A mathematical optimization model was set up for a ground-solar combined system based on in-situ experimental results,in which the solar collector was combined serially with a ground-coupled heat pump(GCHP).The universal optimal equations were solved by the constrained variable metric method considering both the performance and economics.Then the model was applied to a specific case concerning an actual solar assisted GCHP system for space heating.The results indicated a system coefficient of performance(COP)of 3.9 for the optimal method under the seriaI heating mode,and 3.2 for the conventional one.In addition,the optimum solution also showed advantages in energy and cost saving.1eading to a 16.7%improvement in the heat pump performance at 17.2%less energy consumption and 11.8%lower annual cost,respectively.