Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.22/7589
Título: Adaptive Penalty and Barrier function based on Fuzzy Logic
Autor: Matias, João
Correia, Aldina
Mestre, Pedro
Serodio, Carlos
Couto, Pedro
Teixeira, Christophe
Melo-Pinto, Pedro
Palavras-chave: Applications
Fuzzy mathematical programming
Mathematics
Derivative free optimization
Direct search methods
Penalty and Barrier functions
Fuzzy Logic
Data: 2015
Editora: Elsevier
Resumo: Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.
URI: http://hdl.handle.net/10400.22/7589
DOI: 10.1016/j.eswa.2015.04.070
Versão do Editor: http://www.sciencedirect.com/science/article/pii/S0957417415003127
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