The focus of this research is to provide an efficient approach to deal with computationally expensive Multiobjective Optimization Problems (MOP’s). Typically, approximation or surrogate based techniques are adopted to reduce the computational cost. In such cases, the original expensive objective function is replaced by a cheaper mathematical model, where this model mimics the behavior/input-output (i.e. design variable – objective value) relationship. However, it is difficult to model an exact substitute of the targeted objective function. Furthermore, if this kind of approach is used in an evolutionary search, literally, the number of function evaluations does not reduce (i.e. The number of original function evaluation is replaced by the number of surrogate/approximate function evaluation). However, if a large number of individuals are considered, the surrogate model fails to offer smaller computational cost. / To tackle this problem, we have reformulated the concept of surrogate modeling in a different way, which is more suitable for the Multiobjective Evolutionary Algorithm(MOEA) paradigm. In our approach, we do not approximate the objective function; rather we model the input-output behavior of the underlying MOEA itself. The model attempts to identify the search path (in both design-variable and objective spaces) and from this trajectory the model is guaranteed to generate non-dominated solutions (especially, during the initial iterations of the underlying MOEA – with respect to the current solutions) for the next iterations of the MOEA. Therefore, the MOEA can avoid re-evaluating the dominated solutions and thus can save large amount of computational cost due to expensive function evaluations. We have designed our approximation model as a variation operator – that follows the trajectory of the fronts and can be “plugged-in” to any kind of MOEA where non-domination based selection is used. Hence it is termed– the “Pareto-Following Variation Operator (PFVO)”. This approach also provides some added advantage that we can still use the original objective function and thus the search procedure becomes robust and suitable, especially for dynamic problems. / We have integrated the model into three base-line MOEA’s: “Non-dominated Sorting Genetic Algorithm - II (NSGA-II)”, “Strength Pareto Evolutionary Algorithm - II (SPEAII)”and the recently proposed “Regularity Model Based Estimation of Distribution Algorithm (RM-MEDA)”. We have also conducted an exhaustive simulation study using several benchmark MOP’s. Detailed performance and statistical analysis reveals promising results. As an extension, we have implemented our idea for dynamic MOP’s. We have also integrated PFVO into diffusion based/cellular MOEA in a distributed/Grid environment. Most experimental results and analysis reveal that PFVO can be used as a performance enhancement tool for any kind of MOEA.

En optimisation multiobjectif, les connaissances du front et de l’ensemble de Pareto sont primordiales pour résoudre un problème. Un grand nombre de stratégies évolutionnaires sont proposées dans la littérature classique. Ces dernières ont prouvé leur efficacité pour identifier le front de Pareto. Pour atteindre un tel résultat, ces algorithmes nécessitent un grand nombre d’évaluations. En ingénierie, les simulations numériques sont généralement réalisées par des modèles de haute-fidélité. Aussi, chaque évaluation demande un temps de calcul élevé. A l’instar des algorithmes mono-objectif, les gradients des critères, ainsi que les dérivées successives, apportent des informations utiles sur la décroissance des fonctions. De plus, de nombreuses méthodes numériques permettent d’obtenir ces valeurs pour un coût modéré. En s’appuyant sur les résultats théoriques obtenus par Inria, nous proposons un algorithme basé sur l’utilisation des gradients de descente. Ces travaux résument la caractérisation théorique de cette méthode et la validation sur des cas tests analytiques. Dans le cas où les gradients ne sont pas accessibles, nous proposons une stratégie basée sur la construction des métamodèles de Krigeage. Ainsi, au cours de l’optimisation, les critères sont évalués sur une surface de réponse et non par simulation. Le temps de calcul est considérablement réduit, au détriment de la précision. La méthode est alors couplée à une stratégie de progression du métamodèle. / In multiobjective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies have been proposed in the literature and proved to be successful to identify Pareto set. Howerver, these derivative free algorithms are very demanding in computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced presently. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm (MGDA) is defined as a generalization of the steepest-descent method and compared with PAES by numerical experiments. Using MGDA on a multiobjective optimization problem requires the evaluation of a large number of points with regards to criteria, and their gradients. In the particular case of CFD problems, each point evaluation is very costly. Thus here we also propose to construct metamodels and to calculate approximate gradients by local finite difference.

