## 5 Discussions and Future Work
### Future Work  
The CETSP was evaluated in this paper in 2D. The assumption was made that the soil can be considered as a plane and that the UAV flies at a constant altitude (in a free-obstacle workspace). A first interesting perspective is to determine the optimal altitude for the UAV. In fact, the configuration of the problem changes with respect to the flight altitude as highlighted with the illustration on Figure 18. A flight at low altitude is more dangerous for the UAV with the possibility to encounter numerous obstacles (e.g., trees), but better in terms of quality of communication with the buried sensor nodes. On the contrary, a flight at high altitude is safer but the areas of the communication ranges are reduced.  
The problem could also be approached directly in three dimensions to take into account the altitude variations of the ground. The approach presented in this paper will be completed to that end: the georeferenced points will be defined by 3D coordinates (longitude, latitude, altitude). In the first step, the intersections of the communication range will be determined by spheres. In the second step, the calculation of the Euclidean distance in the evolutionary algorithm will be calculated in 3D. Finally, in the third step, the geometrical reduction will be carried out by considering 3D shapes.  
Figure 17: Test of our algorithm on the “eil5” benchmark from TSPLIB composed of 51 nodes. The length of the obtained trajectory is 320.6 m.  
Figure 18: The communication ranges of the buried sensor nodes are represented by hemispherical shapes. The problem consists to find the optimal altitude of the UAV.  
Another interesting way of improvement is to add some constraints on the curvature variations of the trajectory. In fact, the kinematic and dynamic behavior of the UAV could be advantageously considered to avoid sharp movements of the UAV, all the more at high speed. The consideration of obstacles in the workspace of the UAV could also be required when the UAV flies at low altitude, e.g., in case of very short communication ranges of the buried sensor nodes. A preliminary flight could also be performed to learn the actual communication ranges of the buried sensor nodes and model the variations with respect to different environmental measurements. Finally, it would be interesting to complete the trajectory with temporal aspects, in particular to take into account the time to collect the data at each node location.  
C.C. and L.M.-A.: Conceptualization, methodology, software, formal analysis, investigation, writing original draft preparation, supervision. F.P. and J.-PC.: Project administration, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This work was sponsored by a public grant overseen by the French National Research Agency as part of the \"Investissements d'Avenir\" through the IDEX-ISITE initiative CAP 20-25 (16-IDEX-0001).  
The datasets used in this study are available in Appendix A.  
The authors thank the ConnceSenS community, the Federation of environmental research (FRE), and the employees of the National Research Institute for Agriculture, Food and Environment (INRAE) who were involved in this work.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l l l} ATSP & Asymmetric Traveling Salesman Problem \\ CETSP & Close Enough Traveling Salesman Problem \\ CVRP & Capacated Vehicle Routing Problem \\ STSP & Symmetric Traveling Salesman Problem \\ TSP & Traveling Salesman Problem \\ TSPN & Traveling Salesman Problem with Neighborhoods \\ TSP-PC & Precedence Constrained Traveling Salesman Problem \\ UAV & Unmanned Aerial Vehicle \\ WUSN & Wireless Underground Sensor Network \\ \end{tabular}