Modelo de otimização para o controle de plantas daninhas usando programação não linear inteira mista

Abstract

Agradecimentos Primeiramente a Deus, por estar presente em todos os momentos da minha vida, por guiar os meus caminhos e me conceder sabedoria e saúde. A minha família, em especial a minha mãe Neiva Weber, pelo amor, carinho e apoio incondicional. Ao meu avô (in memoriam), Eugem Albino Weber, que tanto fez por mim. A Profa. Dra. Vilma Alves de Oliveira, ao Prof. Dr. Geraldo Nunes Silva e ao Dr. Décio Karam, pela atenção, compreensão e ensinamentos. Ao meu namorado, Renan Corrêa, que sempre esteve ao meu lado, me apoiando em todos os momentos. A todos os meus amigos e colegas do LAC, pela companhia e amizade ao longo destes anos. Ao Marcos Furlan e ao Pedro Munari, pela atenção e ajuda na realização deste trabalho.

An Optimal Control Framework for Resources Management in Agriculture

“…The approach to the multiple herbicide problem consists in, first, reformulating as a Mixed Integer Nonlinear Programming (MINLP) problem, and, after the elimination of control constraints via a quadratic penalization method, in solving it by the Branch and Bound Method and an Active Set Algorithm (check [10] for details). At each stage of the branch and bound method, an NLP relaxed subproblem is solved.…”

“…where is the control variable, and is given by Remark that this is one of the simplest models incorporating resistance: single herbicide, no biological control, and temporal and spatially homogeneous dynamics. The equilibrium analysis in [10] reveals that this dynamic system has 3 points of equilibrium, one unstable and two stable.…”

“…In [10,11], a dynamic optimization problem is formulated to determine the optimal-in the sense of maximizing the crop economic return over a number of production cycles while minimizing environmental impacts-application of two herbicides to control the infestation of the weed Bidens Subalternans in a corn crop, by taking into account the resistance effect that develops over time. Since integer and continuous variables are present, the problem is cast in the framework of mixed-integer nonlinear programming (MINLP) and solved with a branch and bound method.…”

“…This paper reports the recent collaborative research effort between University of S. Paulo (USP) and University of Porto (UP). It draws heavily from the research work that has been taking place at UNESP and USP [9][10][11], with a significant collaboration with EMBRAPA, on optimizing the usage of multiple agrochemicals to control the proliferation of weeds (whose growth models exhibit resistance) to maximize the yield of crops. This experience, coupled with some optimal control theory developments, notably in optimal feedback control, infinite horizon optimal control, and Model Predictive Control [9,[12][13][14][15][16], at FEUP and UNESP, constitutes the basis for the optimal control framework proposed here.…”

“…Given the vast amount of literature, we are forced to address a small sample of research work selected for its pertinence to the framework proposed in this paper so that the general key contributions are spanned. In ensuing Section 3, a control problem addressed by USP and UNESP [10,11] for minimizing the use of agrochemicals in containing weeds while considering the phenomenon of resistance is considered. Here, the benefits of optimization are clear for both the economic and the environment perspectives, in spite of the fact that no specific ingredients were considered for the later.…”