The use of renewable energy sources is increasing day by day due to their economic and environmental benefits. However, improper penetration of renewable energy into power grids can lead to problems such as over-voltages and higher active power losses. Therefore, the voltage regulation problem in distribution networks is critical due to the increasing integration of renewable energy sources. On the other hand, an increase in renewable energy penetration leads to lower operational costs due to decreased energy purchases from the overhead grid. Therefore, it can be challenging for distribution system operators (DSOs) to decide the trade-off between more Photovoltaic (PV) integration for cost minimization or less penetration to minimize voltage deviation from a rated value. In this study, we formulated this trade-off as a novel multi-objective optimization framework, aiming to minimize operating costs and voltage deviations from a rated value in an unbalanced distribution grid. The proposed formulation is applied to the modified IEEE 34-bus unbalanced distribution network, where the $\varepsilon $ -constraint method is utilized for solving the resulting multi-objective optimization problem along with the Exterior Penalty Functions (EPF) method. The simulation results show that the proposed approach provides the DSO with a better view of decision-making in the optimal operation of the distribution networks.