## 2 Previous Works
For larger and more realistic problem sizes, they use convex approximation methods and multiple equivalent transformation to generate suboptimal, but more efficient solutions. Their approximative method relies on the sine cosine optimization algorithm. Their work is limited to a single UAV. In [15], [PERSON] et al. present a planning algorithm for a UAV to visit and collect data from buoys far off the coast. The buoys are equipped with a power source and are able to recharge the UAV using resonant beam charging. The data collection and trajectory planning problems are formulated as a mixed-integer non-convex optimization problem and is solved using an inexact block coordinate descent method. The solution is also limited to a single UAV. In [16], [PERSON] et al. present a two-step approach which consists of finding the locations of the DPs and then solving the TSP problem. In the first step, they linearize the problem and formulate it as the constrained Weber problem which consists of finding the weighted median of a set of points within a limited area. They use an iterative approach where they solve a set of linear equations until the positions of all DPs converge. In the second step, they solve the TSP with a neighbourhood where the UAV does not have to overfly the DPs, but come in close range. As for the previous work, their solution is limited to a single UAV. In [17], [PERSON] et al. present a unique method of grouping the sensors nodes into clusters. They use a Voronoi diagram where the edges are located equidistant from the sensors. They then position the DPs at the intersection of the edges so that data from nearby sensors can be downloaded from the DP. They tested their method for a single UAV and showed that the resulting path was shorter than if the UAV had to travel over each sensor node. Finally, in [2], [PERSON] et al. present a three-step approach to the wireless sensor data acquisition problem. In the first step, they use a k-means clustering algorithm to find optimized location for the position of ground wireless communication devices responsible for collecting the data from the ground wireless sensors and to relay it to the UAVs. In the second step, they use a GA to solve the mTSP problem so the UAVs visit each one of the ground wireless relays and return to the base station. In the third step, they use a geometrical model to adjust the path of the UAVs to fly to the neighborhoods of the relay points instead of directly above the relay point in an effort to minimize the overall distance travelled by the UAVs. There are four main limitations to previous methods that are addressed in this paper. First, the approaches surveyed all tackle the problem of sensor data acquisition in a 2D environment. To be used in a realistic setting, the method must allow for a 3D environment as it is done in this paper. Secondly, environment representation is often very small, this is obvious in [5] where the environment is represented using a 5 \(\times\) 5 grid or a 10 \(\times\) 10 grid in [11]. Thirdly, very few publications actually compute the path between DPs. Most resort to using straight lines. In this paper an SSSP algorithm is used to compute optimal paths between the DPs. Lastly, which is also related to the size of the environment representation, very few publications comment on the runtime of their algorithm. As sensors are discovered, the algorithm must be able to recalculate paths in a relatively short time. In this paper, the SSSP is parallelized on a GPU architecture to speed up the overall framework by a factor of 33.3\(\times\) and accelerate the calculation of the trajectories.