Abstract This work is devoted to the theory of joint interpretation of multimethod geophysical data and its application to the solution of real geophysical inverse problems. The targets of such joint interpretation can be geological bodies with an established dependence between various physical properties that cause anomalies in several geophysical fields (geophysical multiresponse). The establishing of the relationship connecting the various physical properties is therefore a necessary first step in any joint interpretation procedure. Bodies for which the established relationship between physical properties is violated (single-response bodies) can be targets of separate interpretations. The probabilistic (Bayesian) approach provides the necessary formalism for addressing the problem of the joint inversion of multimethod geophysical data, which can be non-linear and have a non-unique solution. Analysis of the lower limit of resolution of the non-linear problem of joint inversion using the definition of e-entropy demonstrates that joint inversion of multimethod geophysical data can reduce non-uniqueness in real geophysical inverse problems. The question can be formulated as a multiobjective optimisation problem (MOP), enabling the numerical methods of this theory to be employed for the purpose of geophysical data inversion and for developing computer algorithms capable of solving highly non-linear problems. An example of such a problem is magnetotelluric impedance tensor inversion with the aim of obtaining a 3-D resistivity distribution. An additional area of application for multiobjective optimisation can be the combination of various types of uncertain information (probabilistic and non-probabilistic) in a common inversion scheme applicable to geophysical inverse problems. It is demonstrated how the relationship between seismic velocity and density can be used to construct an algorithm for the joint interpretation of gravity and seismic wide-angle reflection and refraction data. The relationship between the elastic and electrical properties of rocks, which is a necessary condition for the joint inversion of data obtained by seismic and electromagnetic methods, can be established for solid- liquid rock mixtures using theoretical modelling of the elastic and electrical properties of rocks with a fractal microstructure and from analyses of petrophysical data and borehole log data.

Orientador: Renato Pavanello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T18:05:36Z (GMT). No. of bitstreams: 1 QuispeRodriguez_Sergio_M.pdf: 51003475 bytes, checksum: 7e557fe0fe0448fd7cae415ebca527f8 (MD5) Previous issue date: 2015 / Resumo: A otimização estrutural topológica é uma ferramenta aplicada atualmente em muitos campos da engenharia tendo se consolidado no meio acadêmico e industrial. Em muitos casos práticos os carregamentos mecânicos e térmicos ocorrem simultaneamente nas estruturas. Nestas situações, a aplicação do método de otimização estrutural topológica deve contemplar tanto os requisitos mecânicos, como os requisitos térmicos. Assim, uma abordagem multi-física e multi-objetivo precisa ser desenvolvida para a solução desta classe de problemas. O presente trabalho é dedicado ao estudo da aplicação do método BESO (BESO - Bi-directional Evolutionary Structural Optimization) à sistemas multi-físicos considerando inicialmente os carregamentos termo-mecânicos como forças de corpo ou seja, forças dependentes do projeto. As funções objetivo consideradas são a flexibilidade média da estrutura e a capacidade térmica do sistema. A análise termo-mecânica é realizada usando o método de acoplamento sequencial, onde obtêm-se inicialmente a resposta do campo térmico, ou aplica-se um campo previamente conhecido do ponto da estrutura e na sequência calculam-se as forças térmicas geradas e a dilatação da estrutura. Explora-se também a otimização termo-mecânica multiobjetivo, em que duas funções objetivo são consideradas simultaneamente. Considera-se como o objetivo do problema de otimização, a minimização da flexibilidade média e a minimização da capacidade térmica, usando o método de soma ponderada. Para a validação dos procedimentos de otimização implementados neste trabalho, são apresentados exemplos de otimização para sistemas termo-mecânicos bidimensionais. A viabilidade do método para aplicação em problemas de engenharia e a comparação de resultados com outros métodos de otimização, permite afirmar que as técnicas propostas podem ser usadas na solução de problemas de otimização topológica de sistemas termo-mecânicos / Abstract: The structural topology optimization is an usefull tool applied in many engineering fields, having been established in the academic and industrial environments. In many practical cases, the mechanical and thermal loads occur simultaneously in a structure. In these cases, the aplication of structural topology optimization should consider the thermal and mechanical requirements. For this reason, a multi-physic and multi-objective approach needs to be developed for the solution of these types of problems. The present work is dedicated to the study of the BESO method (BESO - Bi-directional Evolutionary Structural Optimization) applied to multi-physic systems taking in consideration thermo-mechanical loads as design dependent body loads. The objective functions considered are the compliance and heat capacity of the system. The thermo-mechanical analysis is carried out using a sequential coupling method, where the thermal field response is obtained initially, and in the sequence, the thermal loads or dilation loads are calculated. The bi-objective thermo-mechanical optimization problem is also analysed, where two objective functions are considered simultaneously. To validate the procedures implemented in this work, some 2-D examples of thermo-mechancial systems optimization are presented. The feasibility of the method for the aplication in engineering problems and the comparison of the results obtained using other methods, alows to state that the proposed techniques can be used in the solution of optimization problems of thermo-mechanical systems / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

