## 5 Conclusions  
This paper has examined the effect of parameter variation for four cases of DER mix using a dynamic two-objective Pareto-based evolutionary optimization. The objective function has been designed such that the first cost function is similar to the MILP objective function used by DER-CAM for finding the optimal mix of distributed energy resources from an economic and environmental perspective. The microgrid under consideration supplies a mid-rise apartment building, and the energy usage profiles used in the optimization and results obtained are to optimize energy usage for the specific building and microgrid. The paper has made the following research contributions based on the results obtained:  
1. A Pareto-based modeling approach has been used to investigate the ability of DER-CAM to optimize distributed energy resources for real-life applications. 2. The Pareto-based approach has been used to examine the effect of parameter variation on the optimization of an energy cost function. This has been achieved by observing the effect of parameter variation of selected cases of DER mix on the approximation of a two-objective Pareto front \begin{table}
\begin{tabular}{c c c c c} \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Run 1 & **1.5672 \(\times\) 10\({}^{-2}\)** & 2.0148 \(\times\) 10\({}^{-2}\) & 3.7531 \(\times\) 10\({}^{-2}\) & 4.4972 \(\times\) 10\({}^{-1}\) \\ Run 2 & **2.2234 \(\times\) 10\({}^{-1}\)** & 3.5951 \(\times\) 10\({}^{0}\) & 2.1093 \(\times\) 10\({}^{0}\) & 1.7693 \(\times\) 10\({}^{1}\) \\ Run 3 & **2.0087 \(\times\) 10\({}^{-3}\)** & 3.8502 \(\times\) 10\({}^{-2}\) & 1.1096 \(\times\) 10\({}^{-1}\) & 3.0875 \(\times\) 10\({}^{2}\) \\ Run 4 & 2.5073 \(\times\) 10\({}^{-1}\) & **1.9617 \(\times\) 10\({}^{-1}\)** & 1.0462 \(\times\) 10\({}^{0}\) & 2.9839 \(\times\) 10\({}^{2}\) \\ Run 5 & **2.3394 \(\times\) 10\({}^{-1}\)** & 3.5183 \(\times\) 10\({}^{0}\) & 5.1907 \(\times\) 10\({}^{-1}\) & 4.4097 \(\times\) 10\({}^{0}\) \\ Run 6 & **1.9431 \(\times\) 10\({}^{-3}\)** & 2.6783 \(\times\) 10\({}^{-2}\) & 4.4219 \(\times\) 10\({}^{-1}\) & 3.8519 \(\times\) 10\({}^{1}\) \\ Run 7 & 2.1104 \(\times\) 10\({}^{-2}\) & **1.5072 \(\times\) 10\({}^{-3}\)** & 6.0173 \(\times\) 10\({}^{-2}\) & 6.3184 \(\times\) 10\({}^{-1}\) \\ Run 8 & **1.8257 \(\times\) 10\({}^{-1}\)** & 2.3725 \(\times\) 10\({}^{0}\) & 3.2038 \(\times\) 10\({}^{0}\) & 5.0318 \(\times\) 10\({}^{1}\) \\ Run 9 & **1.9736 \(\times\) 10\({}^{-3}\)** & 4.5932 \(\times\) 10\({}^{-2}\) & 1.2563 \(\times\) 10\({}^{-1}\) & 2.3058 \(\times\) 10\({}^{0}\) \\ Run 10 & 2.8847 \(\times\) 10\({}^{-1}\) & 2.7931 \(\times\) 10\({}^{-1}\) & **3.5072 \(\times\) 10\({}^{-2}\)** & 1.9417 \(\times\) 10\({}^{1}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Mean inverted generational distance (MIGD) values over 10 runs for each case of distributed energy resources (DER) mix. The Pareto-based approach has the capability to allocate DER in a sustainable and cost-effective manner. Further research will examine the relationship between energy usage profiles with and without considerable peak energy usage profiles, and the economic viability of combining load shifting with energy export to the grid. Also, the effect of parameter selection and interaction in the objective function space will be investigated. The aim of this will be to improve the integrity of the non-dominated candidate solutions. Overall, it has been established that DER-CAM is indeed an effective tool for optimization of distributed energy resources for specific energy usage profiles. Also, the Pareto-based EA optimization approach provides an effective means of examining the effect of parameter variation on the behavior of the energy cost function. I.O.E. carried out the analysis and simulation under the supervision of [PERSON] and [PERSON]; [PERSON] and [PERSON] proofread and confirmed the analysis. This research is supported partially by South African National Research Foundation Grants (No.