# Path Planning for Conformal Antenna Surface Detection Based on Improved Genetic Algorithm
## 4 Experiments  
### Standard Two-Dimensional TSP  
TSPLIB is a database created and maintained by Heidelberg University which contains symmetric TSPs, asymmetric TSPs, vehicle path problems, etc., and is an authoritative database of combinatorial optimization problems. Therefore, the data in TSPLIB were used to verify the effectiveness of the algorithm proposed in this paper and to compare it with the TGA, the multi-population genetic algorithm based on cross accessibility evaluation (AEMPGA) [25], and the discrete spider monkey optimization algorithm (SMO) [26]. The computer used for the experiment ran Windows 10 and was configured with an Intel Core i5-7300 HQ processor and 16 GB of RAM. The algorithm in this work set the population size to be approximately twice the city size; the initial value of crossover probability was 0.9; the initial value of mutation probability was 0.1; the number of trials was 20. The results of the comparison are shown in Table 4. The optimal solutions obtained from some medium- and small-sized datasets are shown in Figure 13a-e, and the iteration curves are shown in Figure 13f. It is important to note that this work used a realistic calculation of lengths, i.e., without rounding the distance between two points, which may have led to different optimal paths. For example, in eil51, the path length as a real number is 428.87, which is a more realistic length, while the path length as an integer is 426, when the corresponding paths are different.  
From Table 4, it can be seen that CHOP-IGA achieved better results compared to those reported in the literature [25,26] and the TGA, and produced a known optimal solution in all 20 experiments. As can be seen in Figure 13, CHOP-IGA iterated faster. For smaller TSPs, such as bzyg29, dantzig42, and eil51, the optimal solution could be iterated within 50 iterations in the best case; for medium-sized TSPs, such as pr144, the optimal solution could be iterated within 100 iterations in the best case, and it had a certain ability to jump out of the local optimal solution. It can be seen that the proposed CHOP-IGA was able to solve medium- and small-scale TSPs better.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Data Sets**} & \multirow{2}{*}{**Shortest Distance**} & \multicolumn{4}{c}{**Average Length**} & \multicolumn{4}{c}{**Minimum Length**} \\ \cline{2-9}  & & **TGA** & **AEMYGA** & **SMO** & **CHOP-IGA** & **TGA** & **AEMYGA** & **SMO** & **CHOP-IGA** \\ \hline ulysses16 & 30.88 & 74.19 & **73.99 \(\ast\)** & **73.99** & **73.99** & **73.99** & **73.99** & **73.99** & **73.99** \\ ulysses22 & 75.31 & 75.76 & 75.51 & — & **75.31** & **75.31** & **75.31** & — & **75.31** \\ bayg29 & 9074.1 & 9224.4 & — \(\ast\) & 9074.2 & 9074.1 & 9074.1 & — & 9074.2 & 9074.1 \\ dantzig42 & 679.2 & 708.22 & 686.21 & — & 679.52 & 685.52 & 692.91 & — & 679.2 \\ eil51 & 428.87 & 446.02 & — & 436.96 & **431.49** & 432.16 & — & **428.87** & **428.87** \\ berlin52 & 7544.4 & 8038.4 & — & 7633.36 & 7561.6 & 773.58 & — & **754.44** & **7564.4** \\ kora100 & 21,285 & 22,454 & — & 22,024 & 21,332 & 21,698 & — & 21,298 & **21,285** \\ lin105 & 14,383 & 15,264 & — & 15,114