The purpose of this paper is to present a genetic algorithm (as a software) to optimize engine main parameters through the application of "genetic algorithm" and also introduced the new and modified thermodynamic cycles with analysing their performance. This software objective function is to achieve the highest and optimum level of 'final velocity'. In this study, the strategy of using fuel booster turbo pump and 2nd stage fuel pump is followed primarily to moderate the effect of cavitation on pumps. Although the use of booster pumps increase the weight, arise pumps' rpm and possibility to reduce the tanks pressure came with a decrease in weight of propulsion system. The developed software is applied to Russian RD-180 engine in construction of propulsion system of first stage of ATLAS IIIB LV, and experimental results have been demonstrating the improvement of engine performance which results from a multi-variable sensitivity study on a staged-combustion engine will be highlighted. This algorithm is under the limitation of constraints to control the critical variation of combustion pressure, turbine rpm, and pumps cavitation margin and turbine temperature. Results show that, supply flow rate of gas generation from 2nd stage of fuel pump and divide flow rate of exhaust of fuel booster turbine to 2nd stage of fuel pump and combustion chamber, will increase the final velocity of launch vehicle.