## 4 Conclusions  
This paper presents a multi-objective modeling for the DG sizing and siting problem based on technical, economical and environmental aspects, where a multi-objective Genetic Algorithm and Maximin metric (MOHGA) were applied in the searching process to obtain Pareto sets with diversity of solutions. Locations (buses) for possible DG insertions and maximum capacity divided in generation modules were considered. Two case-studies were carried out to testify algorithm effectiveness and decision criteria considering the concept of preference were applied to choose a final solution from Pareto sets. Management decisions typically involve considerations from a wide range of criteria and multi-objective modeling can be of interest to stakeholders, especially when tradeoffs among conflicting aspects are needed to support a more efficient decision-making. Pareto frontier plots demonstrate that the applied methodology of solution process (MOHGA) obtained a satisfactory set of solution alternatives in terms of diversity, which can be understood as an acceptable sampling of the space of decision variables is achieved, thus providing an efficient option for solving multiobjective optimization problems. The case-studies carried out demonstrate that several criteria (such as minimal losses solution, maximum NPV solution and MMA solution) allow decision makers (planners, DG owners, regulatory agencies, etc.) to develop strategies to meet their necessities (such \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Decision** & **(PV-01)** & **(PV-02)** & **(PV-01)** & **(PV-02)** & **\(C_{instal}\)** & **\(LAE_{daily}\)** & **\(EqCO_{2}EF\)** & **
\begin{tabular}{} \end{tabular}** \\
**Criteria** & **Bus** & **Bus** & **NDG** & **NDG** & **(10\({}^{6}\) USD)** & **(MWh)** & **(ton/10 Years)** & **(10\({}^{6}\) USD–10 Years)** \\ \hline Min. losses and Max. NPV & 666 & 468 & 14 & 20 & 5.57 & 3.42 & 0.31 & 0.99 \\ MMA & 565 & 468 & 1 & 17 & 2.28 & 3.72 & 0.14 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Case study II: final solution phenotypes of minimum power losses, maximum NPV and MMA decision criteria. as reduction of costs, CO\({}_{2}\) emissions and technical losses, etc.) at the same time, which is consistent with a more systematic strategy of generation expansion planning. Intermittent sources with higher capacity factors also show a prevalence compared to the others, which can be noticed by the higher dimensions of wind and hydro DG's in case study I. This result points out the continuous need for a technological advance in DG technologies, especially photovoltaic, to increase their capacity factors before other energy sources. Finally, this work also illustrates the high complexity of renewables integration in distribution networks and emphasizes the necessity of research in this field. Conceptualization, P.S.Z.J., L.P.G.N. and G.A.A.B. ; methodology, P.S.Z.J., L.P.G.N. and G.A.A.B. ; software, P.S.Z.J. and L.P.G.N. ; validation, P.S.Z.J., L.P.G.N., G.A.A.B. and J.M.L.-L.; formal analysis, P.S.Z.J., L.P.G.N., G.A.A.B. and J.M.L.-L.; investigation, P.S.Z.J., L.P.G.N., G.A.A.B. and J.M.L.-L.; resources, P.S.Z.J., L.P.G.N., G.A.A.B. and J.M.L.-L.; data curation, P.S.Z.J. ; writing--original draft preparation, P.S.Z.J. ; writing--review and editing, P.S.Z.J., L.P.G.N., G.A.A.B. and J.M.L.-L.; visualization, L.P.G.N., G.A.A.B. and J.M.L.-L.; supervision, L.P.G.N., G.A.A.B. and J.M.L.-L.; project administration, L.P.G.N., G.A.A.B. and J.M.L.-L.; funding acquisition, L.P.G.N., G.A.A.B. and J.M.L.-L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Colombia Scientific Program within the framework of the so called _Ecosistema Cientifico_ (Contract No. FP44842-218-2018) and Programa de Pos-graduacao em Engenharia Eletrica e de Computacao--Universidade Federal de Goias. The authors gratefully acknowledge the Colombia Scientific Program within the framework of the so called _Ecosistema Cientifico_ (Contract No.