In this work, a computational model for optimization of material gain of the active region of a multiple quantum well (MQW) edge emitting laser (EEL) using genetic algorithm has been developed. Through this optimization procedure, the values of the width of quantum wells (QW), width of barriers, lattice temperature, injection carrier density and number of QWs which are related to material gain of the active region are optimized for optimizing the design of a MQW EEL. For the above mentioned optimization the numerical simulation of the optical gain expression of MQW EEL along with the solution of the Schrodinger's equation has been performed using MATLAB. The developed optimization based design technique has been applied for the design of (i) a 1550nm In 0.72 Ga 0.28 As 0.82 P 0.18 / In 0.42 Ga 0.58 As 0.82 P 0.18 MQW EEL having 3 QWs and also (ii) for a 1550nm In 0.72 Ga 0.28 As 0.82 P 0.18 / In 0.42 Ga 0.58 As 0.82 P 0.18 MQW EEL having 5 QWs for testing the validity. The computation indicates clearly that the optimization based computational model works well and can be easily used for the design of MQW EELs.