The max-stable Paretian distribution is analyzed in this Master’s work.

This research aims to improve our understanding of multiobjective optimization, by comparing the performance of five multiobjective optimization algorithms, and by proposing a new formulation to consider input uncertainty in multiobjective optimization problems. Four deterministic multiobjective optimization algorithms and one probabilistic algorithm were compared: the Weighted Sum, the Adaptive Weighted Sum, the Normal Constraint, the Normal Boundary Intersection methods, and the Nondominated Sorting Genetic Algorithm-II (NSGA-II). The algorithms were compared using six test problems, which included a wide range of optimization problem types (bounded vs. unbounded, constrained vs. unconstrained). Performance metrics used for quantitative comparison were the total run (CPU) time, number of function evaluations, variance in solution distribution, and numbers of dominated and non-optimal solutions. Graphical representations of the resulting Pareto fronts were also presented. No single method outperformed the others for all performance metrics, and the two different classes of algorithms were effective for different types of problems. NSGA-II did not effectively solve problems involving unbounded design variables or equality constraints. On the other hand, the deterministic algorithms could not solve a problem with a non-continuous objective function. In the second phase of this research, design under uncertainty was considered in multiobjective optimization. The effects of input uncertainty on a Pareto front were quantitatively investigated by developing a multiobjective robust optimization framework. Two possible effects on a Pareto front were identified: a shift away from the Utopia point, and a shrinking of the Pareto curve. A set of Pareto fronts were obtained in which the optimum solutions have different levels of insensitivity or robustness. Four test problems were used to examine the Pareto front change. Increasing the insensitivity requirement of the objective function with regard to input variations moved the Pareto front away from the Utopia point or reduced the length of the Pareto front. These changes were quantified, and the effects of changing robustness requirements were discussed. The approach would provide designers with not only the choice of optimal solutions on a Pareto front in traditional multiobjective optimization, but also an additional choice of a suitable Pareto front according to the acceptable level of performance variation. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-08-10 21:59:13.795

Savo darbe mes nagrinėjame Gerber-Shiu baudos funkciją klasikiniame rizikos modelyje atveju, kai žalų dydžiai pasiskirstę pagal Pareto dėsnį. Pagrindinis uždavinys yra susikonstruoti algoritmą funkcijos reikšmių gavimui. Tiriamas Gerber-Shiu diskontuotos baudos funkcijos atvejis, kada vidinė baudos funkcija w tapačiai lygi vienetui. Dėl sudėtingos transformuoto Pareto skirstinio formos analitiškai paskaičiuoti sąsūkų nepavyko. Tam tikslui naudojamas interpoliavimas kubiniu splainu. N kartų kartodami sukonstruotą algoritmą gauname pirmąsias n sąsūkas laisvai pasirinktiems pradiniams parametrams: Pareto skirstinio laipsnio rodikliui α, pradiniam kapitalui u, santykinei draudimo priemokai θ, diskontavimo parametrui (palūkanų normai) δ ir Puasono proceso parametrui λ. Lentelių pagalba parodome funkcijos priklausomybę nuo skirtingų modeliuojančių parametrų reikšmių. Išvadose teigiame jog pasiūlytas metodas skaičiuoti Gerber-Shiu diskontuotos baudos funkciją nors ir išpildomas tačiau yra neefektyvus. Kai kuriais pradinių parametrų pasirinkimo atvejais susiduriama su tikslumo problema. Norint tiksliai paskaičiuoti funkcijos reikšmes reikia didesnių eilių transformuoto Pareto skirstinio sąsūkų, o tam reikalingi dideli resursai. Kita vertus, pradinio kapitalo u reikšmėms didėjant tikslumas didėja ženkliai. / In this paper we consider Gerber-Shiu discounted penalty function in the classical risk model for Pareto claims. Our main goal is to construct an algorithm for obtaining values of the discounted penalty function (considering penalty function w=1). Due to the complicated form of the transformed Pareto distribution function we cannot obtain its convolutions analiticaly. We use numerical methods provided by Maple (cube spline) to find interpolating functions instead. Continuously applying recursive formulas we obtain first 5 interpolated convolutions. Then we calculate values of Gerber-Shiu discounted penalty function for certain arbitrary parameters: α – degree of Pareto distribution function, initial surplus u, security loading θ, discounting parameter δ and Poison process parameter λ. We present data tables and graphs of the discounted penalty function for some variations of parameters in later sections. Finally we state that the method that we use is quite complicated. For better accuracy of the discounted penalty function values one may require to get many convolutions of the transformed Pareto distribution function and that may require too great of the resources. However the quantity of the convolutions needed rapidly decreases for large values of the initial surplus u.

