Distributionally Robust Optimization for Aerial Multi-Access Edge Computing via Cooperation of UAVs and HAPs

With an extensive increment of computation demands, the aerial multi-access edge computing (MEC), mainly based on uncrewed aerial vehicles (UAVs) and high altitude platforms (HAPs), plays significant roles in future network scenarios. In detail, UAVs can be flexibly deployed, while HAPs are characterized with large capacity and stability. Hence, in this paper, we provide a hierarchical model composed of an HAP and multi-UAVs, to provide aerial MEC services. Moreover, considering the errors of channel state information from unpredictable environmental conditions, we formulate the problem to minimize the total energy cost with the chance constraint, which is a mixed-integer nonlinear problem with uncertain parameters and intractable to solve. To tackle this issue, we optimize the UAV deployment via the weighted K-means algorithm. Then, the chance constraint is reformulated via the distributionally robust optimization (DRO). Furthermore, based on the conditional value-at-risk mechanism, we transform the DRO problem into a mixed-integer second order cone programming, which is further decomposed into two subproblems via the primal decomposition. Moreover, to alleviate the complexity of the binary subproblem, we design a binary whale optimization algorithm. Finally, we conduct extensive simulations to verify the effectiveness and robustness of the proposed schemes by comparing with baseline mechanisms.