Finding optimal configuration of power distribution systems topology is an NP-hard combinatorial optimization problem. It becomes more complex when time varying nature of loads in large-scale distribution systems is taken into account. In the second chapter of this dissertation, a systematic approach is proposed to tackle the computational burden of the procedure. To solve the optimization problem, a novel adaptive fuzzy based parallel genetic algorithm (GA) is proposed that employs the concept of parallel computing in identifying the optimal configuration of the network. The integration of fuzzy logic into GA enhances the efficiency of the parallel GA by adaptively modifying the migration rates between different processors during the optimization process. A computationally efficient graph encoding method based on Dandelion coding strategy is developed which automatically generates radial topologies and prevents the construction of infeasible radial networks during the optimization process. The main shortcoming of the proposed algorithm in Chapter 2 is that it identifies only one single solution. It means that the system operator will not have any option but relying on the found solution. That is why a novel hybrid optimization algorithm is proposed in the third chapter of this dissertation that determines Pareto frontiers, as candidate solutions, for multi-objective distribution network reconfiguration problem. Implementing this model, the system operator will have more flexibility in choosing the best configuration among the alternative solutions. The proposed hybrid optimization algorithm combines the concept of fuzzy Pareto dominance (FPD) with shuffled frog leaping algorithm (SFLA) to recognize non-dominated suboptimal solutions identified by SFLA. The local search step of SFLA is also customized for power systems applications so that it automatically creates and analyzes only the feasible and radial configurations in its optimization procedure which significantly increases the convergence speed of the algorithm. In the fourth chapter, the problem of optimal network reconfiguration is solved for the case in which the system operator is going to employ an optimization algorithm that is automatically modifying its parameters during the optimization process. Defining three fuzzy functions, the probability of crossover and mutation will be adaptively tuned as the algorithm proceeds and the premature convergence will be avoided while the convergence speed of identifying the optimal configuration will not decrease. This modified genetic algorithm is considered a step towards making the parallel GA, presented in the second chapter of this dissertation, more robust in avoiding from getting stuck in local optimums. In the fifth chapter, the concentration will be on finding a potential smart grid solution to more high-quality suboptimal configurations of distribution networks. This chapter is considered an improvement for the third chapter of this dissertation for two reasons: (1) A fuzzy logic is used in the partitioning step of SFLA to improve the proposed optimization algorithm and to yield more accurate classification of frogs. (2) The problem of system reconfiguration is solved considering the presence of distributed generation (DG) units in the network. In order to study the new paradigm of integrating smart grids into power systems, it will be analyzed how the quality of suboptimal solutions can be affected when DG units are continuously added to the distribution network. The heuristic optimization algorithm which is proposed in Chapter 3 and is improved in Chapter 5 is implemented on a smaller case study in Chapter 6 to demonstrate that the identified solution through the optimization process is the same with the optimal solution found by an exhaustive search.

Portfolio optimisation has a number of constraints resulting from some practical matters and regulations. The closed-form mathematical solution of portfolio optimisation problems usually cannot include these constraints. Exhaustive search to reach the exact solution can take prohibitive amount of computational time. Portfolio optimisation models are also usually impaired by the estimation error problem caused by lack of ability to predict the future accurately. A number of Multi-Objective Genetic Algorithms are proposed to solve the problem with two objectives subject to cardinality constraints, floor constraints and round-lot constraints. Fuzzy logic is incorporated into the Vector Evaluated Genetic Algorithm (VEGA) to but solutions tend to cluster around a few points. Strength Pareto Evolutionary Algorithm 2 (SPEA2) gives solutions which are evenly distributed portfolio along the effective front while MOGA is more time efficient. An Evolutionary Artificial Neural Network (EANN) is proposed. It automatically evolves the ANN¿s initial values and structures hidden nodes and layers. The EANN gives a better performance in stock return forecasts in comparison with those of Ordinary Least Square Estimation and of Back Propagation and Elman Recurrent ANNs. Adaptation algorithms for selecting a pair of forecasting models, which are based on fuzzy logic-like rules, are proposed to select best models given an economic scenario. Their predictive performances are better than those of the comparing forecasting models. MOGA and SPEA2 are modified to include a third objective to handle model risk and are evaluated and tested for their performances. The result shows that they perform better than those without the third objective.

