## 5 Experiment and Application
### Algorithm Performance Testing  
To compare the improved FOA with previous FOA and test the performances of three different inertia weights, the four algorithms were tested by searching the minimum points of Schaffer function to compare their performances. The Schaffer function has only one minimum point \(\min\ (0,0)=-1\), and many local extremum points around the minimum point form two loop ditches. The function values are 0.990283 and 0.962776 respectively, so it is easy to fall into these tiny points.  
Some parameters of FOA: maximum number of generation was 90, population size was 20, the initial location range was \([-1.0,1.0]\), fly step range was \([-2.0,2.0]\). The three IFOAs changed the original fly step range with different inertia weights. Because of the inertia weight, the fly step range of improved FOA could be set two times larger than normal step or more. The improved fly range can be expressed as \(\omega(\mathbf{g})\ [-5.0,5.0]\). In Figure 6, IFOA had faster speed in the early stage of the global search.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Configuration** \\ \hline Processor & Intel Xeon E5506, 2.13 GHz \\ RAM & 8 G \\ System & Win7, \(\times\)64 \\ Software & Matlab \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experiment configurations. RAM: random-access memory.  
Figure 5: Original testing gray images (size: 512 \(\times\) 512). (**A**) Lena; (**B**) Columbia; (**C**) Peppers.  
Then, in the later local optimization, IFOA had higher precision of search capabilities and found the extremum more accurately.  
Figure 6 demonstrates that improved FOAs were faster than original FOA in search for extremum at the beginning. When in the later of the process, the local search became more detailed to find accurate extremum. Moreover, different inertia weights had different performances. The IFOA1 and IFOA2 searched quickly, and the IFOA3 was getting faster and faster and surpassed the two algorithms at the fifth generation. In Figures 7-10, the search route of IFOA was much wider than original FOA. The IFOA2 and IFOA3 had almost same search route. Overall, the fly step improved by inertia weights had good performance.  
Then, the FOA and IFOAs were applied in denoising algorithm. Firstly adding Gaussian noise on the original image formed the noisy image. It could be described as \(g(x,y)=f\) (\(x,y\)) + \(v\) (\(x,y\)). To simulate the Gaussian noise on the original image, the test image Lena.bmp (size: 512 \(\times\) 512) was polluted with zero-mean Gaussian noise with the noise variance \(\sigma\) = 0.1. To compare the optimization ability of the FOA and IFOAs, four algorithms were applied to optimize the threshold of DTCWT to remove Gaussian noise on Lena image. The window size of the DTCWT was 5 \(\times\) 5 which was  
Figure 8: (**A**) Optimization process of FOA1; and (**B**) fruit fly flying route of FOA1.  
Figure 10: (**A**) Optimization process of FOA3; and (**B**) fruit fly flying route of FOA3.  
Figure 9: (**A**) Optimization process of FOA2; and (**B**) fruit fly flying route of FOA2.  
convenient for bilateral filter to remove the small noise in the small areas. Some parameters of FOA include: maximum number of generation was 30, population size was 20, the flies' initial location range was [\(-\)10.0, 10.0], and fly step range of [\(-\)1.0, 1.0]. IFOA parameters include: the fly step length of \(\omega(g)\) [\(-\)2.0, 2.0], and other parameters were same as FOA.  
In Figure 11, the IFOAs convergences faster than FOA, and searched more meticulous than FOA. It showed that IFOA possessed the ability of fast global search and precise local search. The IFOA2 with the inertia weight of Formula (22) had the best performance in searching the optimal threshold of the denoising method. As a result, we used IFOA2 to improve the proposed method.