This paper proposes an advanced trigenerative micro compressed air energy storage (CAES) system, which acts as combined cooling, heating and power system by recovering cooling, heating and power energy during or after expansion. The proposed CAES system can be integrated with grid and placed close to users' side. Based on the users' demand, the proposed CAES system can produce different kinds of energy by adjusting the turbine inlet temperature in different seasons. The mathematical model of the proposed system including energy analysis and economic analysis has been set up. A multi-objective optimization by the aid of Non-dominated sorting Genetic Algorithm-II(NSGA-II) is employed to determine the design parameters of the proposed system considering the round trip efficiency and the annual total cost saving. A case application reveals the effectiveness of the above method. At the final optimal point, the round trip efficiency and the annual total cost saving are 0.762 and 147,820.0 $/year, respectively. Then, the design parameters of the proposed system are as follow: the capacity of each compressor is 256.0 kW, the capacity of turbine is 830.0 kW, and the volume of compressed air reservoir is 502.0 m(3). In addition, a sensitivity analysis is performed mainly to assess the influence of key parameters variation on the proposed CAES system performance. This research will provide a guiding principle for design and practical application of trigenerative CAES system to mitigate the power shortage and improve economy for users.