Thesis (Ph. D.)--University of Chicago, Dept. of Philosophy. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Florida, 2005. / Title from title page of source document. Document formatted into pages; contains 97 pages. Includes vita. Includes bibliographical references.

The Brandeis dice problem, originally introduced in 1962 by Jaynes as an illustration of the principle of maximum entropy, was solved using the genetic algorithm, and the resulting solution was compared with that obtained analytically. The effect of varying the genetic algorithm parameters was observed, and the optimum values for population size, mutation rate, and mutation interval were determined for this problem. The optimum genetic algorithm program was then compared to a completely random method of search and optimization. Finally, the genetic algorithm approach was extended to several variations of the original problem for which an analytical approach would be impractical.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 101-107).

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: A method for multi-objective optimisation using the cross-entropy method (MOO CEM) was recently developed by Bekker & Aldrich (2010) and Bekker (2012). The method aims to identify the nondominated solutions of multi-objective problems, which are often dynamic and stochastic. The method does not use a statistical ranking and selection technique to account for the stochastic nature of the problems it solves. The research in this thesis aims to investigate possible techniques that can be incorporated into the MOO CEM. The cross-entropy method for single-objective optimisation is studied first. It is applied to an interesting problem in the soil sciences and water management domain. The purpose of this was for the researcher to grasp the fundamentals of the cross-entropy method, which will be needed later in the study. The second part of the study documents an overview of multi-objective ranking and selection methods found in literature. The first method covered is the multi-objective optimal computing budget allocation algorithm. The second method extends upon the first to include the concept of an indifference-zone. Both methods aim to maximise the probability of correctly selecting the non-dominated scenarios, while intelligently allocating simulation replications to minimise required sample sizes. These techniques are applied to two problems that are represented by simulation models, namely the buffer allocation problem and a classic single-commodity inventory problem. Performance is measured using the hyperarea indicator and Mann-Whitney U-tests. It was found that the two techniques have significantly different performances, although this could be due to the different number of solutions in the Pareto set. In the third part of the document, the aforementioned multi-objective ranking and selection techniques are incorporated into the MOO CEM. Once again, the buffer allocation problem and the inventory problem were chosen as test problems. The results were compared to experiments where the MOO CEM without ranking and selection was used. Results show that the MOO CEM with ranking and selection has various affects on different problems. Investigating the possibility of incorporating ranking and selection differently in the MOO CEM is recommended as future research. Additionally, the combined algorithm should be tested on more stochastic problems. / AFRIKAANSE OPSOMMING: 'n Metode vir meerdoelige optimering wat gebruik maak van die kruisentropie- metode (MOO CEM) is onlangs deur Bekker & Aldrich (2010) en Bekker (2012) ontwikkel. Die metode mik om die nie-gedomineerde oplossings van meerdoelige probleme te identifiseer, wat dikwels dinamies en stogasties is. Die metode maak nie gebruik van 'n statistiese orden-en-kies tegniek om die stogastiese aard van die problem aan te spreek nie. Die navorsing in hierdie tesis poog om moontlike tegnieke wat in die MOO CEM opgeneem kan word, te ondersoek. Die kruis-entropie-metode vir enkeldoelwit optimering is eerste bestudeer. Dit is toegepas op 'n interessante probleem in die grondwetenskappe en waterbestuur domein. Die doel hiervan was om die navorser die grondbeginsels van die kruis-entropie metode te help verstaan, wat later in die studie benodig sal word. Die tweede gedeelte van die studie verskaf 'n oorsig van meerdoelige orden-en-kies metodes wat in die literatuur aangetref word. Die eerste metode wat bespreek word, is die optimale toedeling van rekenaarbegroting vir multi-doelwit optimering algoritme. Die tweede metode brei uit oor die eerste metode wat die konsep van 'n neutrale sone insluit. Beide metodes streef daarna om die waarskynlikheid dat die nie-gedomineerde oplossings korrek gekies word te maksimeer, terwyl dit ook steekproefgroottes probeer minimeer deur die aantal simulasieherhalings intelligent toe te ken. Hierdie tegnieke word toegepas op twee probleme wat verteenwoordig word deur simulasiemodelle, naamlik die buffer-toedelingsprobleem en 'n klassieke enkelitem voorraadprobleem. Die prestasie van die algoritmes word deur middel van die hiperarea-aanwyser en Mann Whitney U-toetse gemeet. Daar is gevind dat die twee tegnieke aansienlik verskillend presteer, alhoewel dit as gevolg van die verskillende aantal oplossings in die Pareto versameling kan wees. In die derde gedeelte van die dokument, is die bogenoemde meerdoelige orden-en-kies tegnieke in die MOO CEM geïnkorporeer. Weereens is die buffer-toedelingsprobleem en die voorraadprobleem as toetsprobleme gekies. Die resultate was met die eksperimente waar die MOO CEM sonder orden-en-kies gebruik is, vergelyk. Resultate toon dat vir verskillende probleme, tree die MOO CEM met orden-en-kies anders op. 'n Ondersoek oor 'n alternatiewe manier om orden-en-kies met die MOO CEM te integreer is as toekomstige navorsing voorgestel. Bykomend moet die gekombineerde algoritme op meer stogastiese probleme getoets word.

