## 4 Results and Discussion  
Figure 5 shows the approximation of the true Pareto front (shown in Figure 4) for each of the specified cases. The approximation is done by using the normal boundary intersection (NBI) \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Setting** \\ \hline Number of dimensions & 100 \\ Number of feature evaluations (FEs) & 10,000 \\ Number of simulation runs per case & 10 \\ Mutation rate & 1/n \\ Crossover rate (adaptive) & 0.5–1.0 \\ Population size & 50 \\ Selection strategy & DE/rand-to-best/1 \\ Number of generations & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter Settings for Two-Objective Pareto-based Evolutionary Algorithm. method [32] to guide the candidates toward the final non-dominated Pareto front. It can be seen that the scenario in which there is no adoption of DER (Case 4) has the worst approximation of the PF, while Case 1 has the best approximation. This demonstrates that in this case study, DER-CAM gave the most economically viable solution based on the adopted DER mix. For cases 2 and 3, it can be seen that the use of the load-shifting strategy marginally improves the cost and energy consumption optimization functions for the consumer. This results in a comparatively more stable and cost-effective energy profile. It can also be seen that cases 1 and 2 take less time to explore and exploit the search space (observed from the axial calibrations of \(f_{1}(x,t)\) and \(f_{2}(x,t)\)) compared with the cases 3 and 4. This means that the parameter selection for the cases involving load-shifting as an economically viable strategy results in a more optimized PF. For each case (particularly Case 3 and Case 4), it is observed that some of the points on the Pareto front are dominated. This is likely due to the interaction of selected parameters in the OF space on the selection pressure of candidates. The manner in which the particles in the search space settle on the final Pareto set is observed by the variation of the Pareto set over the selected number of dimensions (Figure 6). Each particle in the search space explores the best possible solution in 100 different directions before finally converging to the final optimal candidate. For Case 1, it is observed that the particles settle much more quickly compared with the other three cases. In cases 3 and 4, the particles are in a state of almost constant oscillation, which makes it difficult for them to settle on the final PF. This is evidenced by the disoriented PF in both cases. The diversity of the particles that constitute the final Pareto set has also been considered by observing the behavior of the Pareto set over 10,000 feature evaluations (FEs). The ability of the particles to efficiently explore the search space for potential solutions ensures a uniform spread of solutions over the PF. In Case 4 (Figure 6), the evidence of premature convergence, and consequently poor solution spread over the PF is observed over 5000 FEs (between 2000-7000 FEs). Therefore, the OF parameters cannot be fully explored, thus leading to the poor PF observed in Figure 5d. Since parameter selection is made based on the DER mix, it is to be expected that there would be a poor performance over the two-objective space, since \(f_{2}(x,t)\) is almost non-existent for Case 4. By contrast, the spread for Case 1 can be seen to be steady over 7000 FEs (between 2000-9000 FEs). The outlier around 7000 FEs is likely a case of premature converge, which is handled by the DE/rand-to-best/selection strategy in such situations. Cases 2 and 3 are also quite impressive in terms of maintaining the diversity of the Pareto front due to a utilization of elements of the DER mix such as PV panels and load shifting. For Case 2 in particular, the spread over the PF appears to be more stable compared with Case 3, which has no load shifting strategy. Figure 5: Two-objective PF for (**a**) Case 1, (**b**) Case 2, (**c**) Case 3, (**d**) Case 4.