A method using relative distance as penalty factor to construct penalty function is presented in this paper. Combined with float encoding genetic algorithms, it successfully sovle the optimization problem with constrains. Then by using this method, the light weight optimization design is taken for the straight lug of the main joint of horizontal stabilizer control screw of an aircraft. On the premise that the original fatigue margin keeps the same, the weight is reduced 22.7%, meanwhile, the optimal solution correspond to different fatigue margin is given to provide a reference for engineering design