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Due to the prevalence of Human Immuno-deficiency Virus/Acquired Immuno-Deficiency Syndrome (HIV/AIDS) infection in society and the importance of preventing the spread of this disease, a mathematical model for sexual transmission of HIV/AIDS epidemic with asymptomatic and symptomatic phase and public health education is stated as a symmetric system of differential equations in order to reduce the spread of this infectious disease. It is demonstrated that public health education has a considerable effect on the prevalence of the disease. Moreover, the cost of education is very high and for this reason, a cost-optimal control is applied to provide the best possible combination of the parameters corresponding to education in controlling the spread of the disease by means of the Genetic Algorithm (GA) and Simulated Annealing (SA).