Human activities on land have a direct and cumulative impact on water and other natural resources within a catchment. This land-use change can have hydrological consequences on the local and regional scales. Sound catchment assessment is not only critical to understanding processes and functions but also important in identifying priority management areas. The overarching goal of this doctoral thesis was to design a methodological framework for catchment assessment (dependent upon data availability) and propose practical catchment management strategies for sustainable water resources management. The Nyangores and Ruiru reservoir catchments located in Kenya, East Africa were used as case studies. A properly calibrated Soil and Water Assessment Tool (SWAT) hydrologic model coupled with a generic land-use optimization tool (Constrained Multi-Objective Optimization of Land-use Allocation-CoMOLA) was applied to identify and quantify functional trade-offs between environmental sustainability and food production in the ‘data-available’ Nyangores catchment. This was determined using a four-dimension objective function defined as (i) minimizing sediment load, (ii) maximizing stream low flow and (iii and iv) maximizing the crop yields of maize and soybeans, respectively. Additionally, three different optimization scenarios, represented as i.) agroforestry (Scenario 1), ii.) agroforestry + conservation agriculture (Scenario 2) and iii.) conservation agriculture (Scenario 3), were compared. For the data-scarce Ruiru reservoir catchment, alternative methods using digital soil mapping of soil erosion proxies (aggregate stability using Mean Weight Diameter) and spatial-temporal soil loss analysis using empirical models (the Revised Universal Soil Loss Equation-RUSLE) were used. The lack of adequate data necessitated a data-collection phase which implemented the conditional Latin Hypercube Sampling. This sampling technique reduced the need for intensive soil sampling while still capturing spatial variability. The results revealed that for the Nyangores catchment, adoption of both agroforestry and conservation agriculture (Scenario 2) led to the smallest trade-off amongst the different objectives i.e. a 3.6% change in forests combined with 35% change in conservation agriculture resulted in the largest reduction in sediment loads (78%), increased low flow (+14%) and only slightly decreased crop yields (3.8% for both maize and soybeans). Therefore, the advanced use of hydrologic models with optimization tools allows for the simultaneous assessment of different outputs/objectives and is ideal for areas with adequate data to properly calibrate the model. For the Ruiru reservoir catchment, digital soil mapping (DSM) of aggregate stability revealed that susceptibility to erosion exists for cropland (food crops), tea and roadsides, which are mainly located in the eastern part of the catchment, as well as deforested areas on the western side. This validated that with limited soil samples and the use of computing power, machine learning and freely available covariates, DSM can effectively be applied in data-scarce areas. Moreover, uncertainty in the predictions can be incorporated using prediction intervals. The spatial-temporal analysis exhibited that bare land (which has the lowest areal proportion) was the largest contributor to erosion. Two peak soil loss periods corresponding to the two rainy periods of March–May and October–December were identified. Thus, yearly soil erosion risk maps misrepresent the true dimensions of soil loss with averages disguising areas of low and high potential. Also, a small portion of the catchment can be responsible for a large proportion of the total erosion. For both catchments, agroforestry (combining both the use of trees and conservation farming) is the most feasible catchment management strategy (CMS) for solving the major water quantity and quality problems. Finally, the key to thriving catchments aiming at both sustainability and resilience requires urgent collaborative action by all stakeholders. The necessary stakeholders in both Nyangores and Ruiru reservoir catchments must be involved in catchment assessment in order to identify the catchment problems, mitigation strategies/roles and responsibilities while keeping in mind that some risks need to be shared and negotiated, but so will the benefits.:TABLE OF CONTENTS DECLARATION OF CONFORMITY........................................................................ i DECLARATION OF INDEPENDENT WORK AND CONSENT ............................. ii LIST OF PAPERS ................................................................................................. iii ACKNOWLEDGEMENTS ..................................................................................... iv THESIS AT A GLANCE ......................................................................................... v SUMMARY ............................................................................................................ vi List of Figures......................................................................................................... x List of Tables........................................................................................................... x ABBREVIATION..................................................................................................... xi PART A: SYNTHESIS 1. INTRODUCTION ............................................................................................... 