The rapid development of artificial intelligence has led to the evolution of energy demand in data centers with high density and high energy consumption. In order to improve the comprehensive energy efficiency and economy of the energy supply system, a collaborative optimization method of 'parameter-capacity-strategy' for data center combined cooling and power generation system based on solid oxide fuel cell (SOFC) is proposed to simultaneously optimize the thermal parameters and capacity-operation strategy of the system. Firstly, the simulation model of SOFC and single-/double-/triple- effect absorption refrigeration unit is constructed, and then NSGA-II is used to optimize the thermal parameters of the unit. Based on the extended energy hub model, a mixed integer linear programming model is constructed to solve the equipment capacity configuration and typical daily hourly operation strategy, and the Pareto optimal frontier of net power efficiency and life cycle cost is obtained. In the case of a cloud computing data center in Suzhou, the net power efficiency and comprehensive energy efficiency of the co-production system can reach 55% and 79%, respectively. 1% increase in SOFC power generation efficiency can reduce the annual cost by 5.27 million to 7.9 million yuan. The results show that the proposed collaborative optimization method can effectively optimize the design parameters, capacity configuration and operation strategies of the power unit, thereby improving the system's energy efficiency and economic performance.