Bet kokiai įmonei klientų lojalumas yra gyvybiškai svarbus. Per pastaruosius du dešimtmečius, dėmesys ryšio su klientais valdymo sistemoms (angl. CRM- customer relationship management) labai išaugo. Tai galima interpretuoti kaip įmonių siekimą individualiai pažinti savo klientus. Pasikeitė ir marketingo orientyras. Vietoj orientuoto į transakcijas, jis patapo orientuotu į klientą, kadangi praktika parodė, jog tai yra optimalus ryšys su klientu. (Daug pigiau pardavinėti prekes esamiems klientams, nei naujiems, mažesni bendradarbiavimo kaštai) Būtent todėl klientų lojalumo sąvoka interpretuojama kaip viena svarbiausių koncepcijų šiuolaikiniame marketinge. Ryšio su klientais valdymo teorijose aprašoma daug kriterijų bei skaičiavimo metodų kliento lojalumui įvertinti. Egzistuojanti vadybinė taisyklė 55-15 teigia jog bandant klasifikuoti geriausius klientus, maždaug 55 % yra klasifikuojami klaidingai ir dėl to įmonė praranda investicijas (klientams neskiriamas attinkamas dėmesys: nuolaidos, ir t.t.) Pagrindinė tokio netikslaus klasifikavimo priežastis- besikeičianti verslo aplinka. Lojalūs klientai neišlieka tokiais visada. Remiantis CLV pokyčio analize ir Wouter Buckinx pasiūlytais kliento „norą pirkti“ apibūdinančiais rodikliais sudaryti 2 modeliai. Teoriškai šie modeliai yra veiksmingesni nei E.Ksevelonakiso pasiūlytas „CLV ir įmonės tikslinės strategijos sąveikos modelis“, kadangi laiku gavus informaciją apie potencialią kliento klasę (lojalus/nelojalus), įmonė gali nedelsiant... [toliau žr. visą tekstą] / The client loyalty is one of the most vital things to any company. During last two decades the attention to customer relationship management systems has increased significantly. There are many criterias and calculation methods described in customer relationship theories. The existing management rule 80-15 states that when trying to clasify best customers, almost 55% are misclassified and therefore organization losses its investments (there’s not enough attention being paid to the best customers). The main reason of such misclassification is continuous change in business environment and subjective customer loyalty definition. Loyal customers do not stay loyal all the time. Using scientific literature analysis there were selected most widely used methods, which help the company to identify it’s the most important customers. Additionally “wish to buy” indicators were selected, which describe the customer buying potential. Using selected methods and indexes, there is a preposition of a new classifying model, which helps to predict customer class using collected data during contribution period. Model was implemented by using neural network and tested using experiment. It predicted customer class using sales data and the results were as follow: it classified 141 customer from 154 customers in total, made a mistake in 13 cases while classifying loyal customers. When classifying disloyal customers, it made a mistake in 45 cases and classified 102 correctly of 147 in total... [to full text]

