## 3 Proposed Method EETO-GA
### Traversal of UAV- on the Set of Clusterhead (CH)  
Let the set of CHs under one UAV, is denoted as \(cls(1),cls(2),...,cls(\alpha)\). For any CH \(cls(\alpha)\ s.t.\ 1\leq u\leq\alpha\). Let, (lat(u), long(u)) denote the geographical position of the CHs in terms of latitude and longitude. Initially, the UAV starts traversal with cls(v) provided, and the following two conditions are satisfied. \[1\leq v\leq\alpha\text{, and}\]  
\[\sqrt{(x\_UAV-lat(v))^{2}+(y\_UAV-long(v))^{2}}\leq\sqrt{(x\_UAV-lat(u))^{2} +(y\_UAV-long(u))^{2}}\]  
\[for\ all\ u\ \ s.t.\ \ 1\leq u\leq\alpha\]  
The conditions are self-explanatory. Here, cls(u) specifies the CH closest to the UAV. As soon as the UAV arrives on the first CH, it executes all of its tasks in the task queue and insets the information in a table TASK-EXEC, where the attributes are as bellow:  
1. \(CLS\_ID\) -- This specifies the unique identification number of the CH whose task in the task queue has recently been executed by the UAV. 2. \(LATTITUDE\)--Geographical latitude of the current CH is located by the UAV. 3. \(LONGITUDE\)-- Geographical longitude of the current CH is located by the UAV. 4. \(TSK\_DISTINCT\_DEV\)-- Number of distinct IoT devices whose tasks have been executed by the UAV. 5. \(TSK\_NUM\)-- This specifies the number of tasks that were submitted. 6. \(TSK\_NUM\)-- This specifies the number of tasks successfully completed. 7. \(ENRG\_CONSUMED\)-- The amount of energy spent by the UAV in the execution of these tasks, is given by this attribute. For the second CH, the entire \(TASK\_EXEC\) of the first CH is carried by the UAV to the second cluster and is ultimately inserted in \(TASK\_EXEC\) table of the second one. Then all tasks in the task queue of the second CH will be executed and the corresponding entry is also inserted in \(TASK\_EXEC\) of the second CH. Please note that the task of the first CH contains only task execution information of its own whereas the same table of the second CH contains task execution information of both the first and second CH. Like this, \(TASK\_EXEC\) of the third CH will contain task execution information of all three of the first,second, and third CHs. In general, we can say that \(TASK\_EXEC\) table of u-th CH where \(1\leq u\leq\alpha\) will contain information about executed tasks in all CHs 1 to (u-1 ). This will continue for m number of rounds, where m is the minimum number such that every CH has every other CHs task execution information and at least thirty observations exist in \(TASK\_EXEC\) of every CH. At this point, the UAV changes its strategy of traversing always the nearest CH unvisited in the current round. Rather it asks the current CH to know the identification number of the next CH to visit and the current CH applies a GA to answer that question. This GA applied for task execution (GATE) is illustrated in Section 3.5. Details of Genetic Algorithm for Task Execution (GATE)  
Flowchart of GA for Task Execution (GATE) appears in Figure 2. In this example, the identification numbers of CHs are in binary to form individual solutions which are called chromosomes. So, chromosomes are binary numbers whose values between 1 and \(\alpha\), therefore the number of bits present in each chromosome is \(\log_{2}\alpha\). The fitness function of chromosome \(CS\) depends on the factors like the average number of tasks that could be successfully computed, the average number of IoT devices that could be served, the energy consumed in each task execution session, and the physical distance of \(CS\) from the immediate previously visited CH. The mathematical expression of fitness function \(fn(CS)\) of chromosome CS, appears in (12).