  In this paper, we study the problem of gathering data from large-scale
wireless sensor networks using multiple unmanned air vehicles (UAVs) to gather
data at designated rendezvouses, where the goal is to maximize the network
lifetime. Previous proposals often consider a practical approach where the
problem of determining a data gathering scheme is decomposed into 2
sub-problems: i) partitioning the networks into clusters for determining the
rendezvouses as these obtained cluster heads; and ii) determining the paths for
a set of a given number of UAVs to come gathering data at these rendezvouses
which have been harvesting data within each local clusters, respectively. We
try to deal with this as a whole optimization problem, expecting a significant
increase in computation complexity which would bring new challenge in creating
practical solutions for large-scale WSNs. We introduce two alternatives
mixed-integer linear programming (MILP) formulations, namely the 2-index model
with $O(n^2)$ variables and the 3-index model that has $O(n^3)$ variables,
where $n$ denotes the number of sensor nodes. We show that our best model could
solve optimally the problem instances with up to 50 sensor nodes in less than
30 minutes. Next, we propose a heuristic idea to reduce the number of variables
in implementing the 3-index model to effectively handle larger-scale networks
with size in hundreds. The experiment results show that our heuristic approach
significantly prolongs the network lifetime compared to existing most efficient
proposals.