In this study, two new Multi-Objective Optimization (MOO) techniques are developed. The two new techniques, the Objective-Based Gradient Algorithm (OBGA) and the Principal Component Grid Algorithm (PCGA), were developed with the goals of improving the accuracy and efficiency of the Pareto domain approximation relative to current MOO techniques. Both methods were compared to current MOO techniques using several test problems. It was found that both the OBGA and PCGA systematically produced a more accurate Pareto domain than current MOO techniques used for comparison, for all problems studied. The OBGA requires less computation time than the current MOO methods for relatively simple problems whereas for more complex objective functions, the computation time was larger. On the other hand, the efficiency of the PCGA was higher than the current MOO techniques for all problems tested. The new techniques were also applied to complex chemical engineering problems. The OBGA was applied to an industrial reactor producing ethylene oxide from ethylene. The optimization varied four of the reactor input parameters, and the selectivity, productivity and a safety factor related to the presence of oxygen in the reactor were maximized. From the optimization results, recommendations were made based on the ideal reactor operating conditions, and the control of key reactor parameters. The PCGA was applied to a PI controller model to develop new tuning methods based on the Pareto domain. The developed controller tuning methods were compared to several previously developed controller correlations. It was found that all previously developed controller correlations showed equal or worse performance than that based on the Pareto domain. The tuning methods were applied to a fourth order process and a process with a disturbance, and demonstrated excellent performance.

Evolutionary Structural Optimisation (ESO) is a relatively new design tool used to improve and optimise the design of structures. It is a heuristic method where a few elements of an initial design domain of finite elements are iteratively removed. Such a process is carried out repeatedly until an optimum design is achieved, or until a desired given area or volume is reached. There have been many contributions to the ESO procedure since its conception back in 1992. For example, a provision known as Bi-Directional ESO (BESO) has now been incorporated where elements may not only be removed, but added. Also, rather than deal with elements where they are either present or not, the designer now has the option to change the element's properties in a progressive fashion. This includes the modulus of elasticity, the density of the material and the thickness of plate elements, and is known as Morphing ESO. In addition to the algorithmic aspects of ESO, a large preference exists to optimise a structure based on a selection of criteria for various physical processes. Such examples include stress minimisation, buckling and electromagnetic problems. In a changing world that demands the enhancement of design tools and methods that incorporate optimisation, the development of methods like ESO to accommodate this demand is called for. It is this demand that this thesis seeks to satisfy. This thesis develops and examines the concept of multicriteria optimisation in the ESO process. Taking into account the optimisation of numerous criteria simultaneously, Multicriteria ESO allows a more realistic and accurate approach to optimising a model in any given environment. Two traditional methods � the Weighting method and the Global Criterion (Min-max) method have been used, as has two unconventional methods � the Logical AND method and the Logical OR method. These four methods have been examined for different combinations of Finite Element Analysis (FEA) solver types. This has included linear static FEA solver, the natural frequency FEA solver and a recently developed inertia FE solver. Mean compliance minimisation (stiffness maximisation), frequency maximisation and moment of inertia maximisation are an assortment of the specific objectives incorporated. Such a study has provided a platform to use many other criteria and multiple combinations of criteria. In extending the features of ESO, and hence its practical capabilities as a design tool, the creation of another optimisation method based on ESO has been ushered in. This method concerns the betterment of the bending and rotational performance of cross-sectional areas and is known as Evolutionary Moment of Inertia Optimisation (EMIO). Again founded upon a domain of finite elements, the EMIO method seeks to either minimise or maximise the rectangular, product and polar moments of inertia. This dissertation then goes one step further to include the EMIO method as one of the objectives considered in Multicriteria ESO as mentioned above. Most structures, (if not all) in reality are not homogenous as assumed by many structural optimisation methods. In fact, many structures (particularly biological ones) are composed of different materials or the same material with continually varying properties. In this thesis, a new feature called Constant Width Layer (CWL) ESO is developed, in which a distinct layer of material evolves with the developing boundary. During the optimisation process, the width of the outer surrounding material remains constant and is defined by the user. Finally, in verifying its usefulness to the practical aspect of design, the work presented herein applies the CWL ESO and the ESO methods to two dental case studies. They concern the optimisation of an anterior (front of the mouth) ceramic dental bridge and the optimisation of a posterior (back of the mouth) ceramic dental bridge. Comparisons of these optimised models are then made to those developed by other methods.

