## 3 Methods
Because these initial solutions are of greater quality, the GA converges faster and produces solutions of higher quality. This effectively addresses our study's main concern: how can the GA's efficiency in solving the TSP be improved? ### Experiments on Simulated Data

We conducted three experiments on randomly generated instances, C1, C2, and C3, with 100, 200, and 300 cities, respectively. We used a uniform distribution to simulate city locations (x- and y-coordinates), ensuring that cities were randomly but uniformly dispersed over the simulation space. These experiments utilized a variety of seeding approaches, including random seeding, MLRBT seeding, and IAMTSP+ seeding, while

\begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Instance**} & **GA Solution** & **GA Solution** & **GA Solution** & **GA Solution** \\  & **with Random** & **with Random** & **with Initial** & **with** \\  & **Seeding** & **Time \(\star\) 2** & **IAMTSP+** & **Regression** \\ \hline bier127 & 0.009137193 & 0.005238244 & 0.01526165 & 0.014081734 \\ a280 & 0.001612823 & 0.000929945 & 0.004405069



keeping GA parameters constant, as shown in Table 1. Table 8 shows the lengths of the routes obtained by the GA with different seeding approaches. As can be seen from Table 8 and Figure 10, it appears that the IAMTSP+ seeding method consistently outperforms the other methods across all instances. Specifically, using the GA with IAMTSP+ seeding resulted in the shortest routes for all three instances. This finding aligns with outcomes previously observed in real-world TSP instances, suggesting that adopting a more sophisticated and adaptive approach for the initial population in the GA culminates in the enhanced performance of the GA's final solution. By demonstrating the superior performance of the IAMTSP+ method on real-world and simulated data, we can build confidence in its use for generating the initial seeding for the GA to be used not only for solving the classical TSP but also in various other applications, such as networking [60,61], transportation planning, urban design, location-based services, etc. ## 5 Conclusions

We present a GA approach with improved efficiency in this study that makes use of the IAMTSP+ initial population strategy. This approach's main benefits include a considerable reduction in processing time, increased robustness, and better solution quality. We evaluated the new method on popular TSP instances to determine its performance. When we compared our method to previously published ones in the literature, including regression-based and random initial solutions, we found that using IAMTSP+ as an initial population method for GA performed better than the other methods in all TSP instances. Our goal in this work was to investigate the effect of different initiation procedures on the effectiveness of genetic algorithms (GAs). It is important to note, however, that the efficiency of the GA is impacted by a variety of circumstances. In future studies, we plan to thoroughly examine the IAMTSP+ technique by taking into account other factors, such as selection methods, deriving the remaining solutions from a single IAMTSP+ solution, and combining two initialization procedures to seed the population. We want to conduct thorough testing and comparisons in our next study, with the goal of providing a detailed evaluation of the effectiveness of the proposed GA-IAMTSP+ approach. Figure 10: Visualization of the resultant routes from the GA after applying the three initial seeding methods on C1. (**A**) Random seeding, (**B**) MLRBT seeding, (**C**) IAMTSP+ seeding. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & **Number of** & **MLRBT** & **IAMTSP+** & **GA with** & **GA with** & **GA with** \\  & **Cities** & & & **Random** & **MLRBT** & **IAMTSP+** \\ \hline C1 & 100 & 3484 & 3175 & 3813 & 3220 & **3142** \\ C2 & 200 & 6307 & 4514 & 6714 & 5363 & **4418** \\ C3 & 300 & 8630 & 5750 & 12167 & 6510 & **5623** \\ \hline \hline \end{tabular}
\end{table}