With the popularization of different kinds of smart terminals and the development of autonomous driving technology, more and more services based on spatio-temporal data have emerged in our lives, such as online taxi services, traffic flow prediction, and tracking virus propagation. However, the privacy concerns of spatio-temporal data greatly limit the use of them. To address this issue, differential privacy method based on spatio-temporal data has been proposed. In differential privacy, a good aggregation query can highly improve the data utility. But the mainstream aggregation query methods are based on area partitioning, which is difficult to generate trajectory with high utility for they are hard to take time and constraints into account. Motivated by this, we propose an aggregation query based on the relationships between trajectories, so it can greatly improve the data utility as compared to the existing methods. The trajectory synthesis task can be regarded as an optimization problem of finding trajectories that match the relationships between trajectories. We adopt gradient descent to find new trajectories that meet the conditions, and during the gradient descent, we can easily take the constraints into account by adding penalty terms which area partitioning based query is hard to achieve. We carry out extensive experiments to validate that the trajectories generated by our method have higher utility and the theoretic analysis shows that our method is safe and reliable.