This article examines an optimization method to solve the forward kinematics problem (FKP) applied to parallel manipulators. Based on Genetic Algorithms (GA), a non-linear equation system solving problem is converted into an optimization one. The majority of truly parallel manipulators can be modeled by the 6-6 which is an hexapod constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball joints. Parallel manipulator kinematics are formulated using the explicit Inverse Kinematics Model (IKM). The position based equation system is implemented. In order to implement GA, the objective function is formulated specifically for the FKP using one squared error performance criteria applied on the leg lengths augmented by three platform joint distances. The proposed approach implements an elitist selection process where a new mutation operator for Real-Coded GA is analyzed. These experiments are the first to converge towards several exact solutions on a general Gough platform manipulator with fast convergence.