## 5 Results and Discussions  
The QODELFA has been applied on three test systems: The IEEE-33 bus, 69-bus, and large-scale 118-bus systems. Backward-forward sweep algorithm (BFSA) has been used to run the load flow. For each system, three different cases were taken under consideration for the best verification and validity of the proposed algorithm. Case 1 represents the minimization of the system's APL, the minimization of both APL and VD together is addressed in Case 2, and Case 3 is for simultaneously minimizing APL, VD, and VSI\({}^{-1}\). Moreover, for each case, three subcases are tested depending on the power factor value of the DGs; i.e., with unity power factor, and with two different values of power factors. Based on the literature included in this paper, and as mentioned in [18], different types of DGs can be characterized when they are optimally planned in radial distribution systems (RDSs). Those types can be distinguished depending on their capability of injecting active, reactive, or both active and reactive powers. The photovoltaic and fuel cells are good examples of DGs capable of injecting active power only, which means that they operate at a unity power factor. While synchronous machines are an example of DGs capable of injecting both active and reactive power, that means they operate at a non-unity power factor. Furthermore, different fixed power factors will lead to different operations and utilizations of DGs in RDSs. Thus, as observed in several references used for comparisons in this paper, such as [28,29,31,32,39], many types of DGs with unity and non-unity power factors are usually selected to simulate several categories of practical generators allocated in RDSs. Hence, it is important to compare the proposed algorithm's performance with as many algorithms in the literature as possible, and to demonstrate the effect of selecting the best power factor value on achieving the optimal objective functions' values. Therefore, three different power factors are chosen for each case. As it is observed from the literature survey, the concept of \"better compromise among the objectives\" has been used in many references when comparing results, especially for bi-objective and multi-objective optimization problems. Those objectives' importance- and value-wise comparisons are needed when the solutions obtained from any proposed method have one of a total of two objectives or two of a total of three objectives better or worse than the other solutions. Thus, all the comparisons performed in this paper have been done relying on this concept. As it is well known regarding the OPDG problem, the minimization of the system's APL is considered as the most important objective, as it has the biggest effect on the system's operation and performance. Therefore, the APL is usually given the highest significance in bi-objective and multi-objective optimization problems. Furthermore, the minimization of VD and VSI\({}^{-1}\) contribute to enhancing the voltage profile and stability along the distribution feeder. Additionally, they serve to keep the minimum bus voltages within their limits as defined by the system's operators, which is also provided when minimizing the APL. In conclusion, when the APL value of the proposed algorithm is much better than that of another method, and the VD value of the proposed algorithm is slightly higher than that of the other method, also when the solutions obtained from the proposed method have two of the total three objectives better than the others, the proposed method's solutions will be regarded as better solutions due to the better compromise among the objectives. Depending on the system's scale, the main QODELFA's parameters are defined, as mentioned before, using a step-wise variation of stochastic parameters in order to obtain the best performance of the algorithm, where \(cr\) is varied between 0 and 1 with a step of 0.1, and \(\beta\) is varied between 1.2 and 1.8 with step of 0.1. For each system and each case, 20 independent runs are performed to get the best solutions.