# A Novel Dynamic Generalized Opposition-Based Grey Wolf Optimization Algorithm
## 4 Experiments and Discussion
### Analysis and Discussion  
Table 3 shows the mean, best, worst, and standard deviation fitness function values obtained by seven algorithms. From Table 3, the results of the proposed DOGWO are very competitive. It can be observed that for the 23 benchmark functions, DOGWO was superior in performance in the worst, best, mean optimal values, and standard deviation as compared to the original GWO. This indicates that the DOGBL strategy is very effective to increase the population diversity which, consequently, can enhance the performance of the GWO. Moreover, the DOGWO provided a better performance on unimodal benchmark functions F1, F2, F3, F4 as well as the multimodal benchmark functions F7, F8, F10 in comparison to other algorithms. When the DOGWO converged to the global optimum accurately, the standard deviations of these functions were also zeros. For F5 and F9, the precision of best optimal value, worst optimal value, mean optimal value, and standard deviation of DOGWO were collectively better than other algorithms. In addition, for fixed-dimension multimodal functions F14, F15, F16, F17, F18, F19, F21, F22, and F23, DOGWO could find the optimum with small standard deviations. This shows that the proposed DOGWO algorithm performed well in both exploitation and exploration. Its exploitation ability helped to converge to the optimum and the exploration ability assisted with local optima avoidance. The DOGWO also had very competitive optimization ability with high calculation precision and strong robustness for these test functions. It should be mentioned that the enhanced performance of DOGWO took advantages of the dynamic generalized opposition-based learning strategy, as the DOGBL strategy enhanced the population diversity, assisted  
Figure 33: Search history of benchmark functions where N = 10, Iterations = 500.  
the algorithm to explore more promising regions of the search space, and helped with local optima avoidance. For F6 and F12, ALO achieved a better calculation value than DOGWO; ABC showed better performance for F13. However, DOGWO presented a promising performance for the majority of the benchmark functions. Hence, a conclusion can be easily drawn that the DOGWO has a great potential for solving diverse optimization problems from the results in Table 3.  
Figures 4-18 show the convergence curves of F1-F12, F14, F19, and F23. Red and blue asterisked dotted curves were plotted by DOGWO and GWO. Brown, green, and cyan-dotted curves were drawn by ABC, BA, and PSO, respectively. From these figures, it was demonstrated that DOGWO converged rapidly towards the optimum and exploited the optimum accurately for most of benchmark functions. It can also be concluded from the figures that DOGWO had a faster convergence rate and a better calculation precision in contrast to other algorithms. Moreover, Figures 19-32 depict the box plot of ANOVA tests of global optimum for F1-F12, F14, and F21. It can be easily determined that the fluctuate of global optimum of DOGWO was much smaller than other algorithms for most test functions, and the number of outlier was less than other algorithms. This suggests that the proposed DOGWO exhibited strong stability and robustness.  
Furthermore, another test was conducted to draw the search history of search agents by which we could easily perceive the search process of DOGWO. Note that the search population number was 10 and the figures were drawn after 500 iterations. It can be observed from Figure 33 that the search agents of DOGWO tended to extensively search for promising regions of the search space and exploit the best solution. We found that most of candidate search agents were concentrated in the optimum area and other search agents were evenly dispersed in various regions of the search space. Hence, it can be stated that DOGWO had a strong ability of searching for the global optimum and avoiding the local optimum.