A multiobjective non-linear dynamic programming approach for optimal biological control in soy farming via NSGA-II

The biological control of plagues in agriculture, a practice that has been growing around the world, is performed by leaving a suitable quantity of natural enemies of the plague in the farm during the finite time horizon of the farming cycle. This work proposes a multi-objective mathematical solution for the problem of optimal biological plague control for soy farmings, considering the control cost and the cost of farming damage due to plague. The system model is non-linear with impulsive control dynamics, in order to cope with the real-problem feature of control action, that should be performed in a finite number of discrete time instants. The dynamic optimization problem is solved using the NSGA-II, a fast and elitist multiobjective genetic algorithm. The results suggest a dual plague control policy, in which the relative price of control action versus the associated additional harvesting determine the usage of either a low control action or a higher well-defined one.