Satellite-terrestrial integrated networks (S-TINs) are a key enabler for ubiquitous coverage in 6G communication services. However

the satellite-terrestrial resources exhibit multi-dimensional heterogeneity and inherent conflicts

and the rapid topology variations caused by the high-speed motion of low earth orbit (LEO) satellites lead to the difficulty of maintaining a stable mapping of satellite-terrestrial resources. This dynamic nature ultimately reduces the overall resource utilization efficiency. In this paper

we propose a heterogeneous graph cooperative representation approach for satellite-terrestrial resources and a joint optimization method of transmission-computation resources. Firstly

we construct a heterogeneous graph that achieves mapping between multidimensional resources

dynamic topology

and conflict constraints through typed nodes and edges

where resource cooperativeness is explicitly encoded. Secondly

an STIN transmission-computation model is constructed

and an optimization problem is formulated to jointly resolve conflicts between four objectives. Finally

the proposed many-objective double deep Q-network (DDQN) algorithm achieves the cooperative strategy optimization of task transmission-computation scheduling globally. Simulation experiments show that the proposed algorithm improves the overall resource utilization by up to 11.7% under various access points (APs) and user sizes. Meanwhile

the performance is more stable compared with five algorithms

including deep Q-network (DQN)

and a Lyapunov-based optimization method (LyaOpt).