of a discretely sampled Pareto frontier. The second method is based on a modification to an existing "normal boundary intersection" multi-objective optimizer that adaptively redistributes its search basepoints in order to sample from the entire frontier uniformly. The weights associated with each basepoint can then serve as a coordinate system on the frontier. The third method, named "Pareto simplex self-organizing maps" uses a modified a self-organizing map training algorithm with a barycentric-grid node topology to iteratively conform a coordinate grid to the sampled Pareto frontier.

Methodologies designed to support new product development are receiving increasing interest in recent literature. A significant percentage of new product failure is attributed to a mismatch between designed product features and consumer liking. A variety of methodologies have been proposed and tested for consumer liking or preference prediction, ranging from statistical methodologies e.g. multiple linear regression (MLR) to non-statistical approaches e.g. artificial neural networks (ANN), support vector machines (SVM), and belief rule-based (BRB) systems. BRB has been previously tested for consumer preference prediction and target setting in case studies from the beverages industry. Results have indicated a number of technical and conceptual advantages which BRB holds over the aforementioned alternative approaches. This thesis focuses on presenting further advantages and applications of the BRB methodology for consumer liking prediction. The features and advantages are selected in response to challenges raised by three addressed case studies. The first case study addresses a novel industry for BRB application: the fast moving consumer goods industry, the personal care sector. A series of challenges are tackled. Firstly, stepwise linear regression, principal component analysis and AutoEncoder are tested for predictors’ selection and data reduction. Secondly, an investigation is carried out to analyse the impact of employing complete distributions, instead of averages, for sensory attributes. Moreover, the effect of modelling instrumental measurement error is assessed. The second case study addresses a different product from the personal care sector. A bi-objective prescriptive approach for BRB model structure selection and validation is proposed and tested. Genetic Algorithms and Simulated Annealing are benchmarked against complete enumeration for searching the model structures. A novel criterion based on an adjusted Akaike Information Criterion is designed for identifying the optimal model structure from the Pareto frontier based on two objectives: model complexity and model fit. The third case study introduces yet another novel industry for BRB application: the pastry and confectionary specialties industry. A new prescriptive framework, for rule validation and random training set allocation, is designed and tested. In all case studies, the BRB methodology is compared with the most popular alternative approaches: MLR, ANN, and SVM. The results indicate that BRB outperforms these methodologies both conceptually and in terms of prediction accuracy.