The Logistic Positive Exponent (LPE) model from Item Response Theory (IRT) and the Multistage Adaptive Testing (MST) using this model are the focus of this dissertation. For the LPE, item parameter estimations efficiency was studied, it was also analyzed the latent trait estimation for different response patterns to verify the effects it has on guessing and accidental mistakes. The LPE was put in contrast to Rasch, 2 and 3 parameter logistic models to compare the its efficiency. The item parameter estimations were implemented using the Bayesian approach for the Monte Carlo Markov Chain and the Marginal Maximum Likelihood. The latent trait estimation were calculated by the Expected a Posterior method. A goodness of fit analysis were made using the Posterior Predictive model-check method and information statistics. In the MST perspective, the LPE was compared with the Rasch and 2 logistic models. Different tests were constructed using methods that uses optimization functions to select items from a bank. Three functions were chosen to this task: the Fisher and Kullback-Leibler informations and the Continuous Entropy Method. The results were obtained with simulated and real data, the latter was from a general science knowledge test calls General Science test and it was provided by the Educational Testing Service company. Results showed that the LPE might help individuals that made mistakes in earlier stage of the test, especially for easy items. However, the LPE requires a large individual sample and time to estimate the item parameters making it an expensive model. MST based on LPE can be dissolve the impact of accidental mistakes from high performance test takers depending of the item pool available and the way the test is constructed. The optimization function performance vary depending of the situation. / O modelo Logístico de Expoente Positivo (LPE) da Teoria de Resposta ao Item (IRT) e o Teste Adaptativo Multiestágio (MST) sob esse modelo são os focos desta tese. Para o LPE, a eficiência da estimações dos parâmetros dos itens foram estudados, também foi analisado como as estimativas dos parâmetros dos indivíduos foram influenciados por padrões de respostas contendo chutes ou erros acidentais. O LPE foi comparado com os modelos de Rasch, Logístico de 2 e 3 Parâmetros para verificar seu desempenho. A estimação dos parâmetros dos itens foi implementada usando Monte Carlo via cadeias de Markov sob a abordagem Bayesiana e a Máxima Verossimilhança Marginal. As estimações dos traços latentes foram calculadas através do Método da Esperança a Posteriori. A qualidade do ajuste dos modelos foram analisadas usando o método Posterior Predictive model-check e critério de informações. Sob o contexto do MST, o LPE foi comparado com os modelos de Rasch e Logístico de 2 Parâmetro. Os MSTs foram construídos usando diferentes funções de objetivas que selecionaram os itens de bancos para comporem os testes. Três funções foram escolhidas para esse trabalho: As informações de Fisher e Kullback-Leibler e o Continuous Entropy Method. Os resultados para dados simulados e reais foram obtidos, os dados reais eram consituídos de respostas a perguntas sob conhecimento científico de do General Science test que foram fornecidos pela empresa Educational Testing Service. Resultados mostraram que o LPE pode ajudar os indivíduos que cometeram erros acidentais nas primeiras perguntas do teste, especialmente para os itens fáceis. Entretanto, este modelo requer tempo e uma grande quantidade de amostras de indivíduos para calcular as estimativas dos parâmetros dos itens o que o torna um modelo caro. O MST sob o modelo LPE pode diminuir o impacto de erros acidentais cometidos por examinandos com alto desempenho dependendo dos itens disponíveis no banco e a forma de construção do MST. O desempenho das funções objetivas variaram de acordo com cada situação.

