## 4 Experimental Results and Discussion
### Experiments for Different Swarm Intelligence Algorithms  
A preliminary test of the proposed texture classification approach on three public texture databases, namely CGT, Kylberg, and Brodatz, was conducted, as described here. The size of the training samples was extracted as \(128\times 128\) with different angles of rotation. In Table 2, _Fiv_ is the average fitness value calculated by Equation (11) using the integrated optimization for each filter bank handled by different swarm intelligence algorithms, and \(Fn\) and Time, respectively, indicate the selected number of features and CPU time, on average, for each training process.  
As shown in Table 2, the average fitness value using the proposed method was the highest for all databases, proving that the optimization ability of HALO was superior to that of PSO, DE, CS, and GWO. The discrimination ability of each category was enhanced since the fitness value exceeded 16. More importantly, the process of ALO is based on the hunting behavior of antlions and has no parameters to be set. Hybrid decimal and binary encoding qA utilized to conduct integrated optimization of the parameters and features of Gabor filter; this strategy improved the exploitation ability compared with the use of only one ant encoding. Moreover, the selected number of features was the lowest among all of the algorithms involved: the number was higher than 20 for the CGT and Kylberg databases using PSO and DE algorithms, and HALO abandoned more than 50% of the redundant features from Gabor filter. From the aspect of operating efficiency, HALO had a faster convergence rate because it had fewer multiplications compared with the other algorithms. The difference in CPU time reached 0.7 s for the Kylberg and Brodatz databases, and HALO only needed  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline Population size & 8 \\ Dimension & 40 + 13 \\ Number of runs for each technique & 30 \\ \(c_{1}\), \(c_{2}\) Acceleration coefficient in PSO algorithm & 2.0 \\ \(f_{m}\) Mutation factor in DE algorithm & 0.6 \\ \(C_{R}\) Crossover rate in DE algorithm & 0.9 \\ \(G_{0}\) Initial of gravitational variable in GSA & 100 \\ \(\alpha\) User specified constant in GSA & 10 \\ \(p_{a}\) Detecting probability in CS algorithm & 0.25 \\ \(\beta\) Parameter in CS algorithm & 1.5 \\ a Correlation coefficient in GWO & [2,0] \\ \(r_{1}\), \(r_{2}\) Random vectors in GWO & [0,1] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter settings for different algorithms.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Database** & **Meas.** & **PSO** & **DE** & **CS** & **GWO** & **HALO** \\ \hline \multirow{4}{*}{CGT} & _Fiv_ & 15.3503 & 16.1756 & 16.9323 & 17.5238 & 18.3323 \\  & _Fn_ & 20.7667 & 20.3333 & 19.8667 & 19.5000 & 19.0333 \\  & Time & 11.2552 & 10.9532 & 10.8711 & 11.0332 & 10.6732 \\  & _Fiv_ & 15.9803 & 16.8198 & 18.1516 & 19.2445 & 19.7469 \\ [PERSON] & _Fn_ & 20.8667 & 20.4333 & 20.2000 & 19.6667 & 19.2000 \\  & Time & 15.3124 & 14.9997 & 14.9056 & 15.1336 & 14.6008 \\  & _Fiv_ & 13.2545 & 14.2234 & 14.9204 & 16.0043 & 16.9607 \\ [PERSON] & _Fn_ & 18.7333 & 18.4000 & 17.8333 & 17.2667 & 16.9000 \\  & Time & 25.2872 & 24.9488 & 24.8150 & 25.0316 & 24.5248 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Result of different algorithms for public texture databases.  
10.6732 s to select the best feature subset by obvious distinction for the CGT database. Overall, it can be deduced that the optimization ability and operating efficiency are improved by using HALO, which has the desired adaptability to obtain suitable parameters and features of Gabor filter.