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

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

This paper presents an approach to operate multi-objective self-optimizing software systems based on the models@run.time paradigm. In contrast to existing approaches, which are usually specific to a single or selected set of objectives (e.g., performance and/or reliability), the presented approach is generic in that it allows the software architect to model the relevant concerns of interest to self-optimization. At runtime, these models are interpreted and used to generate optimization problems. To evaluate the applicability of the approach, a scalability analysis is provided, showing the approach’s feasibility for at least two objectives.

An option, a type of a financial derivative, is a contract that creates an opportunity for a market player to avoid risks involved in investing, especially in equities. An investor desires to know the accurate value of an option before entering into a contract to buy/sell the underlying asset (stock). There are various techniques that try to simulate real market conditions in order to price or evaluate an option. However, most of them achieved limited success due to high uncertainty in price behavior of the underlying asset. In this study, I propose two new Firefly variant algorithms to compute accurate worth for European and American option contracts and compare them with popular option pricing models (such as Black-Scholes-Merton, binomial lattice, Monte-Carlo, etc.) and real market data. In my study, I have first modelled the option pricing as a multi-objective optimization problem, where I introduced the pay-off and probability of achieving that pay-off as the main optimization objectives. Then, I proposed to use a latest nature-inspired algorithm that uses the bioluminescence of Fireflies to simulate the market conditions, a first attempt in the literature. For my thesis, I have proposed adaptive weighted-sum based Firefly algorithm and non-dominant sorting Firefly algorithm to find Pareto optimal solutions for the option pricing problem. Using my algorithm(s), I have successfully computed complete Pareto front of option prices for a number of option contracts from the real market (Bloomberg data). Also, I have shown that one of the points on the Pareto front represents the option value within 1-2 % error of the real data (Bloomberg). Moreover, with my experiments, I have shown that any investor may utilize the results in the Pareto fronts for deciding to get into an option contract and can evaluate the worth of a contract tuned to their risk ability. This implies that my proposed multi-objective model and Firefly algorithm could be used in real markets for pricing options at different levels of accuracy. To the best of my knowledge, modelling option pricing problem as a multi-objective optimization problem and using newly developed Firefly algorithm for solving it is unique and novel. / October 2016

Latin hypercube designs (LHDs) have broad applications in constructing computer experiments and sampling for Monte-Carlo integration due to its nice property of having projections evenly distributed on the univariate distribution of each input variable. The LHDs have been combined with some commonly used computer experimental design criteria to achieve enhanced design performance. For example, the Maximin-LHDs were developed to improve its space-filling property in the full dimension of all input variables. The MaxPro-LHDs were proposed in recent years to obtain nicer projections in any subspace of input variables. This thesis integrates both space-filling and projection characteristics for LHDs and develops new algorithms for constructing optimal LHDs that achieve nice properties on both criteria based on using the Pareto front optimization approach. The new LHDs are evaluated through case studies and compared with traditional methods to demonstrate their improved performance.

Pas de résumé / CMOS image sensor based on Active pixel sensor has considerably contributed to the imaging market and research interest in the past decade. Furthermore technology advancement has provided the capability to integrate more and more functionality into a single chip in multiple layers leading to a new paradigm, 3D integration. CMOS image sensor is one such application which could utilize the capability of 3D stacked architecture to achieve dedicated technologies in different layers, wire length reduction, less area, improved performancesThis research work is focused mainly on the early stages of design space exploration using hierarchical approach and aims at reducing time to market. This work investigates the imager from the top-down design perspective. Methodical anal y sis of imager is performed to achieve high level of flexibility and modularity. Re-useable models are developed to explore early design choices throughout the hierarchy. Finally, pareto front (providing trade off solutions) methodology is applied to explore the operating range of individual block at system level to help the designer making his design choice. Furthermore the thermal issues which get aggravated in the 3D stacked chip on the performance of the imager are studied. Systeme based thermal model is built to investigate the behavior of imager pixel matrix and to simulate the pixel matrix at high speed with acceptable accuracy compared to electrical simulations. The modular nature of the model makes simulations with future matrix extension straightforward. Validation of the thermal model with respect to electrical simulations is discussed. Finally an integrated design flow is developed to perform 3D floorplanning and to perform thermal anal y sis of the imager pixel matrix.

