A hybrid combined cooling, heating and power (CCHP) system including solar collector, ground source heat pump, photovoltaic system and energy storage equipment is established, and the device configuration scheme of the system is optimized. A multi-objective snake optimization (MOSO) algorithm, including chaotic mapping initialization and opposition-based learning strategy, is proposed for solving the optimization model, and incorporating the technique for order preference by similarity to ideal solution (TOPSIS) method to find optimal configuration scheme. A multi-objective configuration optimization model with the CO2 emission, economic cost and energy consumption is constructed, involving the energy balance constraints and equipment capacity constraints. The hybrid CCHP system with solar and geothermal energy improves the performance of energy supply systems and facilitates the utilization of renewable energy. Three operation strategies are designed to manage the energy flow in the system and coordinate the device operation. The system performance discrepancy under different strategies is analyzed. The results demonstrate that MOSO algorithm significantly outperforms the multi-objective multi-verse optimization algorithm, multi-objective particle swarm optimization algorithm and multi-objective evolutionary algorithm based on decomposition in regards to the distribution of the obtained Pareto solution set. The hybrid CCHP system operating under the proposed following electric-thermal load ratio with variable threshold (FLR-VT) strategy has the best performance, and the cost savings ratio, carbon dioxide emission reduction rate and primary energy savings rate reached 40.6 %, 70.6 % and 64.2 %.