## 3 Methods
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Instance** & **MLRBT** & **IAMTSP+** \\ \hline kroA100 & 22.59121 & 3.592298981 \\ eil51 & 8.387097 & 2.517162471 \\ a280 & 25.74143 & 12.78322624 \\ KroA200 & 36.5277 & 7.612935699 \\ lin318 & 38.63484 & 8.721902487 \\ pr144 & 53.08144 & 6.259808475 \\ att532 & 80.92305 & 69.78401563 \\ rat783 & 39.92769 & 9.449871465 \\ att48 & 74.03942 & 69.5271957 \\ bier127 & 14.19514 & 8.200360114 \\ pr439 & 28.25655 & 8.867828304 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error percentage results for the two seeding methods. Figure 5: Error rates of population seeding methods. Figure 6: Average convergence rates of population seeding methods. The GA efficiency is significantly affected by the genetic operator choices (such as selection, crossover, and mutation), as well as the fine-tuning of the control parameters and the population seeding methods. To obtain near-optimal solutions in an appropriate amount of time, it is important to carefully select GA operators and parameters that balance exploitation and exploration and another parameter, such as the initial population method. Exploration is focused on discovering new and unknown places in the search space, whereas exploitation uses the knowledge gained from previously visited sites to identify better points. Research on GAs focuses on the selection of genetic operators and parameters and their impact on algorithm efficiency. There is no \"best\" answer to these challenges, and the choice of parameters is determined by the problem domain and the structure of the search space. To examine the efficiency of the IAMTSP+ initial population seeding method and its impact on the efficiency of GA, the algorithm was run for a specific time (Millisecond) with the three population seeding methods (IAMTSP+, random, and MLRBT) for each city, and the solutions were obtained. It is worth noting that the GA parameters are the same as those displayed in Table 1, except that the termination criterion was set to a specific time for each city. The time was first calculated for the IAMTSP+ seeding population while filling in the population size for city \(N\), so it was time T1. Then, a specific time was fixed for the genetic algorithm that works after seeding, so it was time T2. The genetic algorithm was run with the random seeding of the population at time \(T1+T2\). Table 5 and Figure 7 show the computational results of the genetic algorithm using the IAMTSP+ initial population seeding method compared to two other methods of initial population seeding: random and MLRBT methods. It is clear from Table 5 that the quality of the resulting solutions for the IAMTSP+ initial population seeding method is the highest, despite the limited time, and it is also clear that the IAMTSP+ seeding method is superior to the other methods from an algorithm efficiency aspect. It is also obvious from Table 5 how the GA proceeds with the doubling of time, as despite the doubling of time for the genetic algorithm that uses random seeding, a local optimum was obtained, and the solutions obtained from the GA with the IAMTSP+ initial population method are still much better than the GA with random seeding solutions, and this justifies our use of the IAMTSP+ seeding method with the GA. \begin{table}
\begin{tabular}{c c c} \hline
**Instance** & **MLRBT** & **IAMTSP+** \\ \hline kroA100 & 72.28744 & 96.44090378 \\ eil51 & 89.00961 & 97.48283753 \\ a280 & 72.85928 & 86.99612076 \\ KroA200 & 61.34001 & 92.29908575 \\ lin318 & 59.83832 & 91.09865029 \\ pr144 & 44.35485 & 93.74019153 \\ att532 & 17.58694 & 30.09596445 \\ rat783 & 57.5251 & 90.4385343 \\ att48 & 25.77303 & 30.47280443 \\ bier127 & 83.43014 & 91.79963989 \\ pr439 & 69.47557 & 90.78746485 \\ \hline \end{tabular}
\end{table} 
Table 4: Average convergence rates %. Figure 8 indicates that the GA with IAMTSP+ initial population seeding reaches the near-optimal solution faster than the GA with random seeding, and the specified time to complete the algorithm for the two methods is 6023 ms.