# A Hybrid Brain Storm Optimization Algorithm to Solve the Emergency Relief Routing Model
## 6 Experimental Results
### Discussion  
After comparing the performance of HBSO, BSO+LNS, and the original BSO at patient numbers of 20, 30, and 50, the following conclusions were reached:  
(1) Comparing the performance of BSO+LNS and the original BSO, it was observed that the addition of LNS significantly improved the convergence and stability of the algorithm. The neighborhood search behavior of LNS was found to be effective in finding optimal solutions, as evidenced by the decrease in the objective function value and total distance traveled. This improvement can be attributed to the local search operation performed during the iterative process of the BSO+LNS algorithm, which enhances the degree of exploitation and facilitates the identification of better individuals. The stability of BSO+LNS was also significantly improved, as evidenced by the two variance metrics. Furthermore, the deprivation cost was significantly optimized at patient number 50, which was not observed at patient numbers 20 and 30. As the number of patients increased, the algorithm with the addition of LNS exhibited superior optimization-seeking performance. These results confirm the effectiveness of incorporating LNS into BSO. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **BSO** & **BSO+LNS** & **HBSO** \\ \hline Objective function value (20) & 145,10.0916 & 8479.3374 & **8213.7213** \\ Objective function value (30) & 21,105.4295 & **15,500.0604** & 15,906.6677 \\ Objective function value (50) & 79,521.7022 & 49,793.3165 & **49,137.4593** \\ \hline \hline \end{tabular} The bolded part of the table indicates the minimum value in the same row, i.e., the optimal value.  
\end{table} 
Table 6: The optimal objective function values. Figure 16: The optimal objective function values. (2) The combined performance of HBSO was found to be superior to that of BSO+LNS, based on the results. At patient numbers 20 and 30, HBSO exhibited smaller variance, indicating greater stability in finding optimal solutions. HBSO only showed a slight optimization in the mean of the objective function and the mean of the total distance traveled. However, at a patient number of 50, HBSO exhibited more significant optimization than BSO+LNS in the mean value of the objective function, the mean value of the total distance traveled, and the deprivation cost. The analysis of the 30 results indicated that the HBSO algorithm with SA added possessed a stronger ability to find the optimal solution. The selective retention of non-optimal individuals according to the probability facilitated a deeper exploration of the solution space, resulting in a strong global search capability. However, HBSO exhibited a slight increase in the variance of the objective function at patient number 50 compared to BSO+LNS, possibly due to an imbalance in the relationship between LNS and SA. This will be addressed in future studies. To demonstrate the efficacy of the model with the inclusion of the deprivation cost, the two models with and without the deprivation cost are compared. The objective functions with and without deprivation costs are used in three cases with patient numbers of 20, 30, and 50, respectively. The HBSO algorithm was then applied to solve the problem, each with 30 independent runs. After averaging the data, the results obtained were shown in Table 7 and plotted as a bar chart in Figure 17, where deprivation cost 1, 3, and 5 are the distress levels of patients in the solutions when the number of patients is 20, 30, and 50, respectively, without adding the deprivation cost to the model. Deprivation cost 2, 4, and 6 are the distress levels of patients in the solutions when the model with deprivation cost is applied, respectively. It is easy to tell from the figure that adding the deprivation cost to the model can significantly reduce the level of patients' suffering. When the concept of deprivation cost is not introduced, although less costly solutions for distribution can be found, the patients will have to endure a greater amount of distress.