# Cyber Firefly Algorithm Based on Adaptive Memory Programming for Global Optimization
## 4 Experimental Results and Discussions
### Performance Evaluation
#### 4.3.2 Comparison against Other Metaheuristics  
We now compare the CFA against other metaheuristics inspired by different nature metaphors, the PSO, the GA, and the cyber swarm algorithm (CSA). The compared PSO is the constriction factor version proposed by [PERSON] and [PERSON] (2018) which has been shown to be one of the best PSO implementations. The implemented GA employs real-value chromosome coding, tournament selection (with \(k=2\), i.e., two competitors in each instance of selection), arithmetic crossover, and Gaussian mutation. The GA is generational without population gap, i.e., the whole parent population is replaced by the offspring population. The implementation and parameter setting of CSA follow the original paper ([PERSON], 2017). All the compared algorithms have the same population size of 60 individuals, and are executed until consuming 160,000 FEs. Table 8 tabulates the mean best function value obtained by the compared algorithms over 30 runs and the merit value among the competitors. For the comparison of the CFA against the PSO and the GA, we observe that the CFA well surpasses the other two algorithms on most of the benchmark functions. The merit product in relation to the PSO and the GA is \(8.80\times 10^{-21}\) and \(2.11\times 10^{-36}\), respectively. When we compare the CFA to the CSA, the merit product is \(1.94\times 10^{18}\). The result seems to suggest that the CSA performs better on the dataset. However, if we take a closer look, the CSA is very effective in solving small functions with less than ten variables, thus CSA gives significantly greater merits for these functions. For the test functions with ten or more variables, the merit value turns to be in favor to the CFA, disclosing that the CFA is more effective than CSA in tackling larger-sized functions. It is worth noting that both CFA and the CSA take advantage of the features contained in the AMP domain, and the two algorithms extremely outperform the other compared algorithms in our experiments. This phenomenon discloses the potential of future research in the direction of marrying the AMP with other types of metaheuristics.  
Figure 5: Online performance analysis with 95% confidence interval for the Rosenbrock (30) function. (**a**) The convergence of the best function value during the whole duration of the execution. (**b**) The convergence of the best function value during the second half duration of the execution.  
Figure 6: Online performance analysis with 95% confidence interval for the Rastrigin (30) function. (**a**) The convergence of the best function value during the whole duration of the execution. (**b**) The convergence of the best function value during the second half duration of the execution.  
Figure 7: Online performance analysis with 95% confidence interval for the Griewank (30) function. (**a**) The convergence of the best function value during the whole duration of the execution. (**b**) The convergence of the best function value during the second half duration of the execution.  
To compare the CFA with the state-of-the-art variants of FA, we quote the results (mean objective value over 30 runs) from the original paper LFA [9], VESFSA [10], WFA [11], CLFA [12], FAtidal [13], and GDAFA [14]. The best mean objective value for each function obtained by all compared methods is printed in bold. As can be seen in Table 9, our CFA wins the most times as obtaining the best mean objective value among all. GDAFA seems to possess better performance as the dimensionality increases. Both CFA and GDAFA can gain an objective value very close to the optimum, while the other competing methods may produce an objective value far away from the optimum in some challenging functions.