## 4 Proposed Model
### Formulation of Multi-Objective Scheduling Problem  
The diversion of the objective function from adaptive and opportunistic modes is formulated for a multi-objective problem by keeping the capacity of beacon node broadcasting and data packet exchange, which is discussed in Equation (7). \[E_{beacon}^{Pmin}(t)\leq E_{beacon}^{P}(t)\leq E_{beacon}^{Pmax}(t) \tag{7}\]  
where \(E_{beacon}^{Pmin}(t)\) and \(E_{beacon}^{Pmax}(t)\) are the maximum and minimum position exchange \(E_{beacon}^{P}(t)\). The value of \(E_{beacon}^{P}(t)\) can be as large as possible at any given time, 't'. The net position exchange, \(E_{beacon}^{P}(t)\), with generation of allocated and deallocated cost of beacon node is computed as in Equation (8) to Equation (11). \[E_{beacon}^{P}(t)=\rm{G}_{all}(t)-\rm{G}_{del}(t) \tag{8}\]  
\[E_{min}^{Ff}(t)\leq E^{H}(t)\leq E_{max}^{Ff}(t) \tag{9}\]where \(E_{min}^{F}\)(t) and \(E_{max}^{F}\)(t) are maximum and minimum function F\({}^{\text{Ff}}\) (t). E\({}^{\text{Ff}}\)(t) = [EFf(t) > 0, if not allocated,  
E\({}^{\text{Ff}}\)(t) < 0, if allocated,  
\[\text{E}^{\text{Ff}}\)(t) = 0, if empty (10)  
\[E_{min}^{\text{SON}}\)(t) \(\leq\) E\({}^{\text{SON}}\)(t) \(\leq\)\(E_{max}^{\text{SON}}\)(t)  
where \(E_{min}^{\text{SON}}\)(t) and \(E_{max}^{\text{SON}}\)(t) are the minimum and maximum state of node (SoN) E\({}^{\text{SON}}\)(t) which is further computed from Equation (12). \[\text{E}^{\text{SON}}\)(t+1) = E\({}^{\text{SON}}\)(t) - B\({}^{\text{unit}}\)(t) \(\frac{E^{F}(t)\times E^{\text{SON}}(t)}{\delta^{\text{SON}}}\) (12)  
where at any given time, '\(\prime\), E\({}^{\text{Ff}}\)(t) is the total function efficiency and \(\delta^{Ff}\) is the related positioning exchange capacity as described in Equation (13). \[\sum_{t=1}^{T}\text{E}^{\text{UB}}\)(t) + \(\sum_{t=1}^{E^{F}}\)(n, t) = E_{loud}^{foreast}\)(t) - E\({}^{\text{Bunit}}\)(t) - E\({}^{\text{LNP}}\)(t) - E\({}^{\text{Gall}}\)(t) - E\({}^{\text{Gdel}}\)(t)  
where at any given time 't' \(E_{load}^{foreast}\)(t) is the forecast load demand. Equation (13) presents the demand and supply of beacon node to balance equation. The opportunistic based allocated demand from UD and unallocated node from UID area are discussed. SRAL adoption and its memory with On\(\backslash\)Off station of dispatched LN\({}^{\text{P}}\) as per Equation (2) and determine which LN\({}^{\text{P}}\) is ON. If the LN\({}^{\text{P}}\) for beacon nodes are dispatched, then it is turned On. If the allocated node is less than the deallocated node, the \(F_{f}\) (fitness function) [37] starts working to explore other criteria options for CB. Otherwise, it again starts to continue allocating more nodes as required. This study considered SON of beacon if the allocated or deallocated nodes are empty. This process continues until the \(F_{f}\) does not stop to explore other nodes. For the B\({}^{\text{unit}}\) operation, it directly depends upon the neighboring list of primary nodes. For the \(F_{f}^{c}\), it depends upon the sub-structuring of all related beacon nodes to meet the allocated criteria. In our scenario, two cases are considered as the \(F_{f}^{c}\) is directly applied to all neighboring nodes or only applied when a node is sent through a proper channel as described in \(Obj_{1}^{\text{G}}\) and \(Obj_{2}^{G}\), respectively. The symbols used in equations and their acronyms are listed in Table 1.