  Wireless rechargeable sensor networks, consisting of sensor nodes with
rechargeable batteries and mobile chargers to replenish their batteries, have
gradually become a promising solution to the bottleneck of energy limitation
that hinders the wide deployment of wireless sensor networks (WSN). In this
paper, we focus on the mobile charger scheduling and path optimization scenario
in which the $k$-coverage ability of a network system needs to be maintained.
We formulate the optimal $k$-coverage charging problem of finding a feasible
path for a mobile charger to charge a set of sensor nodes within their
estimated charging deadlines under the constraint of maintaining the
$k$-coverage ability of the network system, with an objective of minimizing the
energy consumption on traveling per tour. We show the hardness of the problem
that even finding a feasible path for the trivial case of the problem is an
NP-complete one.
  We model the problem and apply dynamic programming to design an algorithm
that finds an exact solution to the optimal $k$-coverage charging problem.
However, the computational complexity is still prohibitive for large size
networks. We then introduce Deep Q-learning, a reinforcement learning algorithm
to tackle the problem.
