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.

DNA microarrays are widely used techniques in molecular biology and DNA computing area. Before performing the microarray experiment, a set of subsequences of DNA called probes which are complementary to the target genes of interest must be found. And its reliability seriously depends on the quality of the probe sequences. Therefore, one must carefully choose the probe set in target sequences. A new method for probe design strategy using multi-objective genetic algorithm is proposed. The proposed algorithm is able to find a set of suitable probes more efficient and uses a model based on suffix tree to speed up the specificity constraint checking. The dry dock experimental results show that the proposed algorithm finds several probes for DNA microarray that not only obey the design properties, but also have specificity.

ABSTRACT PERFORMANCE MEASUREMENT IN MULTI OBJECTIVE COMBINATORIAL OPTIMIZATION Bozkurt, Bilge M.Sc., Department of Industrial Engineering Supervisor: Prof. Dr. Murat K&ouml / ksalan September 2007, 96 pages In this study we address the problem of measuring the quality of different sets of nondominated solutions obtained by different approaches in multi objective combinatorial optimization (MOCO). We propose a new measure that quantitatively compares the sets of nondominated solutions, without needing an efficient frontier. We develop the measure for bi-criteria and more than two criteria cases separately. Rather than considering only the supported solutions in the evaluation, the measure captures both supported and unsupported solutions through utilizing weighted Tchebycheff function characteristics. We also adapt this method for determining the neighborhood relations on the weight space for both bi-criteria and more than two criteria cases. We check the consistency of the neighborhood assumption on the objective space with the neighborhood relations on the weight space by this measure and obtain highly good results. Keywords: Multi objective combinatorial optimization, performance measurement

In this work we introduce PARETO, a multiobjective optimization tool that simultaneously optimizes beam angles and fluence patterns in intensity-modulated radiation therapy (IMRT) treatment planning using a powerful genetic algorithm. We also investigate various objective functions and compare several parameterizations for modeling beam fluence in terms of fluence map complexity, solution quality, and run efficiency. We have found that the combination of a conformity-based Planning Target Volume (PTV) objective function and a dose-volume histogram or equivalent uniform dose -based objective function for Organs-At-Risk (OARs) produced relatively uniform and conformal PTV doses, with well-spaced beams. For two patient data sets, the linear gradient and beam group fluence parameterizations produced superior solution quality using a moderate and high degree of modulation, respectively, and had comparable run times. PARETO promises to improve the accuracy and efficiency of treatment planning by fully automating the optimization and producing a database of non-dominated solutions for each patient.

Session ID: SA-G4-2 / Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, September 17-21, 2008, Nagoya University, Nagoya, Japan

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.

In this work we introduce PARETO, a multiobjective optimization tool that simultaneously optimizes beam angles and fluence patterns in intensity-modulated radiation therapy (IMRT) treatment planning using a powerful genetic algorithm. We also investigate various objective functions and compare several parameterizations for modeling beam fluence in terms of fluence map complexity, solution quality, and run efficiency. We have found that the combination of a conformity-based Planning Target Volume (PTV) objective function and a dose-volume histogram or equivalent uniform dose -based objective function for Organs-At-Risk (OARs) produced relatively uniform and conformal PTV doses, with well-spaced beams. For two patient data sets, the linear gradient and beam group fluence parameterizations produced superior solution quality using a moderate and high degree of modulation, respectively, and had comparable run times. PARETO promises to improve the accuracy and efficiency of treatment planning by fully automating the optimization and producing a database of non-dominated solutions for each patient.

