To improve the flexibility of a combined cooling, heating and power microgrid and reducing operation costs, the ground source heat pumps are integrated into the microgrid in this paper. An economic optimization model with fans, photovoltaics, micro gas turbines, ground source heat pumps, fuel cells, and electricity storage is established. To optimize the output of each unit, a rank pair learning-based Crisscross Optimization algorithm is developed. A heuristic constraint processing method is developed to satisfy the constraints of load balance and output of each unit. To verify the effectiveness of the proposed model and algorithm, an simulation experiment consisting of typical operation scenarios in summer and winter is conducted, and the results are compared with other four optimization algorithms. The results indicate that the proposed algorithm has good global convergence performance and lower cost than the other four optimization algorithms. Thus, the proposed algorithm is an effective method for solving the economic dispatch of a combined cooling, heating and power microgrid. This work is supported by the National Natural Science Foundation of China (No. 61672226), the Natural Science Foundation of Hunan Province (No. 2018JJ2137), and Excellent Youth Project of Education Department of Hunan Province (No.19B200).