The Logistic Positive Exponent (LPE) model from Item Response Theory (IRT) and the Multistage Adaptive Testing (MST) using this model are the focus of this dissertation. For the LPE, item parameter estimations efficiency was studied, it was also analyzed the latent trait estimation for different response patterns to verify the effects it has on guessing and accidental mistakes. The LPE was put in contrast to Rasch, 2 and 3 parameter logistic models to compare the its efficiency. The item parameter estimations were implemented using the Bayesian approach for the Monte Carlo Markov Chain and the Marginal Maximum Likelihood. The latent trait estimation were calculated by the Expected a Posterior method. A goodness of fit analysis were made using the Posterior Predictive model-check method and information statistics. In the MST perspective, the LPE was compared with the Rasch and 2 logistic models. Different tests were constructed using methods that uses optimization functions to select items from a bank. Three functions were chosen to this task: the Fisher and Kullback-Leibler informations and the Continuous Entropy Method. The results were obtained with simulated and real data, the latter was from a general science knowledge test calls General Science test and it was provided by the Educational Testing Service company. Results showed that the LPE might help individuals that made mistakes in earlier stage of the test, especially for easy items. However, the LPE requires a large individual sample and time to estimate the item parameters making it an expensive model. MST based on LPE can be dissolve the impact of accidental mistakes from high performance test takers depending of the item pool available and the way the test is constructed. The optimization function performance vary depending of the situation. / O modelo Logístico de Expoente Positivo (LPE) da Teoria de Resposta ao Item (IRT) e o Teste Adaptativo Multiestágio (MST) sob esse modelo são os focos desta tese. Para o LPE, a eficiência da estimações dos parâmetros dos itens foram estudados, também foi analisado como as estimativas dos parâmetros dos indivíduos foram influenciados por padrões de respostas contendo chutes ou erros acidentais. O LPE foi comparado com os modelos de Rasch, Logístico de 2 e 3 Parâmetros para verificar seu desempenho. A estimação dos parâmetros dos itens foi implementada usando Monte Carlo via cadeias de Markov sob a abordagem Bayesiana e a Máxima Verossimilhança Marginal. As estimações dos traços latentes foram calculadas através do Método da Esperança a Posteriori. A qualidade do ajuste dos modelos foram analisadas usando o método Posterior Predictive model-check e critério de informações. Sob o contexto do MST, o LPE foi comparado com os modelos de Rasch e Logístico de 2 Parâmetro. Os MSTs foram construídos usando diferentes funções de objetivas que selecionaram os itens de bancos para comporem os testes. Três funções foram escolhidas para esse trabalho: As informações de Fisher e Kullback-Leibler e o Continuous Entropy Method. Os resultados para dados simulados e reais foram obtidos, os dados reais eram consituídos de respostas a perguntas sob conhecimento científico de do General Science test que foram fornecidos pela empresa Educational Testing Service. Resultados mostraram que o LPE pode ajudar os indivíduos que cometeram erros acidentais nas primeiras perguntas do teste, especialmente para os itens fáceis. Entretanto, este modelo requer tempo e uma grande quantidade de amostras de indivíduos para calcular as estimativas dos parâmetros dos itens o que o torna um modelo caro. O MST sob o modelo LPE pode diminuir o impacto de erros acidentais cometidos por examinandos com alto desempenho dependendo dos itens disponíveis no banco e a forma de construção do MST. O desempenho das funções objetivas variaram de acordo com cada situação.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A difficult subclass of engineering optimisation problems is the class of optimisation problems which are dynamic and stochastic. These problems are often of a non-closed form and thus studied by means of computer simulation. Simulation production runs of these problems can be time-consuming due to the computational burden implied by statistical inference principles. In multi-objective optimisation of engineering problems, large decision spaces and large objective spaces prevail, since two or more objectives are simultaneously optimised and many problems are also of a combinatorial nature. The computational burden associated with solving such problems is even larger than for most single-objective optimisation problems, and hence an e cient algorithm that searches the vast decision space is required. Many such algorithms are currently available, with researchers constantly improving these or developing more e cient algorithms. In this context, the term \e cient" means to provide near-optimised results with minimal evaluations of objective function values. Thus far research has often focused on solving speci c benchmark problems, or on adapting algorithms to solve speci c engineering problems. In this research, a multi-objective optimisation algorithm, based on the cross-entropy