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.
Abstract. The planning of vaccination campaigns has the purpose of minimizing both the number of infected individuals in a time horizon and the cost to implement the control policy. This planning task is stated here as a multiobjective dynamic optimization problem of impulsive control design, in which the number of campaigns, the time interval between them and the number of vaccinated individuals in each campaign are the decision variables. The SIR (Susceptible-Infected-Recovered) differential equation model is employed for representing the epidemics. Due to the high dimension of the decision variable space, the usual evolutionary computation algorithms are not suitable for finding the efficient solutions. A hybrid optimization machinery composed by the canonical NSGA-II coupled with a local search procedure based on Convex Quadratic Approximation (CQA) models of the objective functions is used for performing the optimization task. The final results show that optimal vaccination campaigns with different trade-offs can be designed using the proposed scheme.
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