En el proceso de diseño e las construcciones industriales, es de vital importancia conocer cual es la ubicación óptima de las diferentes áras de trabajo que conforman un proceso de fabricación, así como de las instalaciones y servicios auxiliares. El problema de distribución en planta (Facilities Layout Problem, FLP) integra a todas las actividades industriales y se ha convertido desde los años 60 en uno de los problemas clásicos de optimización combinatoria, en el que trabajan multiutd de investigadores a nivel internacional. Hasta los años 90, el enfoque que se realizaba del problema era básicamente un enfoque monobjetivo, en el que se primaba fundamentalmente la minimización del coste de transporte de material o personas entre las diferentes áreas productivas o de servicios. Para ello se han venido empleando diferentes técnicas de optimización heurística, que persiguen minimizar el tiempo de cálculo y facilitar la búsqueda de mínimos, aunque sean locales, pues el espacio de soluciones es tan grande, que es difícil garantizar la existencia de un mínimo global del problema. No obstante, el criterio de coste no es el único que se debe considerar en este tipo de planteamientos, pues existen otra serie de indicadores que son de vital importancia, para garantizar que la solución propuesta tiene un nivel de desarrollo tecnológico con la aparición de equipos y programas informáticos más desarrollados, han prosperado las aproximaciones multiobjetivos al problema de distribución en planta. Entre los objetivos principales del presente trabajo se encuentran; la realización de un estado del arte de los indicadores que se han empleado en la bibliografía para la resolución en planta, obteniendo un conjunto de indicadores independientes y suficientes que puedan ser empleados en la obtención de distribuciones en planta óptimas. Se investigará si es necesario definir algún nuevo indicador que cubra los objetivos fundamentales de la distribución en planta establecidos por distintos autores. Una vez seleccionados los indicadores se propone una técnica de optimización multiobjetivo basada en un algoritmo de recocido simulado (Simulated Annealing). Finalmente se presentan los resultados de los experimentos realizados, empleando la técnica de optimización multiobjetivo propuesta, sobre un problema ampliamente utilizado en la bibliografía, el propuesto por Armour y Buffa de 20 actividades. Se obtienen las fronteras de Pareto para diferentes bicriterios, introduciendo puntos que completan las existentes hasta la actualidad, estudiando la posibilidad de extender la optimización a 3 indicadores. / Montalva Subirats, JM. (2011). Optimización multiobjetivo de la distribución en planta de procesos industriales. Estudio de objetivos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11147 / Palancia

In this thesis, two distinct problems in data-driven computational science are considered. The main problem of interest is the multiobjective optimization problem, where the tradeoff surface (called the Pareto front) between multiple conflicting objectives must be approximated in order to identify designs that balance real-world tradeoffs. In order to solve multiobjective optimization problems that are derived from computationally expensive blackbox functions, such as engineering design optimization problems, several methodologies are combined, including surrogate modeling, trust region methods, and adaptive weighting. The result is a numerical software package that finds approximately Pareto optimal solutions that are evenly distributed across the Pareto front, using minimal cost function evaluations. The second problem of interest is the closely related problem of multivariate interpolation, where an unknown response surface representing an underlying phenomenon is approximated by finding a function that exactly matches available data. To solve the interpolation problem, a novel algorithm is proposed for computing only a sparse subset of the elements in the Delaunay triangulation, as needed to compute the Delaunay interpolant. For high-dimensional data, this reduces the time and space complexity of Delaunay interpolation from exponential time to polynomial time in practice. For each of the above problems, both serial and parallel implementations are described. Additionally, both solutions are demonstrated on real-world problems in computer system performance modeling. / Doctor of Philosophy / Science and engineering are full of multiobjective tradeoff problems. For example, a portfolio manager may seek to build a financial portfolio with low risk, high return rates, and minimal transaction fees; an aircraft engineer may seek a design that maximizes lift, minimizes drag force, and minimizes aircraft weight; a chemist may seek a catalyst with low viscosity, low production costs, and high effective yield; or a computational scientist may seek to fit a numerical model that minimizes the fit error while also minimizing a regularization term that leverages domain knowledge. Often, these criteria are conflicting, meaning that improved performance by one criterion must be at the expense of decreased performance in another criterion. The solution to a multiobjective optimization problem allows decision makers to balance the inherent tradeoff between conflicting objectives. A related problem is the multivariate interpolation problem, where the goal is to predict the outcome of an event based on a database of past observations, while exactly matching all observations in that database. Multivariate interpolation problems are equally as prevalent and impactful as multiobjective optimization problems. For example, a pharmaceutical company may seek a prediction for the costs and effects of a proposed drug; an aerospace engineer may seek a prediction for the lift and drag of a new aircraft design; or a search engine may seek a prediction for the classification of an unlabeled image. Delaunay interpolation offers a unique solution to this problem, backed by decades of rigorous theory and analytical error bounds, but does not scale to high-dimensional "big data" problems. In this thesis, novel algorithms and software are proposed for solving both of these extremely difficult problems.