method for single-objective optimisation, is developed and assessed. The aim with this algorithm is to reduce the number of objective function evaluations, particularly when time-dependent (dynamic), stochastic processes, as found in Industrial Engineering, are studied. A brief overview of scholarly work in the eld of multiobjective optimisation is presented, followed by a theoretical discussion of the cross-entropy method. The new algorithm is developed, based on this information, and assessed considering continuous, deterministic problems, as well as discrete, stochastic problems. The latter include a classical single-commodity inventory problem, the well-known buffer allocation problem, and a newly designed, laboratory-sized recon gurable manufacturing system. Near multi-objective optimisation of two practical problems were also performed using the proposed algorithm. In the rst case, some design parameters of a polymer extrusion unit are estimated using the algorithm. The management of carbon monoxide gas utilisation at an ilmenite smelter is complex with many decision variables, and the application of the algorithm in that environment is presented as a second case. Quality indicator values are estimated for thirty-four test problem instances of multi-objective optimisation problems in order to quantify the quality performance of the algorithm, and it is also compared to a commercial algorithm. The algorithm is intended to interface with dynamic, stochastic simulation models of real-world problems. It is typically implemented in a programming language while the simulation model is developed in a dedicated, commercial software package. The proposed algorithm is simple to implement and proved to be efficient on test problems. / AFRIKAANSE OPSOMMING: 'n Moeilike deelklas van optimeringsprobleme in die ingenieurswese is optimeringsprobleme van 'n dinamiese en stogastiese aard. Sulke probleme is dikwels nie-geslote en word gevolglik met behulp van rekenaarsimulasie bestudeer. Die beginsels van statistiese steekproefneming veroorsaak dat produksielopies van hierdie probleme tydrowend is weens die rekenlas wat genoodsaak word. Groot besluitnemingruimtes en doelwitruimtes bestaan in meerdoelige optimering van ingenieursprobleme, waar twee of meer doelwitte gelyktydig geoptimeer word, terwyl baie probleme ook 'n kombinatoriese aard het. Die rekenlas wat met die oplos van sulke probleme gepaard gaan, is selfs groter as vir die meeste enkeldoelwit optimeringsprobleme, en 'n doeltre ende algoritme wat die meesal uitgebreide besluitnemingsruimte verken, is gevolglik nodig. Daar bestaan tans verskeie sulke algoritmes, terwyl navorsers steeds poog om hierdie algoritmes te verbeter of meer doeltre ende algoritmes te ontwikkel. In hierdie konteks beteken \doeltre end" dat naby-optimale oplossings verskaf word deur die minimum evaluering van doelwitfunksiewaardes. Navorsing fokus dikwels op oplossing van standaard toetsprobleme, of aanpassing van algoritmes om 'n spesi eke ingenieursprobleem op te los. In hierdie navorsing word 'n meerdoelige optimeringsalgoritme gebaseer op die kruis-entropie-metode vir enkeldoelwit optimering ontwikkel en geassesseer. Die mikpunt met hierdie algoritme is om die aantal evaluerings van doelwitfunksiewaardes te verminder, spesi ek wanneer tydafhanklike (dinamiese), stogastiese prosesse soos wat dikwels in die Bedryfsingenieurswese te egekom word, bestudeer word. 'n Bondige oorsig van navorsing in die veld van meerdoelige optimering word gegee, gevolg deur 'n teoretiese bespreking van die kruis-entropiemetode. Die nuwe algoritme se ontwikkeling is hierop gebaseer, en dit word geassesseer deur kontinue, deterministiese probleme sowel as diskrete, stogastiese probleme benaderd daarmee op te los. Laasgenoemde sluit in 'n klassieke enkelitem voorraadprobleem, die bekende buffer-toedelingsprobleem, en 'n nuut-ontwerpte, laboratorium-skaal herkon gureerbare vervaardigingstelsel. Meerdoelige optimering van twee praktiese probleme is met die algoritme uitgevoer. In die eerste geval word sekere ontwerpparameters van 'n polimeer-uittrekeenheid met behulp van die algoritme beraam. Die bestuur van koolstofmonoksiedbenutting in 'n ilmeniet-smelter is kompleks met verskeie besluitnemingveranderlikes, en die toepassing van die algoritme in daardie omgewing word as 'n tweede geval aangebied. Verskeie gehalte-aanwyserwaardes word beraam vir vier-en-dertig toetsgevalle van meerdoelige optimeringsprobleme om die gehalte-prestasie van die algoritme te kwanti seer, en dit word ook vergelyk met 'n kommersi ele algoritme. Die algoritme is veronderstel om te skakel met dinamiese, stogastiese simulasiemodelle van regtew^ereldprobleme. Die algoritme sal tipies in 'n programmeertaal ge mplementeer word terwyl die simulasiemodel in doelmatige, kommersi ele programmatuur ontwikkel sal word. Die voorgestelde algoritme is maklik om te implementeer en dit het doeltre end gewerk op toetsprobleme.

PRICAI 2008: Trends in Artificial Intelligence 10th Pacific Rim International Conference on Artificial Intelligence, Hanoi, Vietnam, December 15-19, 2008. Proceedings

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 114-121). Also available on the Internet.