Abstract: In this study, optimization problems for a cluster of gas lift wells system, which are coupled with a production and gas injection manifold, are discussed. The main goal is to determine the optimum gas injection rate for each well that maximizing the total oil production rate. The total gas for injection is constrained by the maximum availability and the total liquid production rate is constrained by separator capacity. The mathematical model for gas lift problem could be written as a boundary value problem, where the two parameter family non linear differential equation of the boundary value problem represents steady flow equation along the tubing, satisfying wellhead pressure and bottom hole pressure as boundary conditions. Oil production rate is a non-linear function of gas injection rate, which is given implicitly from the gas lift model. A computation scheme based on genetic algorithms is developed to solve the constrained optimization problem with and without considering separator capacity. Our results show quite good estimation for optimum solution. This approach is also flexible to accommodate separator capacity constraints.