Time Efficient Unmanned Aircraft Systems Deployment in Disaster Scenarios Using Clustering Methods and a Set Cover Approach
Abstract
:1. Introduction
2. Related Work
3. Problem Description
4. Proposed Approach
4.1. Set Covering Optimization Problem Formulation
4.2. Generating SCP Instances
Algorithm 1 Single pass algorithm 

5. Redundancy and Connectivity
 perform a first phase of generating good positions of interest for the aircraft around ground targets,
 use an MIP solver to filter out as many positions generated in step 1 as possible and keep the ones that cover more efficiently the targets with the minimum number of aircraft, while at the same time satisfy the redundancy requirement,
 connect (only if necessary) the different components into a single one.
6. Experimental Results and Scalability of the Solution
6.1. Simulation SetUp
6.2. Simulation Results
6.2.1. Results of First Series of Experiments
6.2.2. Scalability (Results of Second Series of Experiments)
 the cost of the clustering phase revolves on the number of targets but also on the distance between them, since the generated positions depend on these distances and thus the number of iterations until the stopping criterion is reached. This phase is the one with a relatively more consistent runtime growth that is unlikely to explode.
 the execution cost of the MIP solver depends on the number of targets (the constraints) and the positions generated in the first step (the decision variables), but it most importantly depends on the structure of the problem. Indeed, the branchandcut method used by glpk is most sensitive to the steps needed to reach the optimal integer solution than on the size of the problem.
 the time cost of the connectivity step depends on the gaps in the separate connected components.
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Simulations Parameters  Simulation 1  Simulation 2 

Area dimensions  1000 m × 1000 m  (see Table 2) 
Number of instances  5  6 sets of 20 instances each 
Number of targets per instances  [50, 75, 100, 125, 50]  (see Table 2) 
Mobility of grounds nodes  static  static 
Range of aircraft  125 m  125 m 
2nd Simulation Parameters  Number of Instances (Number of Targets per Instance)  Average Area Dimensions  Quartiles of Standard Deviations of Targets in Instances (1st Quartile, 2nd, and 3rd) 

set 1  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  871.6 m × 866.9 m  178.11, 230.34, 284.21 
set 2  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  1210.5 m × 1212.1 m  271.88, 331.50, 382.89 
set 3  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  1564.6 m × 1568.2 m  375.19, 434.08, 508.99 
set 4  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  1915.6 m × 1912.1 m  489.15, 534.49, 603.94 
set 5  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  2265.9 m × 2263.5 m  612.87, 660.76, 697.05 
set 6  20 $(\left\{i\times 50\phantom{\rule{0.277778em}{0ex}}\mathrm{targets}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\le i\le 20\right\}$)  2609.3 m × 2609.9 m  705.20, 747.64, 809.67 
Instances  p of (6)  Number of Active Locations  $\sum _{\mathit{v}\in \mathit{T}}\mathit{redund}\left(\mathit{v}\right)$, of (3)  CPU Time (in secs)  

1st Phase  2nd (SCP Results)  Final Graph  
1 (Figure 6a)  1  36  2  5  81  0.005642 
1 (Figure 6a)  2  36  4  7  131  0.007040 
2 (Figure 6b)  1  64  17  35  216  0.012458 
2 (Figure 6b)  2  64  35  48  267  0.015921 
3 (Figure 6c)  1  83  17  33  281  0.016422 
3 (Figure 6c)  2  83  36  49  376  0.019009 
4 (Figure 6d)  1  105  19  39  351  0.018976 
4 (Figure 6d)  2  105  42  56  472  0.022005 
5 (Figure 6e)  1  50  50  97  158  0.015618 
5 (Figure 6e)  2  50  100  147  208  0.044414 
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Mahoro Ntwari, D.; GutierrezReina, D.; Toral Marín, S.L.; Tawfik, H. Time Efficient Unmanned Aircraft Systems Deployment in Disaster Scenarios Using Clustering Methods and a Set Cover Approach. Electronics 2021, 10, 422. https://doi.org/10.3390/electronics10040422
Mahoro Ntwari D, GutierrezReina D, Toral Marín SL, Tawfik H. Time Efficient Unmanned Aircraft Systems Deployment in Disaster Scenarios Using Clustering Methods and a Set Cover Approach. Electronics. 2021; 10(4):422. https://doi.org/10.3390/electronics10040422
Chicago/Turabian StyleMahoro Ntwari, Donald, Daniel GutierrezReina, Sergio Luis Toral Marín, and Hissam Tawfik. 2021. "Time Efficient Unmanned Aircraft Systems Deployment in Disaster Scenarios Using Clustering Methods and a Set Cover Approach" Electronics 10, no. 4: 422. https://doi.org/10.3390/electronics10040422