# Sustainable Power Consumption for Variance-Based Integration Model in Cellular 6G-IoT System
## 3 System Model
### Improved ACO for 6G-IoT Error Minimization  
ACO has issues with delayed convergence and poor search performance while looking for the best path. To address this issue, punishment and reward coefficients are included in the Ant-Colony-Optimization (ACO) pheromone-update equation. An ant will instantly \"reward\" the current path in accordance with the punishment and reward coefficient when it discovers the best path while traveling. In other words, the pheromone is increased by the equivalent value, increasing the pheromone concentration along the path. The punishment and reward coefficient is used to \"punish\" the current path if it is longer than the previous path. To reduce the pheromone concentration along the altered path, deduct the relevant pheromone value. The longest path and hence the worst solution is discovered during the whole search phase of the present ant through correlation. Punish it severely by deducting the greater value of the worst path pheromone in accordance with the punishment and reward coefficient. By doing this, the impact on the ants' decision-making process is reduced. Employ \(\tau_{ij}^{bf}(t)\) for the pheromone level prior to the update and employ \(\tau_{ij}^{ud}(t+1)\) for the pheromone level following the update. The pheromone would be adjusted in accordance with Equation (8) throughout every searching process of an ant [40]. \[\tau_{ij}^{ud}(t+1)=\left\{ \begin{array}{ll}\tau_{ij}^{bf}(t)+\frac{\omega_{ \gamma}^{2}}{l_{cr}},\ J_{cr}\min\,imum\\ \tau_{ij}^{bf}(t)-\frac{\omega_{\gamma}^{2}}{l_{cr}},\ J_{cr}<J_{last}\\ \tau_{ij}^{bf}(t)-\frac{\omega_{\gamma}^{2}}{l_{cr}},\ J_{cr}\text{max}\,imum \end{array} \right. \tag{8}\]  
In Equation (7), \(\omega\) refers to the adaptive reward coefficient, and is evaluated as \(\omega=\frac{l_{int}}{l_{cr}}\times\frac{l_{max}^{\max}}{l_{cr}}\times\frac{l_ {min}^{\min}}{l_{cr}}\) and \(\xi\) refers to the load coefficient initiated by the model that is a predetermined constant. \(l_{cr}\) refers to the entire length of the present path and \(J_{last}\) refers to the entire length of the final path. If the optimal path takes place, \(\frac{\omega_{\gamma}^{2}}{l_{cr}}\) is summed to the present pheromone level as a reward. If a comparatively poor path arises, the present pheromone level is deducted from \(\frac{\omega_{\gamma}^{2}}{l_{cr}}\) as a penalty. If the worst path happens, the present pheromone level minus \(\frac{\omega_{\gamma}^{2}\xi}{l_{cr}}\) is considered as a harsh punishment. Additionally, the rational setting of the volatility coefficient \(\rho\) would affect the searching capability and computation efficiency of the model with respect to discovering the optimal allocation plan. By varying the value of \(\rho\) dynamically, the pheromone size could be adaptively adjusted. As a result, it could efficiently fortify the earlier searching capability of the scheme and improve the variety of solutions. And with the increase in the iteration count, the probability is improved, ensuring the overall performance of the scheme. The adjusting approach of \(\rho\) is shown in Equation (9). \[\rho(t)=\left\{ \begin{array}{ll}\rho_{\min},\ \rho_{b}(t)<\rho_{\min}\\ \rho_{b}(t),\ \rho_{\min}\leq\rho_{b}(t)\leq\rho_{\max}\\ \rho_{\max},\ \rho_{b}(t)\geq\rho_{\max}\end{array} \right. \tag{9}\]  
\[\rho_{b}(t)=1-\ln(t)/\ln(t+a) \tag{10}\]  
In Equation (10), \(a\) refers to a constant, and the dimension of \(\rho\) is restricted to \([\rho_{\min},\rho_{\max}]\). This prevents the \(\rho\) value from being too huge or too small, resulting in slow efficiency of solution or weak searching abilities, to ensure the overall algorithm performance [32]. The key challenges for the ACO algorithms are premature convergence and poor utilization. This research introduces an Improved Ant Colony Optimization (IACO) for addressing nonlinear problems by examining the peculiarities of the network topology.