## 4 Experimental Evaluation
### Comparison with Modern Insights  
In this section, the most recent advances in the field of gradient-based optimization (GBO) and genetic algorithms are presented in order to evaluate and compare them with the proposed solution. Based on simulations obtained by applying the gradient-based optimization of [15], the _TPC_ pertaining to the five-day optimal UC is rated at 2355.145 k$. The high production cost is formed by the increased number of committed generating units \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Assessed Weekday** & **Max (k)** & \(\varepsilon\) & **J (k$)** \\ \hline
1 & 101 & 0.003 & 783.89 \\
2 & 93 & 0.008 & 625.66 \\
3 & 97 & 0.008 & 604.86 \\
4 & 123 & 0.007 & 636.45 \\
5 & 161 & 0.007 & 861.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results obtained through the conventional LR. Figure 3: Optimal UC schedule via the LR approach pertaining to the first 24 h residual demand. Figure 2: Performance of the conventional LR approach during the first 24 h residual demand. responding to the rapid changes in net load. Figure 4 justifies the obtained _TPC_, presenting the respective UC and power dispatch on the participating generating units. With respect to genetic algorithms, the available function GA in the MATLAB optimization toolbox was taken into account, considering two coupling constraints and mixed-integer limitations. The drawback of the developed algorithm lies in the increased number of function evaluations (showing an exponential increase compared with LR) and the violation of coupling constraints. As a result, a penalty cost for the \(P_{\textit{ENS}}\) and \(P_{\textit{SRNS}}\) retrieved as \(\dot{a}=max\ a_{i},\ \dot{b}=max\ b_{i},\ \dot{c}=max\ c_{i}\) was considered, resulting in a final _TPC_ of 2378.296 k$. The power deficits can be seen in Figure 5.  
On the contrary, the variational Bayes alternative completely avoided oscillations based on a proper acquisition function. The employed acquisition function helps the  
Figure 4: Performance of the gradient-based optimization pertaining to the five-day paradigm.  
Figure 5: Power deficits applying the genetic algorithm mechanism.  
optimization move toward regions with lower mean values (lowest cost) and maximum uncertainty (posterior variance) [37]. In this way, the procedure not only avoids trapping at local oscillations but also promises a guaranteed global solution, increasing the exploration space with the minimum number of function evaluations. In normalized values, the performance of the proposed approach during a certain time interval can be explained with the help of Figure 6. Figure 6a shows the estimated objective function across the Lagrange multipliers. The respective minimum TPC over the required function evaluations (iterations) is illustrated in Figure 6b. Assuming that the formulated coupling constraint of power balance is satisfied only when \(\left(\sum S_{i}^{t}P_{i}^{t}-P_{net}^{t}-10^{-9}\right)\leq 0\), its actual violation degree during an optimization loop can be expressed by Figure 7.  
Figure 6: Estimated minimum objective function value across (**a**) the Lagrange multipliers and (**b**) the required function evaluations.  
Figure 7: Power-balance violation degree during a variational Bayes optimization loop.  
Applying simulations pertaining to the five weekdays, the optimal UC schedule greatly improved. Figure 8 presents the obtained contribution of the least committed units. The cumulative _TPC_ achieved a drastic decrease in the order of \(-1.254\) M$ (or a final of 2258.349 k$).