Single-Objective Spreading Algorithm
This paper addresses the problem of finding several different solutions with the same optimum performance in single objective real-world engineering problems. In this paper a parallel robot design is proposed. Thereby, this paper presents a genetic algori
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Single-Objective Spreading Algorithm E.J. Solteiro Pires, Luı´s Mendes, Anto´nio M. Lopes, P.B. de Moura Oliveira, and J.A. Tenreiro Machado
Abstract This paper addresses the problem of finding several different solutions with the same optimum performance in single objective real-world engineering problems. In this paper a parallel robot design is proposed. Thereby, this paper presents a genetic algorithm to optimize uni-objective problems with an infinite number of optimal solutions. The algorithm uses the maximin concept and e-dominance to promote diversity over the admissible space. The performance of the proposed algorithm is analyzed with three well-known test functions and a function obtained from practical real-world engineering optimization problems. A spreading analysis is performed showing that the solutions drawn by the algorithm are well dispersed.
E.J. Solteiro Pires (*) • P.B. de Moura Oliveira INESC TEC - INESC Technology and Science (formerly INESC Porto), Escola de Cieˆncias e Tecnologia, Universidade de Tras-os-Montes e Alto Douro, Vila Real, Portugal e-mail: [email protected]; [email protected] L. Mendes Departamento de Engenharia Electrote´cnica, Escola Superior de Tecnologia e Gesta˜o, Instituto Polite´cnico de Leiria, Portugal Instituto de Telecomunicac¸o˜es, Lisboa, Portugal e-mail: [email protected] A.M. Lopes Instituto de Engenharia Mecaˆnica, Faculdade de Engenharia, da Universidade do Porto, Porto, Portugal e-mail: [email protected] J.A. Tenreiro Machado Grupo de Investigacao em Engenharia do Conhecimento e Apoio a` Decisa˜o, Departamento de Engenharia Electrote´cnica, Instituto Superior de Engenharia do Porto, Instituto Politecnico do Porto, Porto, Portugal e-mail: [email protected] A. Madureira et al. (eds.), Computational Intelligence and Decision Making: Trends and 131 Applications, Intelligent Systems, Control and Automation: Science and Engineering 61, DOI 10.1007/978-94-007-4722-7_13, # Springer Science+Business Media Dordrecht 2013
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E.J. Solteiro Pires et al.
Introduction
Some single-objective problems have several optimal solutions. A finite number of solutions can be found at different peaks of the objective function or an unlimited set of solutions exist along one or more regions in the parameter space. Therefore, achieving a well-spread and non-dominated parameter front is of paramount importance to the decision maker, since he can choose from a set of optimum solutions the one best suited to be developed or implemented in the problem context. Evolutionary algorithms use different approaches to promote the solutions diversity, such as the sharing model, crowding and maximin techniques. The sharing model, originally suggested by Goldberg and Richardson [7], is used to obtain a set of optimal solutions distributed by several optimal peaks. To promote solutions in less crowded regions of the parameter space and, therefore, to force the population to be well distributed, the sharing model degrades the fitness values of similar solutions according to the distance of their cl
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