1 1.1 Catchment management ...................................................................................1 1.2 Tools to support catchment assessment and management ..............................4 1.3 Catchment management strategies (CMSs)......................................................9 1.4 Concept and research objectives.......................................................................11 2. MATERIAL AND METHODS................................................................................15 2.1. STUDY AREA ..................................................................................................15 2.1.1. Nyangores catchment ...................................................................................15 2.1.2. Ruiru reservoir catchment .............................................................................17 2.2. Using SWAT conceptual model and land-use optimization ..............................19 2.3. Using soil erosion proxies and empirical models ..............................................21 3. RESULTS AND DISCUSSION..............................................................................24 3.1. Assessing multi-metric calibration performance using the SWAT model...........25 3.2. Land-use optimization using SWAT-CoMOLA for the Nyangores catchment. ..26 3.3. Digital soil mapping of soil aggregate stability ..................................................28 3.4. Spatio-temporal analysis using the revised universal soil loss equation (RUSLE) 29 4. CRITICAL ASSESSMENT OF THE METHODS USED ......................................31 4.1. Assessing suitability of data for modelling and overcoming data challenges...31 4.2. Selecting catchment management strategies based on catchment assessment . 35 5. CONCLUSION AND RECOMMENDATIONS ....................................................36 6. REFERENCES ............................ .....................................................................38 PART B: PAPERS PAPER I .................................................................................................................47 PAPER II ................................................................................................................59 PAPER III ...............................................................................................................74 PAPER IV ...............................................................................................................88

<p>Process operability represents the ability of a process plant to operate satisfactorily away from the nominal operating or design condition, where flexibility and dynamic operability are two important attributes of operability considered in this thesis. Today's companies are facing numerous challenges, many as a result of volatile market conditions. Key to sustainable profitable operation is a robust process supply chain. Within a wider business context, flexibility and responsiveness, i.e. dynamic operability, are regarded as key qualifications of a robust process supply chain.</p> <p>The first part of this thesis develops methodologies to rigorously evaluate the dynamic operability and flexibility of a process supply chain. A model is developed which describes the response dynamics of a multi-product, multi-echelon supply chain system. Its incorporation within a dynamic operability analysis framework is shown, where a bi-criterion, two-stage stochastic programming approach is applied for the treatment of demand uncertainty, and for estimating the Pareto frontier between an economic and responsiveness criterion. Two case studies are presented to demonstrate the effect of supply chain design features on responsiveness. This thesis has also extended current paradigms for process flexibility analysis to supply chains. The flexibility analysis framework, where a steady-state supply chain model is considered, evaluates the ability to sustain feasible steady-state operation for a range of demand uncertainty.</p> <p>The second part of this thesis develops a decision-support tool for supply chain management (SCM), by means of a robust model predictive control (MPC) strategy. An effective decision-support tool can fully leverage the qualifications from the operability analysis. The MPC formulation proposed in this thesis: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, (iii) addresses multiple supply chain performance metrics including customer service and economics, and (iv) considers both open-loop and closed-loop prediction of uncertainty propagation. The developed robust framework is applied for the control of a multi-echelon, multi-product supply chain, and provides a substantial reduction in the occurrence of back orders when compared with a nominal MPC framework.</p> / Master of Applied Science (MASc)

