Multiobjective dynamic optimization of vaccination campaigns using convex quadratic approximation local search

Authors:
André R. da Cruz;Rodrigo T. N. Cardoso;Ricardo H. C. Takahashi
Affiliations:
Mestrando em Engenharia Elétrica, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil;Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brasil;Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil
Venue:
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Year:
2011

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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.