859 resultados para Multi-objective optimization problem


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In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

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This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

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Most of water distribution systems (WDS) need rehabilitation due to aging infrastructure leading to decreasing capacity, increasing leakage and consequently low performance of the WDS. However an appropriate strategy including location and time of pipeline rehabilitation in a WDS with respect to a limited budget is the main challenge which has been addressed frequently by researchers and practitioners. On the other hand, selection of appropriate rehabilitation technique and material types is another main issue which has yet to address properly. The latter can affect the environmental impacts of a rehabilitation strategy meeting the challenges of global warming mitigation and consequent climate change. This paper presents a multi-objective optimization model for rehabilitation strategy in WDS addressing the abovementioned criteria mainly focused on greenhouse gas (GHG) emissions either directly from fossil fuel and electricity or indirectly from embodied energy of materials. Thus, the objective functions are to minimise: (1) the total cost of rehabilitation including capital and operational costs; (2) the leakage amount; (3) GHG emissions. The Pareto optimal front containing optimal solutions is determined using Non-dominated Sorting Genetic Algorithm NSGA-II. Decision variables in this optimisation problem are classified into a number of groups as: (1) percentage proportion of each rehabilitation technique each year; (2) material types of new pipeline for rehabilitation each year. Rehabilitation techniques used here includes replacement, rehabilitation and lining, cleaning, pipe duplication. The developed model is demonstrated through its application to a Mahalat WDS located in central part of Iran. The rehabilitation strategy is analysed for a 40 year planning horizon. A number of conventional techniques for selecting pipes for rehabilitation are analysed in this study. The results show that the optimal rehabilitation strategy considering GHG emissions is able to successfully save the total expenses, efficiently decrease the leakage amount from the WDS whilst meeting environmental criteria.

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Committees of classifiers may be used to improve the accuracy of classification systems, in other words, different classifiers used to solve the same problem can be combined for creating a system of greater accuracy, called committees of classifiers. To that this to succeed is necessary that the classifiers make mistakes on different objects of the problem so that the errors of a classifier are ignored by the others correct classifiers when applying the method of combination of the committee. The characteristic of classifiers of err on different objects is called diversity. However, most measures of diversity could not describe this importance. Recently, were proposed two measures of the diversity (good and bad diversity) with the aim of helping to generate more accurate committees. This paper performs an experimental analysis of these measures applied directly on the building of the committees of classifiers. The method of construction adopted is modeled as a search problem by the set of characteristics of the databases of the problem and the best set of committee members in order to find the committee of classifiers to produce the most accurate classification. This problem is solved by metaheuristic optimization techniques, in their mono and multi-objective versions. Analyzes are performed to verify if use or add the measures of good diversity and bad diversity in the optimization objectives creates more accurate committees. Thus, the contribution of this study is to determine whether the measures of good diversity and bad diversity can be used in mono-objective and multi-objective optimization techniques as optimization objectives for building committees of classifiers more accurate than those built by the same process, but using only the accuracy classification as objective of optimization

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Problems as voltage increase at the end of a feeder, demand supply unbalance in a fault condition, power quality decline, increase of power losses, and reduction of reliability levels may occur if Distributed Generators (DGs) are not properly allocated. For this reason, researchers have been employed several solution techniques to solve the problem of optimal allocation of DGs. This work is focused on the ancillary service of reactive power support provided by DGs. The main objective is to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). The LOC will be determined for different allocation alternatives of DGs as a result of a multi-objective optimization process, aiming the minimization of losses in the lines of the system and costs of active power generation from DGs, and the maximization of the static voltage stability margin of the system. The effectiveness of the proposed methodology in improving the goals outlined was demonstrated using the IEEE 34 bus distribution test feeder with two DGs cosidered to be allocated. © 2011 IEEE.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Este trabalho apresenta um método para encontrar um conjunto de pontos de operação, os quais são ótimos de Pareto com diversidade, para linhas digitais de assinante (DSL - digital subscriber line). Em diversos trabalhos encontrados na literatura, têm sido propostos algoritmos para otimização da transmissão de dados em linhas DSL, que fornecem como resultado apenas um ponto de operação para os modems. Esses trabalhos utilizam, em geral, algoritmos de balanceamento de espectro para resolver um problema de alocação de potência, o que difere da abordagem apresentada neste trabalho. O método proposto, chamado de diverseSB , utiliza um processo híbrido composto de um algoritmo evolucionário multiobjetivo (MOEA - multi-objective evolutionary algorithm), mais precisamente, um algoritmo genético com ordenamento por não-dominância (NSGA-II - Non-Dominated Sorting Genetic Algorithm II), e usando ainda, um algoritmo de balanceamento de espectro. Os resultados obtidos por simulações mostram que, para uma dada diversidade, o custo computacional para determinar os pontos de operação com diversidade usando o algoritmo diverseSB proposto é muito menor que métodos de busca de “força bruta”. No método proposto, o NSGA-II executa chamadas ao algoritmo de balanceamento de espectro adotado, por isso, diversos testes envolvendo o mesmo número de chamadas ao algoritmo foram realizadas com o método diverseSB proposto e o método de busca por força bruta, onde os resultados obtidos pelo método diverseSB proposto foram bem superiores do que os resultados do método de busca por força bruta. Por exemplo, o método de força bruta realizando 1600 chamadas ao algoritmo de balanceamento de espectro, obtém um conjunto de pontos de operação com diversidade semelhante ao do método diverseSB proposto com 535 chamadas.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Engenharia Elétrica - FEB

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Many combinatorial problems coming from the real world may not have a clear and well defined structure, typically being dirtied by side constraints, or being composed of two or more sub-problems, usually not disjoint. Such problems are not suitable to be solved with pure approaches based on a single programming paradigm, because a paradigm that can effectively face a problem characteristic may behave inefficiently when facing other characteristics. In these cases, modelling the problem using different programming techniques, trying to ”take the best” from each technique, can produce solvers that largely dominate pure approaches. We demonstrate the effectiveness of hybridization and we discuss about different hybridization techniques by analyzing two classes of problems with particular structures, exploiting Constraint Programming and Integer Linear Programming solving tools and Algorithm Portfolios and Logic Based Benders Decomposition as integration and hybridization frameworks.