@PhDThesis{Soterroni:2012:MéQgOt,
               author = "Soterroni, Aline Cristina",
                title = "O m{\'e}todo do q-gradiente para otimiza{\c{c}}{\~a}o global",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
                 year = "2012",
              address = "S{\~a}o Jos{\'e} dos Campos",
                month = "2012-08-28",
             keywords = "q-derivada, q-gradiente, m{\'e}todo do q-gradiente, q-derivative, 
                         q-gradient, q-gradient method.",
             abstract = "O reverendo ingl{\^e}s Frank Hilton Jackson foi o primeiro a 
                         desenvolver o \textit{q}-c{\'a}lculo de forma sistem{\'a}tica 
                         e, no in{\'{\i}}cio do s{\'e}culo XX, reintroduziu a 
                         \textit{q}-derivada, que ficou amplamente conhecida como derivada 
                         de Jackson. O \textit{q}-c{\'a}lculo, por sua vez, surgiu da 
                         generaliza{\c{c}}{\~a}o de express{\~o}es matem{\'a}ticas por 
                         meio de um par{\^a}metro \textit{q}, dando origem a 
                         \textit{q}-vers{\~o}es de fun{\c{c}}{\~o}es, s{\'e}ries, 
                         operadores e n{\'u}meros especiais que, no limite \textit{q} 
                         \$\longrightarrow\$ 1, retomam suas respectivas vers{\~o}es 
                         cl{\'a}ssicas. Este trabalho introduz o conceito de vetor 
                         \textit{q}-gradiente na {\'a}rea de otimiza{\c{c}}{\~a}o por 
                         meio do m{\'e}todo do \textit{q}-gradiente, uma 
                         generaliza{\c{c}}{\~a}o do m{\'e}todo da m{\'a}xima descida 
                         que utiliza a dire{\c{c}}{\~a}o contr{\'a}ria {\`a} 
                         dire{\c{c}}{\~a}o do vetor \textit{q}-gradiente como 
                         dire{\c{c}}{\~a}o de busca. O uso dessa dire{\c{c}}{\~a}o de 
                         busca, juntamente com estrat{\'e}gias apropriadas para a 
                         obten{\c{c}}{\~a}o do par{\^a}metro \textit{q} e do tamanho do 
                         passo, mostrou que o m{\'e}todo do \textit{q}-gradiente realiza, 
                         ao longo do procedimento de otimiza{\c{c}}{\~a}o, uma 
                         transi{\c{c}}{\~a}o suave entre busca global e busca local, 
                         al{\'e}m de possuir mecanismos para escapar de m{\'{\i}}nimos 
                         locais. O m{\'e}todo do \textit{q}-gradiente foi comparado com 
                         algoritmos determin{\'{\i}}sticos e extensivamente comparado com 
                         os Algoritmos Evolutivos (AEs) , que participaram da 
                         competi{\c{c}}{\~a}o do \textit{IEEE Congress on Evolutionary 
                         Computation} (CEC) em 2005, sobre um conjunto de 
                         fun{\c{c}}{\~o}es teste da literatura. Os resultados mostraram 
                         que o m{\'e}todo do \textit{q}-gradiente {\'e} competitivo em 
                         rela{\c{c}}{\~a}o aos AEs, sobretudo nos problemas multimodais. 
                         O m{\'e}todo do \textit{q}-gradiente tamb{\'e}m foi aplicado na 
                         resolu{\c{c}}{\~a}o de um problema da engenharia aeroespacial e 
                         os resultados apontaram para a viabilidade do seu uso em 
                         aplica{\c{c}}{\~o}es pr{\'a}ticas. ABSTRACT: The English 
                         reverend Frank Hilton Jackson was the first to develop the 
                         \textit{q}-calculus in a systematic way, and in the beginning of 
                         the twentieth century he reintroduced the \textit{q}-derivative, 
                         widely known as Jackson´s derivative. The \textit{q}-calculus, by 
                         its turn, carne from generalizations of mathematical expressions 
                         called \textit{q}-versions of functions, series, operators and 
                         special numbers that take into account a parameter \textit{q}. In 
                         the limiting case of \textit{q} \$\longrightarrow\$ 1, the 
                         \textit{q}-versions reduce to its classical versions. In this 
                         work the concept of \textit{q}-gradient is introduced in the 
                         optimization area by the \textit{q}-gradient method, a 
                         generalization of the steepest descent method that uses the 
                         negative of the \textit{q}-gradient as the search direction. The 
                         optimization procedure, with this direc-tion and properly defined 
                         strategies for the parameter \textit{q} and the step length, has 
                         shown that the search process gradually shifts from global in the 
                         beginning to local in the end with an effective mechanism for 
                         escaping from local minima. The \textit{q}-gradiente method was 
                         compared with some deterministic methods and extensively compared 
                         with Evolutionary Algorithms (EAs) of the 2005 IEEE Congress on 
                         Evalutionary Computation (CEC) over benchmark test functions. The 
                         results presented here have shown the competitiveness of the 
                         \textit{q}-gradient over the EAs specially for the multimodal 
                         problems. The \textit{q}-gradient method was also applied to an 
                         optimization problem from aerospace engineering and the results 
                         indicated the viability of the method for solving practical 
                         problems.",
            committee = "Becceneri, Jos{\'e} Carlos (presidente) and Ramos, Fernando 
                         Manuel (orientador) and Galski, Roberto Luiz (orientador) and 
                         Stephany, Stephan and Zuben, Fernando Jos{\'e} Von and de Salles 
                         Neto, Luiz Ledu{\'{\i}}no",
           copyholder = "SID/SCD",
         englishtitle = "The q-gradient method for global optimization",
             language = "pt",
                pages = "148",
                  ibi = "8JMKD3MGP7W/3CDHUH8",
                  url = "http://urlib.net/ibi/8JMKD3MGP7W/3CDHUH8",
           targetfile = "publicacao.pdf",
        urlaccessdate = "27 abr. 2024"
}