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Le fonctionnement d'un système, de façon générale, peut être affecté par un incident imprévu. Lorsque cet incident a de lourdes conséquences tant sur l'intégrité du système que sur la qualité de ses produits, on dit alors qu'il se situe dans le cadre des événements dits extrêmes. Ainsi, de plus en plus les chercheurs portent un intérêt particulier à la modélisation des événements extrêmes pour diverses études telles que la fiabilité des systèmes et la prédiction des différents risques pouvant entraver le bon fonctionnement d'un système en général. C'est dans cette optique que s'inscrit la présente thèse. Nous utilisons la Théorie des Valeurs Extrêmes (TVE) et les statistiques d'ordre extrême comme outil d'aide à la décision dans la modélisation et la gestion des risques dans l'usinage et l'aviation. Plus précisément, nous modélisons la surface de rugosité de pièces usinées et la fiabilité de l'outil de coupe associé par les statistiques d'ordre extrême. Nous avons aussi fait une modélisation à l'aide de l'approche dite du "Peaks-Over Threshold, POT" permettant de faire des prédictions sur les éventuelles victimes dans l'Aviation Générale Américaine (AGA) à la suite d'accidents extrêmes. Par ailleurs, la modélisation des systèmes soumis à des facteurs d'environnement ou covariables passent le plus souvent par les modèles à risque proportionnel basés sur la fonction de risque. Dans les modèles à risque proportionnel, la fonction de risque de base est généralement de type Weibull, qui est une fonction monotone; l'analyse du fonctionnement de certains systèmes comme l'outil de coupe dans l'industrie a montré qu'un système peut avoir un mauvais fonctionnement sur une phase et s'améliorer sur la phase suivante. De ce fait, des modifications ont été apportées à la distribution de Weibull afin d'avoir des fonctions de risque de base non monotones, plus particulièrement les fonctions de risque croissantes puis décroissantes. En dépit de ces modifications, la prise en compte des conditions d'opérations extrêmes et la surestimation des risques s'avèrent problématiques. Nous avons donc, à partir de la loi standard de Gumbel, proposé une fonction de risque de base croissante puis décroissante permettant de prendre en compte les conditions extrêmes d'opérations, puis établi les preuves mathématiques y afférant. En outre, un exemple d'application dans le domaine de l'industrie a été proposé. Cette thèse est divisée en quatre chapitres auxquels s'ajoutent une introduction et une conclusion générales. Dans le premier chapitre, nous rappelons quelques notions de base sur la théorie des valeurs extrêmes. Le deuxième chapitre s'intéresse aux concepts de base de l'analyse de survie, particulièrement à ceux relatifs à l'analyse de fiabilité, en proposant une fonction de risque croissante-décroissante dans le modèle à risques proportionnels. En ce qui concerne le troisième chapitre, il porte sur l'utilisation des statistiques d'ordre extrême dans l'usinage, notamment dans la détection de pièces défectueuses par lots, la fiabilité de l'outil de coupe et la modélisation des meilleures surfaces de rugosité. Le dernier chapitre porte sur la prédiction d'éventuelles victimes dans l'Aviation Générale Américaine à partir des données historiques en utilisant l'approche "Peaks-Over Threshold" / The operation of a system in general may at any time be affected by an unforeseen incident. When this incident has major consequences on the system integrity and the quality of system products, then it is said to be in the context of extreme events. Thus, increasingly researchers have a particular interest in modeling such events with studies on the reliability of systems and the prediction of the different risks that can hinder the proper functioning of a system. This thesis takes place in this very perspective. We use Extreme Value Theory (EVT) and extreme order statistics as a decision support tool in modeling and risk management in industry and aviation. Specifically, we model the surface roughness of machined parts and the reliability of the associated cutting tool with the extreme order statistics. We also did a modeling using the "Peaks-Over Threshold, POT" approach to make predictions about the potential victims in the American General Aviation (AGA) following extreme accidents. In addition, the modeling of systems subjected to environmental factors or covariates is most often carried out by proportional hazard models based on the hazard function. In proportional hazard models, the baseline risk function is typically Weibull distribution, which is a monotonic function. The analysis of the operation of some systems like the cutting tool in the industry has shown that a system can deteriorated on one phase and improving on the next phase. Hence, some modifications have been made in the Weibull distribution in order to have non-monotonic basic risk functions, more specifically, the increasing-decreasing risk function. Despite these changes, taking into account extreme operating conditions and overestimating risks are problematics. We have therefore proposed from Gumbel's standard distribution, an increasingdecreasing risk function to take into account extreme conditions, and established mathematical proofs. Furthermore, an example of the application in the field of industry was proposed. This thesis is organized in four chapters and to this must be added a general introduction and a general conclusion. In the first chapter, we recall some basic notions about the Extreme Values Theory. The second chapter focuses on the basic concepts of survival analysis, particularly those relating to reliability analysis by proposing a function of increasing-decreasing hazard function in the proportional hazard model. Regarding the third chapter, it deals with the use of extreme order statistics in industry, particularly in the detection of defective parts, the reliability of the cutting tool and the modeling of the best roughness surfaces. The last chapter focuses on the prediction of potential victims in AGA from historical data using the Peaks-Over Threshold approach.