Muchas de las nuevas aplicaciones emergentes de Internet tales como TV sobre Internet, Radio sobre Internet,Video Streamming multi-punto, entre otras, necesitan los siguientes requerimientos de recursos: ancho de banda consumido, retardo extremo-a-extremo, tasa de paquetes perdidos, etc. Por lo anterior, es necesario formular una propuesta que especifique y provea para este tipo de aplicaciones los recursos necesarios para su buen funcionamiento.En esta tesis, proponemos un esquema de ingeniería de tráfico multi-objetivo a través del uso de diferentes árboles de distribución para muchos flujos multicast. En este caso, estamos usando la aproximación de múltiples caminos para cada nodo egreso y de esta forma obtener la aproximación de múltiples árboles y a través de esta forma crear diferentes árboles multicast. Sin embargo, nuestra propuesta resuelve la fracción de la división del tráfico a través de múltiples árboles. La propuesta puede ser aplicada en redes MPLS estableciendo rutas explícitas en eventos multicast.En primera instancia, el objetivo es combinar los siguientes objetivos ponderados dentro de una métrica agregada: máxima utilización de los enlaces, cantidad de saltos, el ancho de banda total consumido y el retardo total extremo-a-extremo. Nosotros hemos formulado esta función multi-objetivo (modelo MHDB-S) y los resultados obtenidos muestran que varios objetivos ponderados son reducidos y la máxima utilización de los enlaces es minimizada.El problema es NP-duro, por lo tanto, un algoritmo es propuesto para optimizar los diferentes objetivos. El comportamiento que obtuvimos usando este algoritmo es similar al que obtuvimos con el modelo.Normalmente, durante la transmisión multicast los nodos egresos pueden salir o entrar del árbol y por esta razón en esta tesis proponemos un esquema de ingeniería de tráfico multi-objetivo usando diferentes árboles para grupos multicast dinámicos. (en el cual los nodos egresos pueden cambiar durante el tiempo de vida de la conexión). Si un árbol multicast es recomputado desde el principio, esto podría consumir un tiempo considerable de CPU y además todas las comuicaciones que están usando el árbol multicast serán temporalmente interrumpida. Para aliviar estos inconvenientes, proponemos un modelo de optimización (modelo dinámico MHDB-D) que utilice los árboles multicast previamente computados (modelo estático MHDB-S) adicionando nuevos nodos egreso.Usando el método de la suma ponderada para resolver el modelo analítico, no necesariamente es correcto, porque es posible tener un espacio de solución no convexo y por esta razón algunas soluciones pueden no ser encontradas. Adicionalmente, otros tipos de objetivos fueron encontrados en diferentes trabajos de investigación. Por las razones mencionadas anteriormente, un nuevo modelo llamado GMM es propuesto y para dar solución a este problema un nuevo algoritmo usando Algoritmos Evolutivos Multi-Objetivos es propuesto. Este algoritmo esta inspirado por el algoritmo Strength Pareto Evolutionary Algorithm (SPEA).Para dar una solución al caso dinámico con este modelo generalizado, nosotros hemos propuesto un nuevo modelo dinámico y una solución computacional usando Breadth First Search (BFS) probabilístico.Finalmente, para evaluar nuestro esquema de optimización propuesto, ejecutamos diferentes pruebas y simulaciones.Las principales contribuciones de esta tesis son la taxonomía, los modelos de optimización multi-objetivo para los casos estático y dinámico en transmisiones multicast (MHDB-S y MHDB-D), los algoritmos para dar solución computacional a los modelos. Finalmente, los modelos generalizados también para los casos estático y dinámico (GMM y GMM Dinámico) y las propuestas computacionales para dar slución usando MOEA y BFS probabilístico. / Many new multicast applications emerging from the Internet, such as TV over the Internet, Radio over the Internet, Video Streaming multi-point, etc., need the following resource requirements: bandwidth consumption, end-to-end delay, packet loss ratio, etc. It is therefore necessary to formulate a proposal to specify and provide for these kinds of applications the resources necessary for them to function well. In this thesis, we propose a multi-objective traffic engineering scheme using different distribution trees to multicast several flows. In this case, we are using the multipath approach to every egress node to obtain the multitree approach and of this way to create several multicast tree. Moreover, our proposal solves the traffic split ratio for multiple trees. The proposed approach can be applied in Multiprotocol Label Switching (MPLS) networks by allowing explicit routes in multicast events to be established.In the first instance, the aim is to combine the following weighting objectives into a single aggregated metric: the maximum link utilization, the hop count, the total bandwidth consumption, and the total end-to-end delay. We have formulated this multi-objective function (MHDB-S model) and the results obtained using a solver show that several weighting objectives are decreased and the maximum link utilization is minimized. The problem is NP-hard, therefore, an algorithm is proposed for optimizing the different objectives. The behavior we get using this algorithm is similar to what we get with the solver. Normally, during multicast transmission the egress node can leave and enter of the tree and for this reason in this thesis we propose a multi-objective traffic engineering scheme using different distribution trees for dynamic multicast groups (i.e. in which egress nodes can change during the connection's lifetime). If a multicast tree is recomputed from scratch, it may consume a considerable amount of CPU time and all communication using the multicast tree will be temporarily interrupted. To alleviate these drawbacks we propose an optimization model (dynamic model MHDB-D) that uses a previously computed multicast tree (static model MHDB-S) adding new egress nodes.Using the weighted sum method to solve the analytical model is not necessarily correct, because is possible to have a non-convex space solution and some solutions cannot be found. In addition, other kinds of objectives were found in different research works. For the above reasons, a new model called GMM is proposed and to find a solution to this problem a new algorithm using a Multi-Objective Evolutionary Algorithm (MOEA) is proposed too. This algorithm is inspired by the Strength Pareto Evolutionary Algorithm (SPEA). To give a solution to the dynamic case with this generalized model a dynamic GMM model is proposed and a computational solution using Breadth First Search (BFS) probabilistic is also proposed to give a solution to the dynamic case in multicast.Finally, in order to evaluate our proposed optimization scheme, we performed the necessary simulations and tests. The main contributions of this thesis are the taxonomy, the optimization model and the formulation of the multi-objective function in static and dynamic multicast transmission (MHDB-S and MHDB-D), as well as the different algorithms proposed to give computational solutions to this problem. Finally, the generalized model with several functions found in different research works in static and dynamic multicast transmission (GMM and Dynamic GMM), as well as the different algorithms proposed to give computational solutions using MOEA and BFS probabilistic.

