## 3 Methods
We used IRGIBNNM mutation [14], flip mutation [49], and slide mutation [50]. ## 4 Experimental Settings, Results, and Discussion

Investigations were carried out using TSP instances from the TSPLIB [48], and the TSP was chosen for several reasons, including the fact that it can be used to simulate a wide range of real-world problems, and it serves as a typical testbed for new algorithmic

Figure 3: The initial solution for tsp225. Figure 2: The initial solution for a280. approaches; success on the TSP is frequently seen as evidence of a method's applicability or effectiveness. In addition, it is simple to understand, preventing excessive complexity from obscuring the behavior of the algorithm. Therefore, the TSP may serve as an appropriate benchmark case to assess how well various population seeding approaches perform. In addition to the suggested seeding technique, we give the empirical results and analysis of the performance of the MLRBT [13] population seeding method. Table 1 shows the GA settings that were chosen for our experiments. The experiment was carried out ten times for each instance. Each individual's fitness level was determined using a truncation selection approach. This is a typical method for assigning the fitness function to every chromosome in the GA population, and truncation selection is the most straightforward method of selection. In this type of selection, the population is sorted by fitness, and then the lower-fitness proportion is dropped [51]. For the reproduction process in our experiments, the one-point modified crossover and exchange mutation methods were used, as they are among the simplest methods that have been used with problems that are characterized as permutation problems. The one-point modified crossover process randomly selects a location in the chromosomes, and then the individuals exchange genes to make new offspring [52]. The exchange mutation process works by randomly selecting two genes and altering their locations [53]. We would like to clarify that the primary objective of our research is to propose a new method aimed at enhancing diversity within genetic algorithms. We employ the TSP as an example of an optimization problem to facilitate a comparative analysis of our proposed method against other existing methods. Additionally, our choice of straightforward GA parameters, as depicted in Table 1, was intentional. We did not employ sophisticated parameter control or tuning procedures. This approach aligns with the primary goal of our paper, which is to validate the effectiveness and showcase the benefits of our proposed method when compared to a GA in terms of time and diversity. This choice of parameters was made to ensure that the results obtained were a direct reflection of the proposed method's efficacy, rather than the impact of parameter tuning. ### Experimental Setup

To ensure a fair assessment, all tests were conducted in the same environment for all initialization methods. The findings aid in evaluating the effectiveness and efficiency of the IAM-TSP+ for GA population initialization when compared to other initialization methods. Simulation experiments were performed in the Microsoft Visual Studio 2022 environment, and the system's hardware and software specifications are as follows:

* 11 th Gen Intel(R) Core (TM) i7-1165G7 @ 80 GHz 2.80 GHz;
* 8.00 GB of RAM;
* Windows 11 Pro, 64-bit operating system. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value/Method** \\ \hline Population size & 100 \\ Generation limit & 3000 \\ Initialization method & IAMTSP method and Multi-Linear Regression-Based Technique (MLRBT) [13] \\ Crossover method & One-point modified \\ Crossover rate & 82\% \\ Mutation & Exchange mutation \\ Mutation rate & 100\% \\ Selection mechanism & Truncation Selection \\ Termination criterion & Generation limit \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GA setup parameters. We conducted tests on many TSPs, each having a known optimal solution.