Bulletin of Mathematical Biology (2009) 71: 1463–1481 DOI 10.1007/s11538-009-9409-7 ORIGINAL ARTICLE Multi-Objective Evolutionary Optimization of Biological Pest Control with Impulsive Dynamics in Soybean Crops Rodrigo T.N. Cardoso a , André R. da Cruz b , Elizabeth F. Wanner c , Ricardo H.C. Takahashi b,∗ a Department of Physics and Mathematics, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, Brazil b Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil c Department of Mathematics, Universidade Federal de Ouro Preto, Ouro Preto, Brazil Received: 7 August 2007 / Accepted: 10 February 2009 / Published online: 7 March 2009 © Society for Mathematical Biology 2009 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 solu- tion 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 con- trol 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 trust- worthy 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. Keywords Biological control · Predator-prey · Impulsive control · Multiobjective optimization · Genetic algorithms · Soy farming · Dynamic optimization 1. Introduction Biological control is the reduction of pest populations with the addition of other living organisms like parasitoids, predators and pathogens, often called natural enemies or ben- eficial species (DeBach, 1964, 1991; Caltagirone and Doutt, 1989; Rafikov and Balthazar, 2005). Another approach, employed nowadays by most of the commercial agriculture, is the chemical control of pests, using pesticides. There is another view (Tang et al., 2005; Liu et al., 2006) that defends the hybrid control (integrating the biological control with ∗ Corresponding author. E-mail addresses: rodrigoc@des.cefetmg.br (Rodrigo T.N. Cardoso), andrerc@dcc.ufmg.br (André R. da Cruz), efwanner@iceb.ufop.br (Elizabeth F. Wanner), taka@mat.ufmg.br (Ricardo H.C. Takahashi).