## 3 Proposed TIGSO-EDS System Architecture
During this method, it is guaranteed that these alternatives satisfy the closeness property. The GSO objective function is based on energy and mobility. Let \(N\), the number of nodes, stand for the position vector of a node \(i\) and time \(t\) where \(d_{ij}(t)=|n_{j}(t)-n_{i}(t)|\), which is the distance from node \(i\) to \(j\) at time \(t\). The communication range is computed using Equation (7):  
\[T_{r}=\sqrt{\left(\frac{(dn_{d}/dn_{c})}{coveragearea}\right)} \tag{7}\]  
where the following definitions apply:  
* \(dn_{d}=S+1\) is the degree of the desired node;
* \(S=\textit{nodedensity}*d(C,N)\);
* \(d(C,N)=\sqrt{\sum_{i=1}^{n}(N_{i}-C_{i})^{2}}\);
* \(C\) and \(N\) represent the cluster head and node, respectively;
* \(dn_{c}\) is the degree of the current node;
* The coverage area represents the region covered by the cluster. The consumption of total energy \(E_{t}\) is determined using Equation (8): \[E_{t}S_{i},d= \begin{cases}S_{i}E+S_{i}\varepsilon_{f_{3}}d^{2},d\leq d_{0}\\ S_{i}E+S_{i}\varepsilon_{mp}d^{2},d>d_{0}\end{cases} \] (8) where the following definitions apply:
* \(E\) represents the energy consumed to transmit or receive 1-bit messages;
* \(\varepsilon_{f_{3}}\) stands for the free space signal's augmentation coefficient;
* \(\varepsilon_{mp}\) stands for the fading signal amplification coefficient of multiple paths, which rely on the amplifier model's circuit;
* \(d\) shows the distance between the receiver and transmitter;
* \(s_{i}\) represents the fragment of sent information. The transmission range of the neighborhood nodes is initially checked by the node, and the ID is transmitted with the required information to its neighborhood nodes. In GSO,the physical entities are known as a glowworms. At time \(t\), the condition of the glowworm \(n\) has three limitations:  
* The search space position (\(x_{i}(t)\));
* The level of luciferin (\(l_{i}(t)\));
* The neighborhood range (\(r_{i}(t)\)). The level of luciferin is measured by the node's weight. The level of luciferin selects the CH. GSO has three phases: (1) updating the luciferin level (Equation (9)), (2) glowworm (nodes) movement (Equation (10)), and (3) updating the neighborhood range. The current position of a glowworm \(i\) is used for finding the fitness value:  
\[l_{i}t=(1-\rho)l_{i}(t-1)\gamma J(X_{i}(t)) \tag{9}\]  
where the following definitions apply:  
* \(\rho\) represents the luciferin evaporation factor;
* \(\gamma\) represents the luciferin constant;
* \(J\) represents the objective function. \[X_{i}(t+1)=X_{i}(t)+S*\left(\frac{X_{j}(t)-X_{i}(t)}{\|X_{j}(t)-X_{i}(t)\|}\right) \tag{10}\]  
Here, the following definitions apply:  
* \(s\) denotes the step size;
* \(\|X_{j}(t)-X_{i}(t)\|\) represents the Euclidean norm operator. Each node (glowworm) conducts a trace to find its neighbors based on the \(x_{j}\) and \(x_{i}\) difference values, which determine whether there will be a higher value or a smaller value, respectively. The neighbor is determined by calculating the distance between the glowworm and neighbor (i.e., \(i\) and \(j\), respectively). This is analyzed by two parameters. First, if the glowworm value is brighter and the neighbor value is shorter in GSO, then the neighbor value is considered. The luciferin level and search space position are updated using the aforementioned formulae accordingly. The probability in Equation (11) is used by the glowworm to choose one neighbor when it has several options:  
\[p_{ij}(t)=\frac{l_{j}(t)-l_{i}(t)}{\sum_{k=N_{i}(t)}l_{k}(t)-l_{i}(t)} \tag{11}\]  
The neighborhood range (\(r_{i}(t)\)) is updated to limit the range of communication in a group of nodes.