## 5 Numerical Results
### Testing Performance of COA and ICOA on Different Adjustment Parameters  
In the section, we have presented the result obtained by COA and the proposed ICOA method by setting different values to the number of coyotes in each pack \(N_{oxyote}\) and the number of packs \(N_{pack}\). The task aims to find the most appropriate values for the two adjustment control parameters, \(N_{oxyote}\) and \(N_{pack}\), so that the proposed ICOA can get the highest performance with the best objective and the fastest search ability. In addition, a comparison of performance between COA and the proposed method as setting the same parameter was also investigated. The considered ORPD problem is a complicated problem, and it takes optimization tools very much time to find optimal solutions due to the function of Matpower program. For judging the quality of one solution, the program must be run for dependent variables, and then fitness function can be calculated. Thus, the number of new solutions produced in each iteration \(N_{spi}\) and the number of new solutions produced in each run \(N_{spr}\) are criteria for comparing the search speed of different applied methods. We have set different values (2, 3, 4, 5) to \(N_{pack}\) and the values of \(N_{oxyote}\) have been 9, 6, 4, and 3, accordingly. Although the different setting results in different population size, \(N_{pop}\) = 18, 18, 16, 15, \(N_{spi}\) = 20 is the same for all settings excluding the case of \(N_{pack}\) = 3 and \(N_{oxyote}\) = 6 with \(N_{spi}\) = 21. Over 50 runs, the best, average, and worst fitness values together with the standard deviation and average execution time are reported in Tables 2-4 for TPL, TVD, and \(L\) index objectives, respectively. The best fitness values from the three tables can reveal the small impact of the two control parameters on the performance of the proposed ICOA, once the difference between the smallest best value and the highest best value is very tiny. For instance, the smallest power loss and the highest power loss are 4.5128 and 4.5238 MW. Similarly, the two values for TVD objective and \(L\) index objective are 0.0888 and 0.9833 pu, and 0.1242 and 0.1250 pu, respectively. However, there is a coincidence among the three cases since the smallest best fitness are found by the setting of \(N_{oxyote}\) = 4 and \(N_{pack}\) = 4, and the highest best fitness are found by the selection of \(N_{oxyote}\) = 9 and \(N_{pack}\) = 2. Clearly, a small number of packs could not produce promising quality solutions. However, it does not mean that a high number of packs is a good selection for a better comparison if the number of coyotes is not high enough. The setting of \(N_{oxyote}\) = 3 and \(N_{pack}\) = 5 could not achieve the best result among all settings. In addition, the survey of standard deviation can show the best stability of search by setting \(N_{oxyate}=9\) and \(N_{pack}=2\), while the second-best search stability is recorded by setting \(N_{oxyate}=4\) and \(N_{pack}=4\). The best performance and the second-best stability can lead to a conclusion that the setting of \(N_{oxyate}=4\) and \(N_{pack}=4\) is the most appropriate parameters for the IEEE 30-bus, and they are also applied for the IEEE 57-bus and 118-bus systems. In regard to comparisons with COA method, the results of the proposed method are more favorable since almost all minimum values of the proposed methods are less than those of COA method, and the success rate (SR) of the proposed method is always higher than SR of COA. In fact, with different setting cases for \(N_{oxyate}\) and \(N_{pack}\), COA found different minimum TPL values to be 4.789, 4.682, 4.5777, and 4.595 MW, while those from ICOA are, respectively, 4.5178, 4.5154, 4.5128, and 4.5238 MW. The numbers indicate that the proposed method could reach less TPL by 0.2712, 0.1666, 0.0649, and 0.0712 MW, which are corresponding to the improvement level of 5.66%, 3.558%, 1.418%, and 1.55%.