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Computational and Applied Mathematics

, Volume 36, Issue 2, pp 1043–1065 | Cite as

Optimal weed population control using nonlinear programming

  • Elenice W. Stiegelmeier
  • Vilma A. Oliveira
  • Geraldo N. Silva
  • Décio Karam
Article

Abstract

A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive alleles are taken as state variables of the growing cycle. The control variable is taken as the dose–response function. The goal is to reduce herbicide usage, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The dynamic optimization model takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by selective pressure. The dynamic optimization problem involves discrete variables modeled as a nonlinear programming (NLP) problem which was solved by an active set algorithm (ASA) for box-constrained optimization. Numerical simulations for a case study illustrate the management of the Bidens subalternans in a corn crop by selecting a sequence of only one type of herbicide. The results on optimal control discussed here will give support to make decision on the herbicide usage in regions where weed resistance was reported by field observations.

Keywords

Mathematical modeling Population dynamics Nonlinear programming Weed management 

Mathematics Subject Classification

90C30 Nonlinear programming 

Notes

Acknowledgments

The authors acknowledge the support given by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under the Programa Nacional de Cooperação Acadêmica (PROCAD).

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  • Elenice W. Stiegelmeier
    • 1
  • Vilma A. Oliveira
    • 2
  • Geraldo N. Silva
    • 3
  • Décio Karam
    • 4
  1. 1.Department of MathematicsUniversidade Tecnológica Federal do ParanáCornélio ProcópioBrazil
  2. 2.Department of Electrical and Computer EngineeringUniversidade de São PauloSão CarlosBrazil
  3. 3.Department of Applied MathematicsUniversidade Estadual PaulistaSão José do Rio PretoBrazil
  4. 4.Empresa Brasileira de Pesquisa AgropecuáriaSete LagoasBrazil

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