Balancing Total Energy Consumption and Mean Makespan in Data Offloading for Space-Air-Ground Integrated Networks

We study the data offloading problem in space-air-ground integrated networks (SAGINs) by jointly optimizing task scheduling and power control to balance the total energy consumption and mean makespan. We consider a mixed integer nonlinear programming problem to minimize a normalized weighted combination of these two conflicting objectives. We first propose an approximation algorithm to find a high-quality solution, which is shown to be at most $\frac{1}{2}$ from the optimum to this problem for given power allocation. We further show that optimal power allocation can be obtained in closed form under the assumption that satellite-ground links have low signal-to-noise ratio (SNR). Thus, the proposed approximation algorithm can be directly utilized to obtain a constant-factor solution to the studied problem in low-SNR scenarios. To extend our solution to more general scenarios, we further propose an efficient hybird algorithm based on a genetic framework. Our simulation results demonstrate the near-optimality and correctness of the proposed algorithms, and they unveil the interplay between total energy consumption and mean makespan in SAGINs as well.