Dengue fever is an infectious disease caused by a virus of the Flaviridae family and transmitted to the person by a mosquito of the genus Aedes aegypti. This disease has been a global public health problem because a single mosquito can infect up to 300 people and between 50 and 100 million people are infected annually on all continents. Thus, dengue fever is currently a subject of research, whether in the search for vaccines and treatments for the disease or efficient and economical forms of mosquito control. The current study aims to study techniques of multiobjective optimization to assist in solving problems involving the control of the mosquito that transmits dengue fever. The population dynamics of the mosquito is studied in order to understand the epidemic phenomenon and suggest strategies of multiobjective programming for mosquito control. A Multiobjective Genetic Algorithm (MGA_DENGUE) is proposed to solve the optimization model treated here and we discuss the computational results obtained from the application of this technique.