## 3 Energy Efficiency Problem Model for SONs
### GreenRP Algorithm  
In this section, we aim to explore a satellite dormancy strategy with the goal of maximizing the lifespan of edge-AI-driven SONs while minimizing average service latency and packet loss over a specified period. Given this objective, the energy-efficient routing problem in SONs is defined as a multi-objective optimization problem. This type of problem has been classified as NP-complete, implying a vast and diverse solution space. Therefore, heuristic algorithms are considered an ideal choice for addressing such problems. GreenRP is implemented based on genetic algorithms. Genetic algorithms are heuristic search techniques inspired by the principles of biological evolution. The implementation of genetic algorithms involves several key steps: selection (a natural selection process based on individual fitness), crossover (the pairing of selected individuals to exchange certain genetic information to produce offspring), and mutation (introducing random changes to certain parts of an individual to increase genetic diversity). The cyclical execution of these steps not only enhances diversity within the population but also facilitates the evolution of the entire population towards more optimal solutions, providing an effective means to address multi-objective optimization problems. With carefully designed genetic operations and parameter adjustments, genetic algorithms can effectively address the complexity of solving energy-efficient routing problems based on topology planning, yielding solutions within an acceptable timeframe. The GreenRP algorithm, detailed in Algorithm 1, begins by initializing key parameters such as Population_Size, Gene_Length, Best_Fitness, and No_Improve_Count and then creates an initial population based partly on a Previous_Best_Topology, if available (lines 1-4). The core of the algorithm is an iterative loop (lines 5-24) where, in each generation, the Fitness of each Gene (a weighted sum of normalized energy, packet loss, and delay) is calculated. The Best_Fitness is updated, and if no improvement is seen for a set number of iterations, the loop may terminate early. A new population is then generated through parent selection, crossover or copying, and mutation. Once the iteration is complete, the Best_Gene is selected from the final population (line 25). A Path_Set is determined for this Best_Gene using a shortest path (SP) algorithm, and the corresponding links are marked as active (lines 26-29). Finally, this refined Best_Gene is set as the Final_Topology and returned as the algorithm's output (lines 30-31). In the GreenRP algorithm, the gene represents a complete solution to the problem, encapsulating all necessary information to describe that solution, and the choice of encoding method directly influences the efficiency of problem resolution. Satellites powered by solar energy typically operate in a normal working mode when illuminated by sunlight, as energy consumption is less of a concern under such conditions. Consequently, GreenRP primarily focuses on optimizing satellites situated in Earth's shadow regions. Within these shadow regions, inter-satellite laser links may enter a dormant state to conserve energy; these are visually represented by the dashed lines in Figure 3. The operational status of each such link (i.e., whether it is open or closed) is encoded within the gene chain, with its length corresponding directly to the total number of links. Each unit, or locus, within the gene chain signifies the operational status of a specific inter-satellite link, thereby describing the current network topology. If all inter-satellite links connected to a particular satellite are encoded as closed, it implies that this satellite likely has low remaining energy reserves and is not critical for servicing current traffic demands. In such instances, the satellite transitions into a complete dormancy mode, which further reduces its fixed operational power consumption.