In this research, a multiple generation system based on geothermal energy was modeled and optimized using different Rankin organic cycles and energy storage with compressed air. The system under study consists of geothermal subsystems, Rankin organic cycle, absorption chiller and compressed air energy storage system. The fluid used in the Rankin organic cycle includes refrigerant R123 and organic ammonia. Thermodynamic software for solving EES engineering equations has been used to model the studied system and also to obtain the results of system analysis. According to the studies, the parameters affecting the system outputs include geothermal temperature, geothermal mass flow rate and inlet temperature to Rankin 1 organic cycle turbine. The results of exergy degradation of the system showed that the evaporator has the most exergy degradation and the lowest exergy degradation is related to the pump. The NSGA-II genetic multi-objective algorithm is used to optimize the target functions of the designed system. The two opposite objective functions studied in this dissertation were to increase the exergy efficiency and to reduce the cost rate. Pareto diagrams were obtained to determine the best values ​​for the objective functions of the problem. Finally, the optimal value of exergy efficiency was 63.009% and the cost rate was 2 $/h. Also in this study by selecting four regions in the north, south, center and east of Iran, which included the cities of Zanjan, Bandar Abbas, Isfahan and Mashhad, were selected for a case study and the system performance results in relation to changes in ambient temperature of cities were examined. The best performance of the system was obtained in the climatic conditions of Zanjan.