## 6 Results and Discussion  
In this section, the results obtained from the simulation of metaheuristic algorithms, proposed in the third layer of our SI framework, are discussed for different scenarios. We used MATLAB (MIT, R2017b, Natick, MA, USA) for performing the experiments. The simulation parameters used in the entire experimentation process are shown in Table 4.  
Since Quality has the maximum weight and importance, followed by Delivery and Costs, the suppliers stronger in these three factors secured the top positions in the priority list generated by the simulations of the algorithms. The results show that suppliers 10, 3, and 2 were the most suitable and meet the demands of the company; therefore, they are optimum alternatives. On the contrary, suppliers 1, 7, and 5 were computed to be the least suitable options as they achieved lower scores from the ABC simulation for the above-mentioned critical factors. The results clearly showed that the best-suited algorithm for this problem is the AABC algorithm. It achieved quick convergence towards the optimal value in 35 th cycle with an objective function value of 65,000. However, to ensure avoidance of not getting trapped in local optima, 60 cycles were run. Following the AABC algorithm, the original ABC approach demonstrated good results and achieved near-optimal solution in a short period of time; to be more specific, 650,000 in 45 th cycle and remained steady until termination. Finally, the PSO algorithm did not effectively achieve an optimum solution on this SI problem, and its performance was slower than those of the AABC and the original ABC algorithm, as it only attained its maximum objective value at its 50 th cycle, which is far less than the one achieved by AABC. Results obtained from the AABC, ABC, and PSO approaches are plotted in Figure 3.  
Analysis of Variance (ANOVA) was conducted on 60 separate runs of each algorithm: ABC, AABC, and PSO to validate it statistically. In Table 5, results from ANOVA are presented, and this test proves to be significant, as the p value is less than 0.05, which depicts that performance of the three algorithms differs. To further explore that which algorithm differed significantly, a Tukey post hoc test was conducted as shown in Figure 4. The Tukey test showed that ABC-PSO and AABC-PSO varied significantly, while AABC was in good agreement. However, the Box plot shown in Figure 5 was \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Maximum number of cycles & 50 \\ Number of food sources & 10 \\ Demand limit & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figure 3: Algorithm Comparison in SI Optimization. A sensitivity analysis was performed by varying the importance levels of the factors to access the responses of implemented algorithms. Thus, different hypothetical scenarios were generated while varying the requirements of the company. This analysis helps us to observe the impact of changing inputs on the final decision. The scenarios are presented in Figure 6.  
Scenario 1 (Quality): in this hypothetical scenario, quality is set to the maximum importance and weight by minimizing other factors. Quality represents the standard of the raw material provided by different suppliers. This scenario shows that supplier number 2, 3, and 10 are the best at meeting the demand of company for quality at a 95% level. These suppliers produce better raw material compared with the others and also meet the constraints defined by the company. Scenario 2 (Cost): high cost is an undesirable factor and should be minimized from the company's business point of view. Suppliers with minimum cost, if they meet the other limitation constraints, should be preferred over the others. When the cost is assigned the highest level of importance, supplier number 3, supplier number 6, and supplier number 9 are the optimal alternatives.