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.

Esta Tese apresenta um framework para análise exploratória de dados via técnicas de agrupamento. O objetivo é facilitar o trabalho dos especialistas no domínio dos dados. O ponto central do framework é um algoritmo de ensemble multi-objetivo, o algoritmo MOCLE, complementado por um método para a visualização integrada de um conjunto de partições. Pela aplicação conjunta das idéias de ensemble de agrupamentos e agrupamento multi-objetivo, o MOCLE efetua atomaticamente importantes passos da análise de agrupamento: executa vários algoritmos conceitualmente diferentes com várias configurações de parâmetros, combina as partições resultantes desses algoritmos e seleciona as partições com os melhores compromissos de diferentes medidas de validação. MOCLE é uma abordagem robusta para lidar com diferentes tipos de estrutura que podem estar presentes em um conjunto de dados. Ele resulta em um conjunto conciso e estável de estruturas alternativas de alta qualidade, sem a necessidade de conhecimento prévio sobre os dados e nem conhecimento profundo em análise de agrupamento. Além disso, para facilitar a descoberta de estruturas mais complexas, o MOCLE permite a integração automática de conhecimento prévio de uma estrutura simples por meio das suas funções objetivo. Finalmente, o método de visualização proposto permite a observação simultânea de um conjunto de partições. Isso ajuda na análise dos resultados do MOCLE. / This Thesis presents a framework for exploratory data analysis via clustering techniques. The goal is to facilitate the work of the experts in the data domain. The core of the framework is a multi-objective clustering ensemble algorithm, the MOCLE algorithm, complemented by a method for integrated visualization of a set of partitions. By applying together the ideas of clustering ensemble and multi-objective clustering, MOCLE automatically performs important steps of cluster analysis: run several conceptually different clustering algorithms with various parameter configuration, combine the partitions resulting from these algorithms, and select the partitions with the best trade-offs for different validation measures. MOCLE is a robust approach to deal with different types of structures that can be present in a dataset. It results in a concise and stable set of high quality alternative structures, without the need of previous knowledge about the data or deep knowledge on cluster analysis. Furthermore, in order to facilitate the discovery of more complex structures, MOCLE allows the automatic integration of previous knowledge of a simple structure via their objective functions. Finally, the visualization method proposed allows the simultaneous observation of a set of partitions. This helps in the analysis of MOCLE results.