Métodos híbridos de pontos interiores e de programação inteira 0-1 para problemas de custo de colheita da cana-de-açúcar e de custo de coleta e geração de energia relacionados à sua biomassa
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Data
2013-07-31
Autores
Lima, Camila de [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
O objetivo desse trabalho foi desenvolver métodos híbridos envolvendo os métodos de pontos interiores e de programação inteira binária para a resolução de problemas mono e multiobjetivo referentes à colheita da cana-de-açúcar, coleta de sua biomassa residual e ao balanço de energia relativo ao aproveitamento desses resíduos. Assim, foram investigados os métodos previsor-corretor primal-dual de pontos interiores e aqueles inseridos em programação inteira: branch-and-bound, planos de corte e branch-and-cut. São apresentados dois métodos híbridos envolvendo o método previsor-corretor primal-dual de pontos interiores, um deles associado ao método branch-and-bound (PDBB), o qual foi investigado, mas não foi implementado e testado nesse trabalho. O método PDBB foi utilizado para a resolução dos modelos matemáticos referentes à minimização do custo de colheita da cana-de-açúcar, minimização de custo e transporte de coleta da biomassa residual da cana-de-açúcar, e maximização do balanço de energia referente a esses resíduos, que consideram áreas de plantio mecanizáveis e semi-mecanizáveis. Além desses, foram explorados, os modelos multiobjetivo de minimização de custo de coleta e transporte e maximização do balanço de energia total. As estratégias utilizadas para a determinação de soluções eficientes dos modelos multiobjetivo relacionaram-se aos métodos da soma ponderada e e-restrito, as quais transformaram o problema multiobjetivo em uma sequência de problemas mono-objetivo. Os resultados obtidos demosntraram que o método híbrido é robusto à resolução desses problemas pois obteve um bom desempenho computacional, determinou as soluções ótimas para os problemas mono-objetivo, as soluções eficientes e a curva de Pareto associadas ao problema multiobjetivo
The aim of this study was to develop hybrid methods involving interior point and binary integer programming methods for solving mono and multiobjective problems related to the sugar cane harvest, the collection of their waste and energy balance related to the urilization of these waste. Thus, the predictor-corrector primal dual interior point method, and those inserted in integer programming: branch-and-bound, cutting planes and branch-and-cut were investigated. We present two hybrid methods involving the predictor-corrector primal-dual interior point method, one is associated to the brach-and-bound method (PDBB), which was developed in this study and implemented in the programming language C++, and another related to the branch-and-cut method (PDBC), which was investigated but was not implemented and tested in this study. The PDBB method was used to resolution of the mathematical models related to minimize the costs of sugar cane harvest, to minimize the collection and transportation cost of residual biomass from sugar cane, and to maximize the energy balance regarding these residues, which consider mechanized and semi-mechanized grow areas. Besides, multiobjective models were explored, such as the minimization of the collection and transportation cost and maximization of the energy balance of the residual biomass, and the total cost minimization and total energy balance maximization. The strategies used for determining efficient solutions of the multiobjective models were the weighted sum and e-constraint methods, which transformed the multiobjective problem into a sequence of mono-objective problems. The obtained results showed that the hybrid method is robust to solve these problems, it got a good computational performance, determined optimal solutions to the mono-objective problems, and the efficient solutions and the Pareto 's frontier associated to multiobjective problem
The aim of this study was to develop hybrid methods involving interior point and binary integer programming methods for solving mono and multiobjective problems related to the sugar cane harvest, the collection of their waste and energy balance related to the urilization of these waste. Thus, the predictor-corrector primal dual interior point method, and those inserted in integer programming: branch-and-bound, cutting planes and branch-and-cut were investigated. We present two hybrid methods involving the predictor-corrector primal-dual interior point method, one is associated to the brach-and-bound method (PDBB), which was developed in this study and implemented in the programming language C++, and another related to the branch-and-cut method (PDBC), which was investigated but was not implemented and tested in this study. The PDBB method was used to resolution of the mathematical models related to minimize the costs of sugar cane harvest, to minimize the collection and transportation cost of residual biomass from sugar cane, and to maximize the energy balance regarding these residues, which consider mechanized and semi-mechanized grow areas. Besides, multiobjective models were explored, such as the minimization of the collection and transportation cost and maximization of the energy balance of the residual biomass, and the total cost minimization and total energy balance maximization. The strategies used for determining efficient solutions of the multiobjective models were the weighted sum and e-constraint methods, which transformed the multiobjective problem into a sequence of mono-objective problems. The obtained results showed that the hybrid method is robust to solve these problems, it got a good computational performance, determined optimal solutions to the mono-objective problems, and the efficient solutions and the Pareto 's frontier associated to multiobjective problem
Descrição
Palavras-chave
Cana-de-açúcar - Colheita, Biomassa, Biomassa vegetal, Custo, Sugar-cane - Harvesting
Como citar
LIMA, Camila de. Métodos híbridos de pontos interiores e de programação inteira 0-1 para problemas de custo de colheita da cana-de-açúcar e de custo de coleta e geração de energia relacionados à sua biomassa. 2013. 121 f. Dissertação (metrado) - Universidade Estadual Paulista Júlio de Mesquita Filho, Faculdade de Engenharia, 2013.