Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones

Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to $1/2^{m-1}$, i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems

A Posteriori And Interactive Approaches For Decision-making With Multiple Stochastic Objectives

Computer simulation is a popular method that is often used as a decision support tool in industry to estimate the performance of systems too complex for analytical solutions. It is a tool that assists decision-makers to improve organizational performance and achieve performance objectives in which simulated conditions can be randomly varied so that critical situations can be investigated without real-world risk. Due to the stochastic nature of many of the input process variables in simulation models, the output from the simulation model experiments are random. Thus, experimental runs of computer simulations yield only estimates of the values of performance objectives, where these estimates are themselves random variables. Most real-world decisions involve the simultaneous optimization of multiple, and often conflicting, objectives. Researchers and practitioners use various approaches to solve these multiobjective problems. Many of the approaches that integrate the simulation models with stochastic multiple objective optimization algorithms have been proposed, many of which use the Pareto-based approaches that generate a finite set of compromise, or tradeoff, solutions. Nevertheless, identification of the most preferred solution can be a daunting task to the decisionmaker and is an order of magnitude harder in the presence of stochastic objectives. However, to the best of this researcher’s knowledge, there has been no focused efforts and existing work that attempts to reduce the number of tradeoff solutions while considering the stochastic nature of a set of objective functions. In this research, two approaches that consider multiple stochastic objectives when reducing the set of the tradeoff solutions are designed and proposed. The first proposed approach is an a posteriori approach, which uses a given set of Pareto optima as input. The second iv approach is an interactive-based approach that articulates decision-maker preferences during the optimization process. A detailed description of both approaches is given, and computational studies are conducted to evaluate the efficacy of the two approaches. The computational results show the promise of the proposed approaches, in that each approach effectively reduces the set of compromise solutions to a reasonably manageable size for the decision-maker. This is a significant step beyond current applications of decision-making process in the presence of multiple stochastic objectives and should serve as an effective approach to support decisionmaking under uncertaint

Facing-up Challenges of Multiobjective Clustering Based on Evolutionary Algorithms: Representations, Scalability and Retrieval Solutions

Aquesta tesi es centra en algorismes de clustering multiobjectiu, que estan basats en optimitzar varis objectius simultàniament obtenint una col•lecció de solucions potencials amb diferents compromisos entre objectius. El propòsit d'aquesta tesi consisteix en dissenyar i implementar un nou algorisme de clustering multiobjectiu basat en algorismes evolutius per afrontar tres reptes actuals relacionats amb aquest tipus de tècniques. El primer repte es centra en definir adequadament l'àrea de possibles solucions que s'explora per obtenir la millor solució i que depèn de la representació del coneixement. El segon repte consisteix en escalar el sistema dividint el conjunt de dades original en varis subconjunts per treballar amb menys dades en el procés de clustering. El tercer repte es basa en recuperar la solució més adequada tenint en compte la qualitat i la forma dels clusters a partir de la regió més interessant de la col•lecció de solucions ofertes per l’algorisme.Esta tesis se centra en los algoritmos de clustering multiobjetivo, que están basados en optimizar varios objetivos simultáneamente obteniendo una colección de soluciones potenciales con diferentes compromisos entre objetivos. El propósito de esta tesis consiste en diseñar e implementar un nuevo algoritmo de clustering multiobjetivo basado en algoritmos evolutivos para afrontar tres retos actuales relacionados con este tipo de técnicas. El primer reto se centra en definir adecuadamente el área de posibles soluciones explorada para obtener la mejor solución y que depende de la representación del conocimiento. El segundo reto consiste en escalar el sistema dividiendo el conjunto de datos original en varios subconjuntos para trabajar con menos datos en el proceso de clustering El tercer reto se basa en recuperar la solución más adecuada según la calidad y la forma de los clusters a partir de la región más interesante de la colección de soluciones ofrecidas por el algoritmo.This thesis is focused on multiobjective clustering algorithms, which are based on optimizing several objectives simultaneously obtaining a collection of potential solutions with different trade¬offs among objectives. The goal of the thesis is to design and implement a new multiobjective clustering technique based on evolutionary algorithms for facing up three current challenges related to these techniques. The first challenge is focused on successfully defining the area of possible solutions that is explored in order to find the best solution, and this depends on the knowledge representation. The second challenge tries to scale-up the system splitting the original data set into several data subsets in order to work with less data in the clustering process. The third challenge is addressed to the retrieval of the most suitable solution according to the quality and shape of the clusters from the most interesting region of the collection of solutions returned by the algorithm

A study of evolutionary multiobjective algorithms and their application to knapsack and nurse scheduling problems

Evolutionary algorithms (EAs) based on the concept of Pareto dominance seem the most suitable technique for multiobjective optimisation. In multiobjective optimisation, several criteria (usually conflicting) need to be taken into consideration simultaneously to assess a quality of a solution. Instead of finding a single solution, a set of trade-off or compromise solutions that represents a good approximation to the Pareto optimal set is often required. This thesis presents an investigation on evolutionary algorithms within the framework of multiobjective optimisation. This addresses a number of key issues in evolutionary multiobjective optimisation. Also, a new evolutionary multiobjective (EMO) algorithm is proposed. Firstly, this new EMO algorithm is applied to solve the multiple 0/1 knapsack problem (a wellknown benchmark multiobjective combinatorial optimisation problem) producing competitive results when compared to other state-of-the-art MOEAs. Secondly, this thesis also investigates the application of general EMO algorithms to solve real-world nurse scheduling problems. One of the challenges in solving real-world nurse scheduling problems is that these problems are highly constrained and specific-problem heuristics are normally required to handle these constraints. These heuristics have considerable influence on the search which could override the effect that general EMO algorithms could have in the solution process when applied to this type of problems. This thesis outlines a proposal for a general approach to model the nurse scheduling problems without the requirement of problem-specific heuristics so that general EMO algorithms could be applied. This would also help to assess the problems and the performance of general EMO algorithms more fairly

Um Modelo evolucionário de otimização multiobjetivo para exploração do espaço de projeto em sistemas embarcados

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2011O projeto de sistemas embarcados tem se tornado mais complexo à medida em que ocorrem avanços na tecnologia e nas aplicações, forçando novas abordagens e metodologias de projeto. Em praticamente todas as metodologias modernas a etapa de exploração do espaço de projeto tem merecido destaque, pois é a responsável por gerar e analisar diferentes possíveis soluções de projeto e selecionar a melhor. A exploração do espaço de projeto é, então, um problema de otimização multiobjetivo em que o conjunto de possíveis soluções costuma ser enorme, caso em que técnicas heurísticas como os algoritmos evolucionários têm recebido grande destaque. Nesta tese foram desenvolvidos metamodelos que representam o projeto de sistemas embarcados pela metodologia de sistemas dirigidos pela aplicação (ADESD) e seus componentes lógicos e físicos. Esses metamodelos foram mapeados a um novo modelo evolucionário com modificações de inspiração biológica que é utilizado para otimização multiobjetivo e, assim, para a exploração do espaço de projeto em sistemas embarcados. A exploração hierárquica, a representação e evolução tanto dos suportes de hardware físico quanto sintetizável, as modificações incluídas no modelo evolucionário e sua avaliação usando indicadores e conjuntos de teste consagrados correspondem às principais contribuições desta tese. Os resultados demonstram a viabilidade do modelo desenvolvido para exploração do espaço de projeto no contexto proposto e um aumento da qualidade das soluções encontradas em alguns problemas de teste, com consequente aumento do sobrecusto computaciona