Subsequently, a more detailed and precise cost OF was built in order to represent all possible costs including loss, total installed capacitors, installation and operation costs. This OF was adopted in some of the latest research works [26; 27; 28]. The utilization of sensitivity-based indices (SBIs) has recently become a common procedure for significantly reducing the search space of the OPSC problem in RDSs. Those indicators are basically derived from the most critical aspects of RDSs, i.e., power losses and voltage profile, where the base-case load flow is used for their calculations. In [29], based on Lagrange multipliers, voltages, and reactive powers, an interior point optimal power flow method was developed to calculate the sensitivity indices. Power loss index (PLI) was used to identify the candidate buses for capacitor allocation in [8; 27; 30]. Based on the active power loss formula in a distribution line, loss sensitivity factors (LSFs) were derived and then employed to reduce the search space by determining the highest potential buses for capacitor placement in [11; 24; 28]. In [31], a stability index was presented to find the weak buses. DifferentSBIs were also presented in several works, including combined loss sensitivity factor (CLSF) [32; 33], index vector (IV) [32; 34; 33], voltage sensitivity index (VSenI) [32; 33], voltage stability index (VSI) [32; 35], and voltage stability margin (VSM) [32]. The combination between both LSF and VSM was used for selecting the candidate buses in [9; 26]. As revealed by the literature reviewed in this paper, various approaches and techniques with their own advantages and drawbacks have been presented so far for solving the OPSC problem. In general, the main disadvantages that have been noticed in those methods can be summarized as follows:  
* Only few previous works consider a comprehensive cost OF that includes all required costs especially for large-scale RDSs. * Some EA approaches do not guarantee obtaining the optimal solutions especially for large-scale RDSs. * Most of the methods utilize only one or two SBIs for reducing the search space of the OPSC problem. * Some SBIs are employed to find the candidate buses for distributed generators (DGs) allocation (single or multiple DGs). However, they have to be tested for the OPSC problem as well, since the optimal locations for DG installation could not be the same as for SC installation. * Some optimal locations for SC placement might be excluded from the reduced search space when only one or two SBIs are used, because of their limited ability, especially when different-scale RDSs are studied. Hence, taking the aforementioned drawbacks under consideration, an improved hybridization of EA method called permutated oppositional differential evolution sine cosine algorithm (PODESCA) and a sensitivity-based decision-making technique (SBDMT) are proposed in this paper for solving the OPSC problem. The evolved PODESCA uniquely utilizes three effective search techniques in order to present a new and robust method, where the mechanisms of differential evolution (DE) and enhanced sine cosine algorithm (SCA) constitute the algorithm's main loop. In addition, to better improve the search ability, quasi-oppositional technique (QOT) is used in two positions throughout the algorithm; at the initialization stage to generate the initial population (IP), and also inside the main loop. PODESCA is implemented to tackle the OPSC problem in different-scale RDSs, where the objective is to minimize the system's total cost with the presence of SCs subject to different operational constraints. Furthermore, the SBDMT is developed by using a multi-criteria decision-making (MCDM) approach; namely the technique for the order of preference by similarity to ideal solution (TOPSIS). By applying this approach, four SBIs (VSI, PLI, VSenI, and VSM) are set as inputs of TOPSIS, while the output is the highest potential buses for SC placement. As a result, the search space of the OPSC problem is extensively and effectively reduced.