## 4 Timer Value Methodology of a Forwarder Node for the Proposed Scheme
After further discussion, it is clear that if we wish to improve packet delivery ratio, it has an impact on the energy tax of protocols, and hence the network's throughput. The objective function has been also optimized with the help of different optimization algorithms, including Genetic Algorithm (GA), Simulated Annealing (SA), Particle Swarm Optimization (PSO), and Whale Optimization algorithm (WOA), as shown in Figures 3-6. The purpose of the objective function is to reduce the total energy consumption. The results represent the fitness function value against iterations. All the algorithms are working to find the best function value for the objective function (Energy tax). This means that to find the best value for energy tax function, the network will perform optimum aligning with the lower and upper bound requirements. In the lower and upper bounds, the total energy and number of nodes are specified for deployment and for the total number of packets to be successfully received from a specific transmission of the source node. For lower iterations, WOA is reached to find the best minimum value compared to GA, SA, and PSO. The fitness function of DOW-PR can be further enhanced by using the energy tax value of the forwarding locality, i.e., the fitness function value of BDREA can be calculated as given below in Equation (2):  
\[FF_{BDREA}=\frac{H}{DIV_{PPN}+DIV_{SUP}\times Hop\_to\_sink}\times e^{-(E_{ tax}/E_{residual})} \tag{2}\]  
where H is the fitness function value of DOW-PR, which contains the advancement from the source node to its expected next potential forwarding, \(DIV_{PPN}\) and \(DIV_{SUP}\) is the factor of the potential forwarding nodes and suppressed nodes from set 3, correspondingly, \(HOP\_to\_sink\) is the number of hops from the surface sink to the forwarding nodes, and \(E_{tax}\) is the amount of energy constrained within the forwarding zone as from Equation (1),  
Figure 5: Objective Function plotting using Particle Swarm Optimization Algorithm for the proposed scheme. Figure 6: Objective Function plotting using Whale Optimization Algorithm for the proposed scheme. while \(E_{residual}\) is the total residual energies in the network. The timer value is the function of the fitness function value of \(FF_{BDREA}\):  
\[FF_{BDREA}=k\times(FF_{BDREA})+\beta \tag{3}\]  
\[FF_{BDREA}=k\times\frac{H}{DIV_{PFN}+DIV_{SUP}\times Hop\_to\_sink}\times e^{-( E_{\text{max}}/E_{residual})}+\beta \tag{4}\]  
If the fitness value (H) for node A is greater than node B, then the following condition should be satisfied:  
\[T(FF_{(BDREA\_A)})<T(FF_{(BDREA\_B)}) \tag{5}\]  
The holding time between two neighboring nodes should be different in such a way that the forwarder node that has a greater fitness function \((T(FF_{(BDREA)}))\) value transmits the packet before the transmission of the same packet from other nodes. For instance, if node A has the highest fitness function value, then it will transmit prior to node B. Upon receiving a duplicate packet from node A, it simply drops the packet. The following equation must be satisfied to avoid duplicate packets:  
\[t_{1}+T(FF_{(BDREA\_A)})<t_{2}+T(FF_{(BDREA\_B)})+t_{12} \tag{6}\]  
Substituting Equation (3) in Equation (6) results in:  
\[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]0  
if we replace the \(FF_{BDREA\_A}-FF_{BDREA\_B}\) with a global variable \(\sigma\), as in DOW-PR. \[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]1  
Solving the value of k and putting it in the above equation, then the timer value can be calculated as given below:  
\[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]2  
The sensor nodes are set up in the various locations. When the packet is ready to be forwarded, the timer mechanism is used to choose the next forwarder. The packet is transmitted by the source node to all of the potential forwarding nodes (PFNs), which then receive it.