Des problèmes de Bandit constituent une séquence d’allocation dynamique. D’une part, l’agent de système doit explorer son environnement ( à savoir des bras de machine) pour recueillir des informations; d’autre part, il doit exploiter les informations collectées pour augmenter la récompense. Comment d’équilibrer adéquatement la phase d’exploration et la phase d’exploitation, c’est une obscurité des problèmes de Bandit, et la plupart des chercheurs se concentrent des efforts sur les stratégies d’équilibration entre l’exploration et l’exploitation. Dans cette dissertation, nous nous concentrons sur l’étude de deux problèmes spécifiques de Bandit: les problèmes de Bandit contextuel et les problèmes de Bandit Multi- objectives. Cette dissertation propose deux aspects de contributions. La première concerne la classification sous la surveillance partielle, laquelle nous codons comme le problème de Bandit contextuel avec des informations partielles. Ce type des problèmes est abondamment étudié par des chercheurs, en appliquant aux réseaux sociaux ou systèmes de recommandation. Nous proposons une série d’algorithmes sur la base d’algorithme Passive-Aggressive pour résoudre des problèmes de Bandit contextuel. Nous profitons de sa fondations, et montrons que nos algorithmes sont plus simples à mettre en œuvre que les algorithmes en état de l’art. Ils réalisent des biens performances de classification. Pour des problèmes de Bandit Multi-objective (MOMAB), nous proposons une méthode motivée efficace et théoriquement à identifier le front de Pareto entre des bras. En particulier, nous montrons que nous pouvons trouver tous les éléments du front de Pareto avec un budget minimal dans le cadre de PAC borne. / Bandit problems constitute a sequential dynamic allocation problem. The pulling agent has to explore its environment (i.e. the arms) to gather information on the one hand, and it has to exploit the collected clues to increase its rewards on the other hand. How to adequately balance the exploration phase and the exploitation phase is the crux of bandit problems and most of the efforts devoted by the research community from this fields has focused on finding the right exploitation/exploration tradeoff. In this dissertation, we focus on investigating two specific bandit problems: the contextual bandit problems and the multi-objective bandit problems. This dissertation provides two contributions. The first contribution is about the classification under partial supervision, which we encode as a contextual bandit problem with side informa- tion. This kind of problem is heavily studied by researchers working on social networks and recommendation systems. We provide a series of algorithms to solve the Bandit feedback problem that pertain to the Passive-Aggressive family of algorithms. We take advantage of its grounded foundations and we are able to show that our algorithms are much simpler to implement than state-of-the-art algorithms for bandit with partial feedback, and they yet achieve better perfor- mances of classification. For multi-objective multi-armed bandit problem (MOMAB), we propose an effective and theoretically motivated method to identify the Pareto front of arms. We in particular show that we can find all elements of the Pareto front with a minimal budget.

The aim and objective of this research is to formulate and solve a multi-objective optimization problem for the optimal placement of multiple rows and multiple columns of fixed flat-plate solar collectors in a field. This is to maximize energy collected from the solar collectors and minimize the investment in terms of the field and collector cost. The resulting multi-objective optimization problem will be solved using genetic algorithm techniques. It is necessary to consider multiple columns of collectors as this can result in obtaining higher amounts of energy from these collectors when costs and maintenance or replacement of damaged parts are concerned. The formulation of such a problem is dependent on several factors, which include shading of collectors, inclination of collectors, distance between the collectors, latitude of location and the global solar radiation (direct beam and diffuse components). This leads to a multi-objective optimization problem. These kind of problems arise often in nature and can be difficult to solve. However the use of evolutionary algorithm techniques has proven effective in solving these kind of problems. Optimizing the distance between the collector rows, the distance between the collector columns and the collector inclination angle, can increase the amount of energy collected from a field of solar collectors thereby maximizing profit and improving return on investment. In this research, the multi-objective optimization problem is solved using two optimization approaches based on genetic algorithms. The first approach is the weighted sum approach where the multi-objective problem is simplified into a single objective optimization problem while the second approach is finding the Pareto front. / Dissertation (MEng)--University of Pretoria, 2012. / Electrical, Electronic and Computer Engineering / MEng / Unrestricted

