# Investigation of the iCC Framework Performance for Solving Constrained LSGO Problems +
## 4 Numerical Experiments and Results
### Benchmark Set for Constrained Large-Scale Global Optimization Problems
Hence, on the one hand, if we reduce the number of subcomponents, the algorithm needs to evaluate fewer solutions in each generation. Thus, the total number of generations increase, provided that \(MaxFEV\) is fixed. With regards to the iCC framework, at the end of the optimization process, the algorithm can calculate many generations, as a consequence, it finds better local solutions. As a result, the performance increases. On the other hand, the strategy of increasing the total number of subcomponents has demonstrated bad performance. Figure 1 demonstrates the average ranking results for the Eas performance with population size equal to 25, 50, 75, and 100, respectively, using boxplot diagrams. On the x-axis, there are labels of optimization algorithms. On the y-axis, the average ranks for each algorithm are presented. The best EA has the smallest average rank (median value). The ranking is based on the median best-found values averaged over all cLSGO benchmark problems. Figures 2 and 3 demonstrate the average ranking results for non-separable and separable problems, respectively. Figures 2 and 3 have the same structure as Figure 1. As we can see from Figure 1, the proposed \(\varepsilon\)-iCC-SHADE performs better on average than \(\varepsilon\)-CC-SHADE (m) with different fixed numbers of subcomponents. Figure 2 shows that \(\varepsilon\)-iCC-SHADE does not demonstrate a better average performance on non-separable problems. At the same time, Figure 3 shows that \(\varepsilon\)-iCC-SHADE outperforms \(\varepsilon\)-CC-SHADE (m) by the average rank on separable problems. Figure 5: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for separable problems. Figure 6: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for non-separable problems. Figure 7: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for separable problems. Figure 8: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for non-separable problems. Figure 10: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for non-separable problems. Figure 9: The ranking of \(\varepsilon\)-CC-SHADE (m) and \(\varepsilon\)-iCC-SHADE for separable problems. Tables 3-6 prove the statistical difference in the results of estimating the performance of \(\varepsilon\)-iCC-SHADE (iCC) and \(\varepsilon\)-CC-SHADE (m) (CC (m)) using the Mann-Whitney U test with normal approximation and tie correction with p-value equal to 0.01. The first column contains the names of the algorithms, the second, third, and fourth columns contain the numbers of benchmark problems, and the EA in the head of the table shows better (+), worse (-), and equal performance (\(\approx\)). The performance of the proposed \(\varepsilon\)-iCC-SHADE versus \(\varepsilon\)-CC-SHADE (m) algorithms has been investigated. Tables 3-6 demonstrate that \(\varepsilon\)-  
In addition to the Mann-Whitney U test, we used post-hoc Dunn and Kruskal-Wallis multiple comparison p-values adjusted with the Holm post-hoc test; p-value equals 0.05. The comparison results are presented in Table 7. The values, in Table 7, are based on the number of cases when the performance estimates were significantly different. Each value indicates the sum of performance differences for all cLSGO problems. The table rows indicate the number of individuals. The last row shows the total difference sum. As we can see from Table 7, \(\varepsilon\)-CC-SHADE (4) and \(\varepsilon\)-CC-SHADE (8) demonstrate the minimum value for the sum of differences. At the same time, \(\varepsilon\)-CC-SHADE (1) demonstrates the biggest performance differences versus other algorithms. Both \(\varepsilon\)-CC-SHADE (10) and the proposed \(\varepsilon\)-iCC-SHADE demonstrate medium values of differences.