Método de Zimmermann-Werners aplicado na otimização de sistemas de microaspersão em terrenos com declive
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Data
2019-02-19
Autores
Castro, Evanize Rodrigues
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Universidade Estadual Paulista (Unesp)
Resumo
A otimização linear possibilita a obtenção de uma rede hidráulica de menor custo, dentre todas as alternativas viáveis de combinações de diâmetros e comprimentos. Um modelo apresentado na bibliografia minimiza o custo anual total de sistemas de microaspersão em áreas com desnível. Porém, a solução ótima deste modelo depende totalmente dos parâmetros de entrada, que podem conter uma certa imprecisão. A programação linear difusa é uma ferramenta que permite a incorporação dessas incertezas. Diante disso, o objetivo do trabalho é reformular o modelo de otimização de sistemas de microaspersão, possibilitando a aplicação de um método de otimização fuzzy nos coeficientes independentes imprecisos, para a determinar uma faixa de novas soluções de menores custos e que, também, atenda as restrições de área e hidráulica. Para isto, foram desenvolvidos dois capítulos e em ambos foram utilizados algoritmos criados no software MatLab para a resolução dos modelos. No primeiro capítulo é apresentado as alterações no modelo através de dois lemas que permitiram alcançar o propósito de determinar apenas as variáveis de decisão, sendo este modelo contendo cento e nove variáveis e duzentos e catorze restrições. E, para o mesmo conjunto de dados de aplicação do modelo original, esta modificação no modelo se mostrou eficaz e com custo total anual menor que o modelo original. Enquanto que no segundo capítulo, é exibido a aplicação dos método de Zimmermann-Werners no modelo modificado, obtendo sessenta modelos de programação linear fuzzy que encontram valores menores para a função objetivo do que o modelo original, sendo a maior diferença de custo de US$ 809,91 ocorrendo no desnível de 3%. Portanto, os sessenta e um modelos criados são eficientes no dimensionamento de sistemas de microaspersão, apresentam a redução de custo anual total e são uma ferramenta para o projetista e produtor.
The linear optimization makes possible the obtaining of a hydraulic network of smaller cost, between all the viable alternatives of combinations of diameters and lengths. A model presented in the bibliography minimizes the total annual cost of microirrigation systems in sloping lands. However, the great solution of this model is totally depends on the input parameters, that can contain a certain imprecision. The diffuse linear programming is a tool that allows the incorporation of those uncertainties. Before that, the objective of the work is to reformulate the model of optimization of microirrigation systems, making possible the application of a fuzzy optimization method in the imprecise independent coefficients, for to determine of a range of new solutions of smaller costs and that, also, assist the constraints of area and hydraulics. For this, two chapters were developed and in both algorithms were used created in the MatLab software for the resolution of the models. In the first chapter it is presented the alterations in the model through two lemmas that allowed to reach the purpose of just determining the variables of decision, being this model containing hundred nine variables and two hundred and fourteen constraints. In addition, for the same group of data of application of the original model, this modification model if it showed effective and with annual total cost smaller than the original model. While in the second chapter, the application of the Zimmermann-Werners method is exhibited in the modified model, obtaining sixty models of fuzzy linear programming that find smaller values for the function objective than the original model, being the largest difference of cost of US$ 809,91 happening in the slope of 3%. Therefore, the sixty and a models servants are efficient in the design of microirrigation systems, they present the reduction of total annual cost and they are a tool for the designer and producer.
The linear optimization makes possible the obtaining of a hydraulic network of smaller cost, between all the viable alternatives of combinations of diameters and lengths. A model presented in the bibliography minimizes the total annual cost of microirrigation systems in sloping lands. However, the great solution of this model is totally depends on the input parameters, that can contain a certain imprecision. The diffuse linear programming is a tool that allows the incorporation of those uncertainties. Before that, the objective of the work is to reformulate the model of optimization of microirrigation systems, making possible the application of a fuzzy optimization method in the imprecise independent coefficients, for to determine of a range of new solutions of smaller costs and that, also, assist the constraints of area and hydraulics. For this, two chapters were developed and in both algorithms were used created in the MatLab software for the resolution of the models. In the first chapter it is presented the alterations in the model through two lemmas that allowed to reach the purpose of just determining the variables of decision, being this model containing hundred nine variables and two hundred and fourteen constraints. In addition, for the same group of data of application of the original model, this modification model if it showed effective and with annual total cost smaller than the original model. While in the second chapter, the application of the Zimmermann-Werners method is exhibited in the modified model, obtaining sixty models of fuzzy linear programming that find smaller values for the function objective than the original model, being the largest difference of cost of US$ 809,91 happening in the slope of 3%. Therefore, the sixty and a models servants are efficient in the design of microirrigation systems, they present the reduction of total annual cost and they are a tool for the designer and producer.
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Modelo reestruturado, Variabilidade, Otimização linear fuzzy