Techn. Universiẗat, Diss., 2005--Darmstadt.

Zugl.: München, Techn. Univ., Diss., 2009

abstract: The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work. The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-01-30T15:19:41Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Ana Lucia Machado dos Santos.pdf: 4208303 bytes, checksum: fd85afa25ce5a97dbb3161b53c2cdb05 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-01-30T15:20:07Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Ana Lucia Machado dos Santos.pdf: 4208303 bytes, checksum: fd85afa25ce5a97dbb3161b53c2cdb05 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-01-30T15:20:22Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Ana Lucia Machado dos Santos.pdf: 4208303 bytes, checksum: fd85afa25ce5a97dbb3161b53c2cdb05 (MD5) / Made available in DSpace on 2017-01-30T15:20:22Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Ana Lucia Machado dos Santos.pdf: 4208303 bytes, checksum: fd85afa25ce5a97dbb3161b53c2cdb05 (MD5) Previous issue date: 2016-06-13 / This dissertation investigates the factors that impacts the quality of post-graduate programs in the Federal University of Amazonas using the triennial evaluations of CAPES as data source and, Pareto Diagrams and Histograms as tools for analysis. This study highlights some approaches about the evaluation, in a conceptual sense or by comparison with other methods, and also with respect to the process flow. This study allowed us to visualize each of the post graduate programs of the Federal University of Amazonas during the three CAPES evaluations through the application of a methodology available in the literature, identifying and demonstrating the principal points that had negative impacts on this process. It highlights a general overview of the situation of the programs with respect to the impact items as well as the cumulative percentage of the factors impacting all the programs. This study corroborates that the items which impacted the most during the last three CAPES evaluations were concentrated on the areas that refer to the quality of theses and dissertations of the students (item 3.3), the quality of publications by the techers (item 4.1) and distribution of these publications within the program faculty (item 4.2). This study also points out that these three items are responsible for more than 40% of the points which were ignored by fifteen post-graduate programs in the last three CAPES evaluations. In light of these facts, it can be concluded, that this methology can be used to identify the negative impact factors on the quality of post graduate programs. / Investiga os fatores que impactam a qualidade dos programas de pós-graduação da UFAM, utilizando como fonte de dados as avaliações trienais da CAPES e como ferramentas de análise o Diagrama de Pareto e o Histograma. A literatura destaca algumas abordagens sobre a avaliação, no sentido conceitual ou de comparação com outros métodos e ainda, com relação ao fluxo do processo. Este estudo permitiu visualizar, mediante a aplicação de uma metodologia disponível na literatura pesquisada, a situação de cada um dos programas de pósgraduação da Universidade Federal do Amazonas nas três avaliações da CAPES identificando e demonstrando os principais itens que causaram um impacto negativo nesse processo. Destaca uma visão geral da situação dos programas com relação aos itens de impacto, bem como o percentual acumulado dos fatores impactantes a todos os programas. Constata que os itens que mais impactaram nas três últimas avaliações da CAPES estão concentrados naqueles que se referem à qualidade das teses e dissertações dos discentes (item 3.3), na qualidade das publicações dos docentes (item 4.1) e na distribuição dessas publicações entre o corpo docente do programa (item 4.2). Aponta que esses três itens são responsáveis por mais de 40% dos pontos que deixaram de ser atendidos pelos quinze programas de pós-graduação nas três últimas avaliações da CAPES. Diante dessa constatação, conclui-se que a metodologia poderá ser utilizada para identificar os fatores de impacto negativo na qualidade dos programas de pós-graduação.