  Unmanned aerial vehicles (UAVs) can serve as aerial base stations (ABSs) to
provide wireless connectivity for ground users (GUs) in diverse scenarios.
However, it is an NP-hard problem with exponential complexity in $M$ and $N$,
in order to maximize the coverage rate (CR) of $M$ GUs by jointly placing $N$
ABSs with limited coverage range. This problem becomes even more intricate when
the coverage range becomes irregular due to site-specific obstructions (e.g.,
buildings) on the air-ground channel, and/or when the GUs are in motion. To
address the above challenges, we study a multi-ABS movement optimization
problem to maximize the average coverage rate of mobile GUs within a
site-specific environment. We tackle this challenging problem by 1)
constructing the global connectivity map (GCM) which contains the connectivity
information between given pairs of ABS/GU locations; 2) partitioning the ABS
movement problem into ABS placement sub-problems and formulate each sub-problem
into a binary integer linear programing (BILP) problem based on GCM; 3)
proposing a fast online algorithm to execute (one-pass) projected stochastic
subgradient descent within the dual space to rapidly solve the BILP problem
with near-optimal performance. Numerical results demonstrate that our proposed
algorithm achieves a high CR performance close to that obtained by the open
source solver (SCIP), yet with significantly reduced running time. In addition,
the algorithm also notably outperforms one of the state-of-the-art deep
reinforcement learning (DRL) methods and the K-means initiated evolutionary
algorithm in terms of CR performance and/or time efficiency.