The job scheduling problem is a type of scheduling problem where a list of jobs and machines are given. A solution consists of a schedule where each job is assigned to one or multiple machines at a certain time. In this study, a multiobjective evolutionary algorithm called NSGA-II was applied to optimize schedules for a particular scheduling problem given by a board game made by the Swedish educative company INSU. The scheduling problem features novel restrictions on the schedules, such as transportation delay between the jobs, skill requirements for the machines to fulfill. The board game also allows pre-emption, i.e., that the jobs can be paused and resumed by the same or other machines. These restrictions impose a challenge for creating a genetic representation for the evolutionary algorithm and a decoder which decodes the representation into a schedule. This problem was solved by proposing a new genetic representation based on previous work and testing it with a few crossover and mutation methods in two experiments. The experiments found that the new representation is effective in creating high-quality schedules, but it is inconclusive as to which crossover and mutation method is the most effective. The decoder’s execution time was also measured, which showed that the decoder scales rapidly with an increasing number of jobs. Despite this, the new representation and decoder are useful for optimizing other scheduling problems with pre-emption and other restrictions.

Optimization problems of location-assignment correspond to a wide range of real situations, such as factory network design. However most of the previous works seek in most cases at minimizing a cost function. Traffic incidents routinely impact the performance and the safety of the supply. These incidents can not be totally avoided and must be regarded. A way to consider these incidents is to design a network on which multiple assignments are performed. Precisely, the problem we focus on deals with power supplying that has become a more and more complex and crucial question. Many international companies have customers who are located all around the world; usually one customer per country. At the other side of the scale, power extraction or production is done in several sites that are spread on several continents and seas. A strong willing of becoming less energetically-dependent has lead many governments to increase the diversity of supply locations. For each kind of energy, many countries expect to deal ideally with 2 or 3 location sites. As a decrease in power supply can have serious consequences for the economic performance of a whole country, companies prefer to balance equally the production rate among all sites as the reliability of all the sites is considered to be very similar. Sharing equally the demand between the 2 or 3 sites assigned to a given area is the most common way. Despite the cost of the network has an importance, it is also crucial to balance the loading between the sites to guarantee that no site would take more importance than the others for a given area. In case an accident happens in a site or in case technical problems do not permit to satisfy the demand assigned to the site, the overall power supply of this site is still likely to be ensured by the one or two available remaining site(s). It is common to assign a cost per open power plant and another cost that depends on the distance between the factory or power extraction point and the customer. On the whole, such companies who are concerned in the quality service of power supply have to find a good trade-off between this factor and their overall functioning cost. This situation exists also for companies who supplies power at the national scale. The expected number of areas as well that of potential sites, can reach 100. However the targeted size of problem to be solved is 50. This thesis focuses on devising an efficient methodology to provide all the solutions of this bi-objective problem. This proposal is an investigation of close problems to delimit the most relevant approaches to this untypical problem. All this work permits us to present one exact method and an evolutionary algorithm that might provide a good answer to this problem. / Master of Science

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21752号 / 工博第4569号 / 新制||工||1712(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 准教授 泉井 一浩, 教授 椹木 哲夫, 教授 松原 厚 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent searching and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, a new vector/matrix-based definition for multiobjective optimization problems is introduced, which is dynamic in nature and easily modified. Additionally, a set of exploration metrics is developed to help guide designers while exploring the formulation space. Finally, several examples are presented to illustrate the use of this new, dynamic approach to multiobjective optimization.