## 3 Proposed TIGSO-EDS System Architecture  
A WSN is a cluster of sensors that engage in monitoring and sharing information with the central server. Transmitting the information over a wireless medium (sensor) needs to be performed with a minimized packet loss rate. Clustering models are used to overcome the overhead of energy, which is a challenging issue in these networks. In the proposed method, a hybrid VIKOR GSO model is used for selecting the CH. The overview of the proposed model which used VIKOR GSO is presented in Figure 2.  
Step 1: The best and worst values, \({f_{i}}^{*}\) and \({f_{i}}^{-}\), respectively, for all the criterion functions are determined, where \(i\) ranges from 1 to \(n\). Equations (1) and (2) represent the best and worst values, respectively:  
\[f_{i}^{\sim}=\min_{j}f_{ij}\text{ if }i^{\text{th}}\text{ function symbolizes a benefit} \tag{1}\]  
\[f_{i}^{*}=\min_{j}f_{ij},f_{i}^{\sim}=\min_{j}f_{ij}\text{ if }i^{\text{th}} \text{ function symbolizes a cost} \tag{2}\]  
Step 2: The values of \(S_{j}\) and \(R_{j}\) are given by Equations (3) and (4), respectively, where \(j=1,2,3,\ldots J\):  
\[S_{j}=W_{i}(f_{i}^{*}-f_{ij})/(f_{i}^{*}-f_{i}^{\sim}) \tag{3}\]  
\[R_{j}=W_{i}(f_{i}^{*}-f_{ij})/(f_{i}^{*}-f_{ij}^{\sim}) \tag{4}\]  
Step 3: Determine the values of \(Q_{i}\) using the relation represented in Equation (5):  
\[Q_{j}=v(S_{i}-S^{*})/(S^{\sim}-S^{*})+(1-v)(R_{j}-R^{*})/R^{\sim}-R^{*} \tag{5}\]  
where the following definitions apply:  
* \(S^{*}=\min_{j}S_{j}\);
* \(S^{\sim}=\max_{j}S_{j}\);
* \(R^{*}=\min_{j}R_{j}\);
* \(R^{\sim}=\max_{j}R_{j}\);
* \(v\) represents the weight strategy for the majority criteria;
* (\(1-V\)) represents the weight of individual regrets. Step 4: After ranking the alternatives, the values of \(S\), \(R\), and \(Q\) are sorted in decreasing order for three ranking lists. Step 5: A compromised solution is proposed with the attentive (\(F^{(1)}\)), which is considered the best-ranked value with the (minimum) measure \(Q\) if the subsequent conditions are satisfied. Condition 1 depicts the \"acceptable advantage\" and is represented as \(Q(F(2)-F(1))\geq DQ\), where F(n) represents an alternative solution in the rank list with the help of \(Q\) (in the \(n^{th}\) position) and \(DQ=1/(M-1)\). Condition 2 represents the \"acceptable stability\" (\(F(1)\)), which must be ranked as the best by either the \(S\) and \(R\) or \(S\) or \(R\) values. Within this decision-making process, the  
Figure 2: System architecture of TIGSO-EDS. compromised solution is stable, and it is the scenario of the maximal group utility. Here, the values of \(V\) vary based on the requirements, which are \(v\geq 0.5\) when needed, \(v=0.5\) by concurrence, or \(v\leq 0.5\), where the \"v\" signifies the weight of the decision-making strategy. The set of compromised solutions is proposed if any one of the conditions is not satisfied. The compromised solutions are the following:  
* If condition 2 is not satisfied, then the alternatives are \(F(1)\) and \(F(2)\);
* If condition 1 is not satisfied, then the alternatives are \(F(1),F(2),F(3),\ldots F(M)\), where \(F(M)\) is determined using the relation represented in Equation (6) with the maximum \(M\): \[Q(F^{(M)})-Q(F^{(1)})<DQ\] (6)  
During this method, it is guaranteed that these alternatives satisfy the closeness property. GSO has glowworms, which carry a luminescence quantity along with the agents, which are called luciferin. Based on the objective function of the value of luciferin broadcasted by the glowworms to their neighbors, the fitness of their current locations is evaluated. The best possible CH selection is ensured by combining the VIKOR technique with GSO for selecting the node to be the CH. Condition 1 depicts the \"acceptable advantage\" and is represented by \(Q(F(2)^{*}F(1))\geq DQ\), where \(F(n)\) represents an alternative solution in the rank list with the help of \(Q\) (in the \(n^{th}\) position) and \(DQ=\frac{1}{M-1}\).