# Cyber Firefly Algorithm Based on Adaptive Memory Programming for Global Optimization
## 4 Experimental Results and Discussions
### Performance Evaluation
#### 4.3.3 Comparison on the CEC 2005 Dataset  
To further justify the performance of CFA, we compare CFA with the investigated methods reported in [26] on 12 CEC 2005 benchmark functions [30]. The IEEE CEC Repository [27] provides fruitful benchmark datasets for optimization problems with various purposes such as unconstrained, constrained, and multi-objective optimization. The CEC 2005 dataset is designed for unconstrained real-parameter optimization which is addressed in this paper. We selected 12 CEC 2005 functions which are very challenging and have never been solved to optimal by any known methods [26]. We executed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Functions** & **(a) PSO** & **(b) GA** & **(c) CSA** & **(d) CFA** & **Merit (d, a)** & **Merit (d, b)** & **Merit (d, c)** \\ \hline [PERSON] (2) & \(-1.0\) & \(-1.0\) & \(-1.0\) & \(-1.0\) & \(1.0\) & \(1.0\) & \(1.0\) \\ [PERSON] (2) & \(-186.7309\) & \(-186.7309\) & \(-186.7309\) & \(-186.7232\) & \(1.54\times 10^{4}\) & \(1.54\times 10^{4}\) & \(1.54\times 10^{4}\) \\ [PERSON] (2) & \(0.0\) & \(0.1015\) & \(0.0\) & \(0.0\) & \(1.0\) & \(4.93\times 10^{-6}\) & \(1.0\) \\ [PERSON] (2) & \(0.0\) & \(0.0\) & \(0.0\) & \(0.0\) & \(1.0\) & \(1.0\) & \(1.0\) \\ [PERSON] (3) & \(0.0\) & \(0.0\) & \(0.0\) & \(0.0\) & \(1.0\) & \(1.0\) & \(1.0\) \\ [PERSON] (4, 5) & \(-6.6329\) & \(-10.0535\) & \(-10.1532\) & \(-8.0961\) & \(5.84\times 10^{-1}\) & \(2.06\times 10^{1}\) & \(4.11\times 10^{6}\) \\ [PERSON] (4, 7) & \(-8.0176\) & \(-10.0637\) & \(-10.4029\) & \(-10.2611\) & \(5.94\times 10^{-2}\) & \(4.18\times 10^{-1}\) & \(2.84\times 10^{5}\) \\ [PERSON] (4, 10) & \(-7.4195\) & \(-10.0750\) & \(-10.5364\) & \(-10.3554\) & \(5.81\times 10^{-2}\) & \(3.92\times 10^{-1}\) & \(3.62\times 10^{5}\) \\ [PERSON] (10) & \(0.0\) & \(0.0009\) & \(0.0\) & \(0.0\) & \(1.0\) & \(5.55\times 10^{-4}\) & \(1.0\) \\ [PERSON] (10) & \(0.4727\) & \(8.1009\) & \(0.1595\) & \(0.0025\) & \(5.29\times 10^{-3}\) & \(3.09\times 10^{-4}\) & \(1.57\times 10^{-2}\) \\ [PERSON] (10) & \(6.4672\) & \(0.0004\) & \(0.7464\) & \(0.6463\) & \(9.99\times 10^{-2}\) & \(1.61\times 10^{3}\) & \(8.66\times 10^{-1}\) \\ [PERSON] (10) & \(0.0644\) & \(0.0493\) & \(0.0474\) & \(0.0164\) & \(2.55\times 10^{-1}\) & \(3.33\times 10^{-1}\) & \(3.46\times 10^{-1}\) \\ [PERSON] (10) & \(0.0\) & \(0.1809\) & \(0.0\) & \(0.0\) & \(1.0\) & \(2.76\times 10^{-6}\) & \(1.0\) \\ [PERSON] (20) & \(0.0\) & \(0.0069\) & \(0.0\) & \(0.0\) & \(1.0\) & \(7.25\times 10^{-5}\) & \(1.0\) \\ [PERSON] (20) & \(0.3992\) & \(9.0326\) & \(0.4788\) & \(0.2671\) & \(6.69\times 10^{-1}\) & \(2.96\times 10^{-2}\) & \(5.85\times 10^{-1}\) \\ [PERSON] (20) & \(18.7052\) & \(0.0036\) & \(6.8868\) & \(2.4661\) & \(1.32\times 10^{-1}\) & \(6.85\times 10^{2}\) & \(3.58\times 10^{-1}\) \\ [PERSON] (20) & \(0.0227\) & \(0.0533\) & \(0.0128\) & \(0.0072\) & \(3.17\times 10^{-1}\) & \(1.35\times 10^{-1}\) & \(5.63\times 10^{-1}\) \\ [PERSON] (20) & \(2.683\) & \(37.1846\) & \(0.0\) & \(0.0\) & \(1.86\times 10^{-7}\) & \(1.34\times 10^{-8}\) & \(1.0\) \\ [PERSON] (30) & \(0.0\) & \(0.0226\) & \(0.0\) & \(0.0\) & \(1.0\) & \(2.21\times 10^{-5}\) & \(1.0\) \\ [PERSON] (30) & \(9.2089\) & \(83.0118\) & \(0.3627\) & \(0.8011\) & \(8.70\times 10^{-2}\) & \(9.65\times 10^{-3}\) & \(2.21\) \\ [PERSON] (30) & \(33.9281\) & \(0.0115\) & \(11.9425\) & \(4.6807\) & \(1.38\times 10^{-1}\) & \(4.07\times 10^{2}\) & \(3.92\times 10^{-1}\) \\ [PERSON] (30) & \(0.0093\) & \(0.0893\) & \(0.0052\) & \(0.0034\) & \(3.66\times 10^{-1}\) & \(3.81\times 10^{-2}\) & \(6.54\times 10^{-1}\) \\ [PERSON] (30) & \(5.4347\) & \(136.7129\) & \(0.0\) & \(0.0\) & \(9.20\times 10^{-8}\) & \(3.66\times 10^{-9}\) & \(1.0\) \\ \hline
**Merit Product** & & & & & \(\mathbf{8.80\times 10^{-21}}\) & \(\mathbf{2.11\times 10^{-36}}\) & \(\mathbf{1.94\times 10^{18}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The performance comparison between the CFA and other metaheuristics.