Managing traffic during oversaturated conditions is a current challenge for practitioners due to the lack of adequate tools that can handle such situations. Unlike under-saturated conditions, operation of traffic signal systems during congestion requires careful consideration and analysis of the underlying causes of the congestion before developing mitigation strategies. The objectives of this research are to provide a practical guidance for practitioners to identify oversaturated scenarios and to develop a multi-objective methodology for selecting and evaluating mitigation strategy/ or combinations of strategies based on a guiding principles. The research focused on traffic control strategies that can be implemented by traffic signal systems. The research did not considered strategies that deals with demand reduction or seek to influence departure time choice, or route choice. The proposed timing methodology starts by detecting network's critical routes as a necessary step to identify the traffic patterns and potential problematic scenarios. A wide array of control strategies are defined and categorized to address oversaturation problematic scenarios. A timing procedure was then developed using the principles of oversaturation timing in cycle selection, split allocation, offset design, demand overflow, and queue allocation in non-critical links. Three regimes of operation were defined and considered in oversaturation timing: (1) loading, (2) processing, and (3) recovery. The research also provides a closed-form formula for switching control plans during the oversaturation regimes. The selection of optimal control plan is formulated as linear integer programming problem. Microscopic simulation results of two arterial test cases revealed that traffic control strategies developed using the proposed framework led to tangible performance improvements when compared to signal control strategies designed for operations in under-saturated conditions. The generated control plans successfully manage to allocate queues in network links. / Ph. D.

Muitos problemas de otimização multi-objetivo utilizam os algoritmos evolutivos para encontrar as melhores soluções. Muitos desses algoritmos empregam as fronteiras de Pareto como estratégia para obter tais soluções. Entretando, conforme relatado na literatura, há a limitação da fronteira para problemas com até três objetivos, podendo tornar seu emprego insatisfatório para os problemas com quatro ou mais objetivos. Além disso, as propostas apresentadas muitas vezes eliminam o emprego dos algoritmos evolutivos, os quais utilizam tais fronteiras. Entretanto, as características dos algoritmos evolutivos os qualificam para ser empregados em problemas de otimização, como já vem sendo difundido pela literatura, evitando eliminá-lo por causa da limitação das fronteiras de Pareto. Assim sendo, neste trabalho se buscou eliminar as fronteiras de Pareto e para isso utilizou a lógica Fuzzy, mantendo-se assim o emprego dos algoritmos evolutivos. O problema escolhido para investigar essa substituição foi o problema de predição de estrutura terciária de proteínas, pois além de se encontrar em aberto é de suma relevância para a área de bioinformática. / Several multi-objective optimization problems utilize evolutionary algorithms to find the best solution. Some of these algoritms make use of the Pareto front as a strategy to find these solutions. However, according to the literature, the Pareto front limitation for problems with up to three objectives can make its employment unsatisfactory in problems with four or more objectives. Moreover, many authors, in most cases, propose to remove the evolutionay algorithms because of Pareto front limitation. Nevertheless, characteristics of evolutionay algorithms qualify them to be employed in optimization problems, as it has being spread out by literature, preventing to eliminate it because the Pareto front elimination. Thus being, this work investigated to remove the Pareto front and for this utilized the Fuzzy logic, remaining itself thus the employ of evolutionary algorithms. The choice problem to investigate this remove was the protein tertiary structure prediction, because it is a open problem and extremely relevance to bioinformatic area.