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This work focuses on statistical methods to understand how frequently rare events occur and what the magnitude of extreme values such as large losses is. It lies in a field called extreme value analysis whose scope is to provide support for scientific decision making when extreme observations are of particular importance such as in environmental applications, insurance and finance. In the univariate case, I propose new techniques to model tails of discrete distributions and illustrate them in an application on word frequency and multiple birth data. Suitably rescaled, the limiting tails of some discrete distributions are shown to converge to a discrete generalized Pareto distribution and generalized Zipf distribution respectively. In the multivariate high-dimensional case, I suggest modeling tail dependence between random variables by a graph such that its nodes correspond to the variables and shocks propagate through the edges. Relying on the ideas of graphical models, I prove that if the variables satisfy a new notion called asymptotic conditional independence, then the density of the joint distribution can be simplified and expressed in terms of lower dimensional functions. This generalizes the Hammersley- Clifford theorem and enables us to infer tail distributions from observations in reduced dimension. As an illustration, extreme river flows are modeled by a tree graphical model whose structure appears to recover almost exactly the actual river network. A fundamental concept when studying limiting tail distributions is regular variation. I propose a new notion in the multivariate case called one-component regular variation, of which Karamata's and the representation theorem, two important results in the univariate case, are generalizations. Eventually, I turn my attention to website visit data and fit a censored copula Gaussian graphical model allowing the visualization of users' behavior by a graph.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-06T14:18:54Z No. of bitstreams: 1 ROSILDA SOUSA SANTOS - DISSERTAÇÃO PPGMAT 2012..pdf: 864926 bytes, checksum: 9d85b58c8bca6174ef968354411068a1 (MD5) / Made available in DSpace on 2018-08-06T14:18:54Z (GMT). No. of bitstreams: 1 ROSILDA SOUSA SANTOS - DISSERTAÇÃO PPGMAT 2012..pdf: 864926 bytes, checksum: 9d85b58c8bca6174ef968354411068a1 (MD5) Previous issue date: 2012-09 / Capes / A proposta desta dissertação está relacionada com o estudo das principais famílias de distribuições de probabilidade generalizadas. Particularmente, estudamos as distribuições Beta Pareto, Beta Exponencial Generalizada, Beta Weibull Modificada, Beta Fréchet e a Kw-G. Para cada uma delas foram obtidas expressões para as funções densidades de probabilidade, funcões de distribuição acumuladas, funções de taxa de falha, funções geratrizes de momentos, bem como foram obtidos os estimadores dos parâmetros pelo método da máxima verossimilhança. Finalmente, para cada distribuição foram feitas aplicações com dados reais. / The purpose of this dissertation is to study the main families of generalized probability distributions. Particularly we study the distributions Beta Pareto, generalized Beta Exponential, Beta Modified Weibull, Beta Fréchet and Kw-G. For each one of these distributions we obtain expressions for the probability density function, cumulative distribution function, hazard function and moment generating function as well as parameter estimates by the method of maximum likelihood. Finally, we make real data applications for each one of the studied distributions.

Le modèle classique de la finance (Markowitz, Sharpe, Black, Scholes, Fama) a, dès le début, été remis en cause par le mathématicien Benoît Mandelbrot (1924-2010). Il démontre que la loi normale ne correspond pas à la réalité des marchés, parce qu’elle sous-estime les risques extrêmes. Il faut au contraire utiliser les lois de puissance, comme la loi de Pareto. Nous montrons ici toutes les implications de ce changement fondamental sur la finance, mais aus-si, ce qui est nouveau, en ce qui concerne la gestion des entreprises (à travers le calcul du coût des capitaux propres). Nous tentons de mettre à jour les raisons profondes de l’existence des lois de puissance en économie à travers la notion d’entropie. Nous présen-tons de nouveaux outils théoriques pour comprendre la formation des prix (la théorie de la proportion diagonale), des bulles (la notion de réflexivité), des crises (la notion de réseau), en apportant une réponse globale à la crise actuelle (un système monétaire diversifié). Toutes ces voies sont très peu, ou pas du tout exploitées. Elles sont surtout, pour la pre-mière fois, mises en cohérence autour de la notion de loi de puissance. C’est donc une nou-velle façon de comprendre les phénomènes économiques que nous présentons ici. / The classical model of finance (Markowitz, Sharpe, Black, Scholes, Fama) has, from the be-ginning, been challenged by the mathematician Benoit Mandelbrot (1924-2010). It shows that the normal distribution does not match the reality of the market, because it underesti-mates the extreme risks. Instead, we must use the power laws, such as the Pareto law. We show the implications of this fundamental change in the finance, but also in the manage-ment of companies (through the calculation of cost of capital). We try to update the underly-ing reasons for the existence of power laws in economics through the concept of entropy. We present new theoretical tools to understand price formation (the theory of diagonal proportion), bubbles (the notion of reflexivity), crisis (network concept), providing a com-prehensive response to the current crisis (a diversified monetary system). All these ways are very little or not at all exploited. They are mostly for the first time, made consistent around the notion of power law. This is a new way of understanding economic phenomena present-ed here.