## 4 Methodology
### Domain Clustering Based on Multi-Path Transmission
#### 4.2.6 Problem Modeling and Optimization Algorithm Design
The network topology matrix \(\mathbf{A}=\{a_{ij}\}\) describes the connection characteristics between nodes, where \(a_{ij}\) represents the bandwidth or latency between node \(i\) and node \(j\), and is a non-negative real number. The task allocation matrix \(\mathbf{T}=\{t_{ij}\}\) represents the amount of resources allocated to task \(j\) at satellite node \(i\), with each element \(t_{ij}\) being a non-negative real number. The resource demand vector for each task \(\mathbf{T}_{j}=(C_{j},B_{j},P_{j})\) corresponds to the computational demand \(C_{j}\), bandwidth demand \(B_{j}\), and storage demand \(P_{j}\), all of which are non-negative real numbers. Additionally, the task transmission latency \(d_{j}\) and the adjusted resource

Figure 3: Main simulation interface of the CSTK platform. allocation \(t^{\prime}_{ij}\) are defined as non-negative real numbers, to ensure the rationality and feasibility of the scheduling process. Satellite orbit parameters include the semi-major axis (_semi_major_axis_), eccentricity (_eccentricity_), inclination (_inclination_), argument of perigee (_argument_of_perigee_), longitude of ascending node (_longitude_of_ascending_node_), and mean anomaly (_mean_anomaly_). These parameters were obtained from the CelesTrak database and were used to define the satellites' orbits, simulating their trajectories and communication windows. The semi-major axis typically ranges from 6000 km to 42,164 km for Low Earth Orbit (LEO) to Geostationary Orbit (GEO) satellites, the eccentricity ranges from 0 (circular orbit) to just below 1 (highly elliptical orbit), the inclination ranges from 0\({}^{\circ}\) to 180\({}^{\circ}\), the argument of perigee ranges from 0\({}^{\circ}\) to 360\({}^{\circ}\), the longitude of ascending node ranges from 0\({}^{\circ}\) to 360\({}^{\circ}\), and the mean anomaly ranges from 0\({}^{\circ}\) to 360\({}^{\circ}\). These orbital parameters are crucial for simulating the relative positions and communication conditions between satellites. The Common Satellite Tool Kit (CSTK) simulation platform was utilized to emulate a realistic satellite network environment, supporting the simulation of various satellite configurations and task loads. CSTK provides modules for satellite orbits, communication links, and task scheduling, enabling precise simulation of communication windows (_visibility_window_) between satellites and ground stations. Using this platform, visibility windows for each task were calculated based on target region information and satellite orbit parameters. Additionally, CSTK generated a network graph that described the connection relationships between the source node (_source_node_j_) and destination node (_destination_node_j_) for each task \(j\), ensuring that each task had a feasible transmission path (_transmission_path_j_ belonging to _available_paths_). The simulation scenarios encompassed a variety of satellite configurations and task loads, to evaluate the system performance under different conditions. The simulation time was defined by _scenario_start_time_ and _scenario_end_time_, for example, from 3 September 2023, 00:00 UTC to 15 September 2023, 23:59 UTC. Task demand parameters included the task priority, data size, and execution time. These parameters were customized based on specific remote sensing task regions and user requirements. Task priority reflected the urgency of the task, the data size was set according to the scale and resolution requirements of the target area, and the execution time was determined by the complexity of the task and the resource allocation. ### Comparative Algorithms

This study selected four representative algorithms for performance evaluation, each offering unique strengths in handling complex optimization tasks.