## 3 Proposed Algorithm
### Optimized Transfer Energy Distribution  
To determine the optimum energy which can increase the network lifespan, the overall energy criteria should satisfy \(E_{t}^{S}+E_{t}^{r_{n}}\leq E_{overall}\), which is a linear optimization dilemma. Let a network with relay nodes, \(r_{n},n\in\left\{1,\ldots,N\right\}\), the major goal is to increase the network lifetime and maintain a greater throughput in the MAC layer when minimizing the overall power use during data transfer. The optimized energy distribution will increase the possible rates and guarantee fairness among the relay nodes by certifying that the overall transfer energy using collaboration is lower than the direct transfer energy and then increase the network efficiency. The neighboring data are essential by every node in the MANET for lessening the overall transfer of energy while collaborating. Because the transfer rate is related to the transfer energy, multiple relay nodes will have an equal possible rate; however, at many transfer energies. This means that an asymmetric transfer energy strategy is applied, and the overall power use is reduced than the utilization of the same energy at all nodes and its root selections for adhoc networks are represented in Algorithm 1. An optimization dilemma is formulated for increasing the network lifetime:  
\[\max_{E_{t}^{S}+E_{t}^{rn}\geq 0,n\in N}E_{\text{overall}} \tag{5}\]  
\[\text{s.t}\ E_{t}^{S}+E_{t}^{rn}\leq E_{\text{overall}},\forall n\in N \tag{5a}\]  
\[R\leq C,\forall n\in N \tag{5b}\]  
\[E_{S}-E_{t}^{S}T_{S,rn}\geq E_{min},\forall n\in N \tag{5c}\]  
\[E_{rn}-E_{t}^{rn}T_{rn,D}\geq E_{min},\forall n\in N \tag{5d}\]  
\[0\leq E_{t}^{S}\leq E_{t-max},\forall n\in N \tag{5e}\]  
\[0\leq E_{t}^{rn}\leq E_{t-max},\forall n\in N \tag{5f}\]  
The fitness factor, as mentioned in (5), is obtained from (2). Here, \(Max_{E}^{S}\) denote the ratio of maximum energy at the source \(S\) and the energy at time \(t\). \(E^{rn}\) denote the energy of the relay node. \(N\) denote the total node, and \(E_{\text{overall}}\) denote the maximum energy threshold that a network can accommodate, and the same is constant for a given number of nodes. The criteria for overall energy transfer are as per (5a). Here, s.t is the product of source and time, \(n\) denotes the node at the instance, and N denotes the total number of nodes. \(E_{\text{overall}}\) denotes the maximum energy threshold. The optimal Shannon capability is arrived at using (5b). The Shannon capability, or the channel capacity \(C\), is the theoretical tightest upper bound on the information rate of a message that can be communicated in a network N at an arbitrarily low error rate \(R\) using an average received nodes n through a multi-hop collaborative transfer,  
The remaining power after the present transfer is depicted in (5c) and (5d) at the origin and relay nodes, accordingly, and the highest transfer energy is depicted in (5e) and (5f). The solution to this optimization dilemma is achieved by discovering the optimum transfer energy at the origin and relay nodes. To find the best decision, the Lagrangian operation is applied as follows:  
\[\mathcal{L}\left\{E_{t}^{S},E_{t}^{rn},\lambda,\mu,z,u,\sigma,\rho\right\}=E- \lambda\left(E_{t}^{S}+E_{t}^{rn}-E_{overall}\right)\dots\mu(R-C)-z\left(E_{ min}-E_{s}+E_{t}^{S}T_{S,rn}\right)\dots\mu(E_{min}-E_{r_{s}}E_{t}^{rn}T_{r,D})- \sigma\left(E_{t}^{S}-E_{t-max}\right)\dots\rho(E_{t}^{rn}-E_{t-max}) \tag{6}\]  
In Equation (6), \(\lambda,\mu,z,u,\sigma,\rho\) are the Lagrangian multiplier operators for the overall transfer energy criteria, possible collaboration rate, origin, and relay remaining power after contributing in collaboration; the origin forwards energy and relay nodes forward energy criteria, accordingly. In an asymmetric scenario, consider that \(E_{t}^{S}\
eq E_{t}^{rn},d_{S,rn}\
eq d_{r_{n},D}\) and \(|h_{S,rn}|^{2}\
eq|h_{r_{n},D}|^{2}\) are not equal for the 2-hop; however, it has an equal data transfer rate because of the IEEE802.11 PHY multi-rate facility.