Distributed generations (DGs) have become an attractive option for integrating power distribution systems due to their economic, technical, and environmental advantages ^[1][2][1,2]. Although DGs can offer several benefits to the system, their installation is subject to their primary energy source’s availability and geographical location [3]. On the other hand, DGs can cause undesired effects in the system, such as fluctuations in the voltage profile, increased fault current, and inversion in the power flow direction, etc. ^[4][5][4,5]. These effects become more evident when DGs use renewable energy resources (RER). RER play an energetic role in resolving environmental and security issues. They have a probabilistic nature, such as wind speed and solar irradiation [6]. Therefore, technical studies should be conducted to properly install DGs in passive systems, avoiding the degradation of reliability, system operation, and supply quality [3].

In a radial distribution system (RDS), the reactive power flow is considered the main reason for power quality issues [6]. The compensation of reactive power plays the leading part in power system planning. The capacitor banks (CBs) are treated as the familiar reactive power resources that offer loss reduction, voltage regulation, stability improvement, and a financial return for distribution companies when optimally installed in distribution systems ^[3][7][8][3,7,8].

To reduce the overall production costs and improve system reliability, both the DGs and CBs are commissioned as real and reactive power injection sources [7]. The installation of DG and the capacitor in the distribution network has various technical and economic benefits [9]. These multiple benefits cannot be achieved without the appropriate allocation of the DGs and CBs in power system networks. Further, the optimal allocation of both DG and CB can be carried out using optimization techniques using several methodologies [10]. The complete analysis of the existing works relating to the optimization is described in the following section.

The techniques proposed for the placement of DG and CB in distribution networks can be divided into four types: numerical, analytical, metaheuristic, and hybrid optimization ^[10][11][10,11]. The analytical methods have fast convergence, but their computational time and complexity become high when the type and number of DGs and CBs increases [12]. This is particularly true for multi-objective formulations with a large number of equality and inequality constraints. Analytical approaches require more robust algorithms to solve differential and nonlinear equations. In this respect, metaheuristic techniques are helpful in solving the distribution system problems which do not involve differential equations. However, the algorithms need to be appropriately tuned to reach the global solution for DG sizing and placement ^[12][13][12,13].

Among various metaheuristic optimization techniques, particle swarm optimization (PSO) is the most widely used for the siting and sizing DGs. PSO has significantly better computation efficiency, i.e., its functional evaluation. A vital issue with PSO is the trapping of particles into local optima that could consume a large amount of time to converge to an optimal solution. Additionally, there is no guarantee that the optimal solution will be global optima. As a result, several research works highlighted the hybridization of the standard PSO with analytical approaches or other optimization techniques for achieving better results [14]. By using a hybrid optimization technique, better optimization results can be produced by merging two optimization algorithms [9]. Instead of searching in the whole area, the search space is limited by loss sensitivity factor (LSF), increasing the possibility of finding a good solution. After selecting the candidate buses by LSF, an optimizer finds the optimum size of DGs and CBs on the buses. Consequently, a fast convergence is achieved without compromising the siting and sizing aspects ^[10][14][10,14].

A complete survey of numerous literary works associated with the optimal installation of DGs and CBs is elaborated in Table 1 ^[15][16][15,16].