## 5 Arithmetic Example
### Comparison of Different Algorithms  
In this section, a transportation network including highway and railway transportation modes is used to verify the effectiveness of the FAGA algorithm. There are 1-2 modes of transportation in railway transportation and highway transportation between each two urban nodes. In this paper, MATLAB is used to solve the case model. The path optimization effects of general GA, adaptive genetic algorithm (AGA), and the elite genetic algorithm used in [10] are compared with those of this algorithm. \begin{table}
\begin{tabular}{c c c c} \hline
**Originating Node** & **Arrival Node** & **Railway** & **Highway** \\ \hline \multirow{4}{*}{Changsha} & Wuhan & 358 & 334 \\  & Huaihua & 142 & 385 \\  & Chongqing & 954 & 901 \\  & Guangzhou & 706 & 670 \\  & Shanghai & 1199 & 1054 \\ \hline \multirow{4}{*}{Wuhan} & Zhengzhou & 536 & 514 \\  & Xi’an & 1047 & 740 \\  & Chongqing & 871 & 866 \\  & Shanghai & 1230 & 820 \\ \hline \multirow{4}{*}{Chongqing} & Huaihua & 602 & 602 \\  & Chengdu & 302 & 300 \\  & Xi’an & 728 & 710 \\  & Guiyang & 339 & 406 \\ \hline \multirow{2}{*}{Huaihua} & Guiyang & 314 & 449 \\  & Nanning & 708 & 675 \\ \hline \multirow{2}{*}{Zhengzhou} & Xi’an & 511 & 479 \\  & Manzhouli & 3020 & 2728 \\  & Erenhot & 2137 & 1173 \\ \hline \multirow{2}{*}{Xi’an} & Alashankou & 3045 & 3037 \\  & Kasbbar & 3796 & 3803 \\ \hline \multirow{2}{*}{Chengdu} & Xi’an & 842 & 726 \\  & Kunming & 1100 & 856 \\  & Nanning & 1832 & 1224 \\ \hline \multirow{2}{*}{Guiyang} & Kunming & 639 & 516 \\  & Nanning & 865 & 574 \\ \hline \multirow{2}{*}{Nanning} & Beihai & 197 & 229 \\ \hline \multirow{2}{*}{Manzhouli} & Warsaw & 9412 & - \\  & Dusburg & 10090 & - \\  & Hamburg & 9824 & - \\ \hline \multirow{2}{*}{Erenhot} & Warsaw & 8150 & - \\  & Duisburg & 8845 & - \\  & Hamburg & 8579 & - \\ \hline \multirow{2}{*}{Alashankou} & Warsaw & 6278 & - \\  & Duisburg & 6955 & - \\  & Hamburg & 6689 & - \\ \hline \multirow{2}{*}{Kashgar} & Gwadar & 3352 & 3485 \\ \hline \multirow{2}{*}{Kumming} & Yangon & 1542 & 1638 \\  & Bangkok & 1740 & 1890 \\  & Ho Chi Minh & 2056 & 2164 \\ \hline \multirow{2}{*}{Yangon} & Bangkok & 816 & 923 \\ \hline \multirow{2}{*}{Ho Chi Minh} & Bangkok & 928 & 1027 \\  & Singapore & 586 & 1023 \\ \hline \multirow{2}{*}{Bangkok} & Singapore & 2154 & 2306 \\ \hline \multirow{2}{*}{Singapore} & Rotterdam & 820 & 1364 \\ \hline \multirow{2}{*}{Warsaw} & Berlin & 780 & 1158 \\ \hline \multirow{2}{*}{Duisburg} & Berlin & 859 & 735 \\ \hline \multirow{2}{*}{Hamburg} & Berlin & 375 & 289 \\ \hline \multirow{2}{*}{Rotterdam} & Berlin & 778 & 824 \\ \hline \end{tabular}
\end{table} 
Table 5: Transport mileage of each mode of transportation. The crossover probability is 0.2, and the mutation probability is 0.8 in GA. Given the maximum genetic algebra gen = 400, the AGA algorithm adaptively adjusts the crossover and mutation parameters according to the fitness of all individuals in each iteration. The FAGA algorithm uses the fuzzy reference system as the mechanism to adaptively select the crossover probability and mutation probability, ensure the diversity of the population, and finally obtain the best route from Nanchang Station to Berlin using the different parameters set above. Figure 7 shows the optimization path of the ordinary GA algorithm. Nanchang is the starting city, and Berlin is the destination city. It successively passes through 23 cities, including Wuhan, Zhengzhou, Chongqing, Huaihua, Guiyang, Nanning, Beihai, Kunming, Guangzhou, Shanghai, Manzhouli, Erenhot, Alataw Pass, Kashgar, Gwadar, Yangon, Bangkok, Ho Chi Minh, Singapore, Rotterdam, Hamburg, Warsaw, and Duisburg.