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Multi-Objective Evolutionary Optimization of Biological Pest Control with Impulsive Dynamics in Soybean Crops

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Abstract

The biological pest control in agriculture, an environment-friendly practice, maintains the density of pests below an economic injury level by releasing a suitable quantity of their natural enemies. This work proposes a multi-objective numerical solution to biological pest control for soybean crops, considering both the cost of application of the control action and the cost of economic damages. The system model is nonlinear with impulsive control dynamics, in order to cope more effectively with the actual control action to be applied, which should be performed in a finite number of discrete time instants. The dynamic optimization problem is solved using the NSGA-II, a fast and trustworthy multi-objective genetic algorithm. The results suggest a dual pest control policy, in which the relative price of control action versus the associated additional harvest yield determines the usage of either a low control action strategy or a higher one.

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References

  • Bertsekas, D.P., 1995. Dynamic Programming and Optimal Control. Athena Scientific, Nashua.

    MATH  Google Scholar 

  • Bertsekas, D.P., 2005. Dynamic programming and suboptimal control: a survey from ADP to MPC. Eur. J. Control. 11(4–5), 310–334.

    Article  MathSciNet  Google Scholar 

  • Bor, Y.J., 2003. Uncertain control of dynamic economic threshold in pest management. Agric. Syst. 78, 105–118.

    Article  Google Scholar 

  • Burden, R.L., Faires, J.D., 2003. Numerical Analysis. Thomson, Belmont.

    Google Scholar 

  • Caltagirone, L.E., Doutt, R.L., 1989. The history of the vedalia beetle importation to California and its impact on the development of biological control. Ann. Rev. Entomol. 34, 01–16.

    Article  Google Scholar 

  • Cardoso, R.T.N., Takahashi, R.H.C., Fonseca, C.M., 2009. An open-loop invariant-set approach for multiobjective dynamic programming problems. In: Proceedings of the IFAC Workshop on Control Applications of Optimization, Jyvaskyla, Finland, May 2009. IFAC.

  • Dar’in, A.N., Kurzhanskii, A.B., Selesznev, A.V., 2005. The dynamic programming method in impulsive control synthesis. Ordinary Differ. Equ. 41(11), 1491–1500.

    Google Scholar 

  • Darwin, C.R., 1882. The Variation of Animals and Plants under Domestication. Murray, London.

    Google Scholar 

  • Deb, K., Agrawal, S., Pratab, A., Meyarivan, T., 2000. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the VI Conference in Parallel Problem Solving from Nature, Lecture Notes in Computer Science, vol. 1917, pp. 849–858. Springer, Berlin

    Chapter  Google Scholar 

  • DeBach, P., 1964. Biological Control of Insects Pests and Weeds. Van Nostrand-Rheinhold, New York.

    Google Scholar 

  • DeBach, P., 1991. Biological Control by Natural Enemies. Cambridge University Press, Cambridge.

    Google Scholar 

  • Feltrin, C.C., Rafikov, M., 2002. Aplicação da função de Lyapunov num problema de controle ótimo de pragas. Tend. Mat. Apl. Comput. 3(2), 83–92 (in portuguese).

    MathSciNet  Google Scholar 

  • Freeman, R., Primbs, J., 1996. Control Lyapunov functions: New ideas from and old sources. In: Proceedings of the 35th IEEE Conference on Decision and Control, pp. 3926–3931.

  • Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading.

    MATH  Google Scholar 

  • Griffiths, G.J.K., Holland, J.M., Bailey, A., Thomas, M.B., 2008. Efficacy and economics of shelter habitats for conservation biological control. Biol. Control 45(2), 200–209.

    Article  Google Scholar 

  • Holland, J.H., 1962a. Concerning efficient adaptive systems. In: Yovits, M.C., Jacobi, G.T., Goldstein, G.D. (Eds.), Self-Organizing Systems, pp. 215–230. Spartan Books, Washington

    Google Scholar 

  • Holland, J.H., 1962b. Outline for a logical theory of adaptive systems. J. Assoc. Comput. Mach. 9, 297–314.

    MATH  Google Scholar 

  • Holland, J.H., 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.

    Google Scholar 

  • Liu, B., Teng, Z., Chen, L., 2006. Analysis of a predator–prey model with Holling II functional response concerning impulsive control strategy. J. Comput. Appl. Math. 193(2), 347–362.

    Article  MATH  MathSciNet  Google Scholar 

  • Rafikov, M., Balthazar, J.M., 2005. Optimal pest control problem in population dynamics. Comput. Appl. Math. 24(1), 65–81.

    MathSciNet  Google Scholar 

  • Srinivas, N., Deb, K., 1994. Multi-objective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248.

    Article  Google Scholar 

  • Tang, S., Xiao, Y., Chen, L., Cheke, R., 2005. Integrated pest management models and their dynamical behavior. Bull. Math. Biol. 67, 115–135.

    Article  MathSciNet  Google Scholar 

  • Yang, T., 1999. Impulsive control. IEEE Trans. Automat. Contr. 44(5), 1081–1083.

    Article  MATH  Google Scholar 

  • Yang, T., 2001. Impulsive Control Theory. Springer, New York.

    MATH  Google Scholar 

  • Zhang, H., Jiao, J., Chen, L., 2007. Pest management through continuous and impulsive control strategies. BioSystems 90, 350–361.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Mathematics, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, Brazil

    Rodrigo T. N. Cardoso

  2. Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    André R. da Cruz & Ricardo H. C. Takahashi

  3. Department of Mathematics, Universidade Federal de Ouro Preto, Ouro Preto, Brazil

    Elizabeth F. Wanner

Authors
  1. Rodrigo T. N. Cardoso
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  2. André R. da Cruz
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  3. Elizabeth F. Wanner
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  4. Ricardo H. C. Takahashi
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Corresponding author

Correspondence to Ricardo H. C. Takahashi.

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Cardoso, R.T.N., da Cruz, A.R., Wanner, E.F. et al. Multi-Objective Evolutionary Optimization of Biological Pest Control with Impulsive Dynamics in Soybean Crops. Bull. Math. Biol. 71, 1463–1481 (2009). https://doi.org/10.1007/s11538-009-9409-7

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  • DOI: https://doi.org/10.1007/s11538-009-9409-7

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