# Adaptive Mutation Dynamic Search Fireworks Algorithm
## 4 Simulation Results and Analysis
### Simulation Results and Analysis
#### 4.2.2 Comparison of AMdynFWA with FWA-Based Algorithms
The \(T\) test [17], which is safe and robust, was utilized at the 5% level to detect significant differences between these pairwise samples for each test function. The _ttest2_ function in Matlab R2014a was used to run the \(T\) test, as shown in Table 4. The null hypothesis is that the results of EFWA, AFWA, and dynFWA are derived from distributions of equal mean, and in order to avoid increases of type I errors, we correct the \(p\)-values using the [PERSON]'s method, and order the \(p\)-values for the three hypotheses being tested from smallest to largest, and we then have three \(T\) tests. Thus, the \(p\)-value 0.05 is changed to 0.0167, 0.025, and 0.05, and then the corrected \(p\)-values were used to compare with the calculated \(p\)-values, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Functions** & \(p\)**/Significance** & **EFWA** & **AFWA** & **dynFWA** \\ \hline f1 & \(p\)-value & 0 & NaN & NaN \\  & significance & + & - & - \\  & \(p\)-value & 1.5080 \(\times\)\(10^{-32}\) & 5.1525 \(\times\)\(10^{-50}\) & 2.6725 \(\times\)\(10^{-49}\) \\ f2 & significance & + & + & + \\ f3 & \(p\)-value & 0.8004 & 0.4302 & 0.0778 \\ f4 & significance & - & - & - \\  & \(p\)-value & 1.5546 \(\times\)\(10^{-136}\) & 1.8922 \(\times\)\(10^{-246}\) & 8.8572 \(\times\)\(10^{-235}\) \\ f5 & significance & + & + & + \\ f6 & \(p\)-value & 0 & NaN & NaN \\  & significance & + & - & - \\  & \(p\)-value & 1.5957 \(\times\)\(10^{-14}\) & 0.7108 & 0.0139 \\ f6 & significance & + & - & + \\ f7 & \(p\)-value & 1.8067 \(\times\)\(10^{-36}\) & 0.5665 & 0.0084 \\  & significance & + & - & + \\  & \(p\)-value & 0.1562 & 0.0137 & 9.2522 \(\times\)\(10^{-6}\) \\ f8 & significance & - & + & + \\  & \(p\)-value & 7.0132 \(\times\)\(10^{-27}\) & 0.0278 & 6.6090 \(\times\)\(10^{-8}\) \\ f9 & significance & + & + & + \\  & \(p\)-value & 2.7171 \(\times\)\(10^{-134}\) & 7.3507 \(\times\)\(10^{-6}\) & 0.0364 \\ f10 & significance & + & + & + \\  & \(p\)-value & 2.2083 \(\times\)\(10^{-100}\) & 3.0290 \(\times\)\(10^{-10}\) & 0.0437 \\ f11 & significance & + & + & + \\  & \(p\)-value & 1.7319 \(\times\)\(10^{-101}\) & 1.3158 \(\times\)\(10^{-11}\) & 1.8212 \(\times\)\(10^{-7}\) \\ f12 & significance & + & + & + \\ f13 & \(p\)-value & 2.3914 \(\times\)\(10^{-89}\) & 4.1645 \(\times\)\(10^{-36}\) & 8.6284 \(\times\)\(10^{-37}\) \\ f13 & significance & + & + & + \\ f14 & \(p\)-value & 0.0424 & 0.0117 & 4.4964 \(\times\)\(10^{-5}\) \\ f14 & significance & + & + & + \\ f15 & \(p\)-value & 1.1749 \(\times\)\(10^{-6}\) & 0.9976 & 0.6064 \\ f15 & significance & + & - & - \\ f16 & \(p\)-value & 2.2725 \(\times\)\(10^{-17}\) & 8.9230\(\times\)\(10^{-12}\) & 2.3427 \(\times\)\(10^{-13}\) \\  & significance & + & + & + \\ \hline \hline \end{tabular}
\end{table} 
Table 4: T test results of AMdynFWA compared with EFWA, AFWA and dynFWA. Where the \(p\)-value is the result of the \(T\) test. The '+' indicates the rejection of the null hypothesis at the 5% significance level, and the '-' indicates the acceptance of the null hypothesis at the 5% significance level. Table 5 indicates that AMdynFWA showed a large improvement over EFWA in most functions. However, in Unimodal Functions, AMdynFWA is not significant when compared with AFWA and dynFWA. In Basic Multimodal Functions and Composition Functions, the AMdynFWA also showed a large improvement over AFWA and dynFWA. Figure 4 shows the mean fitness searching curves of the 28 functions for EFWA, AFWA, dynFWA, and AMdynFWA.