# Optimizing Perishable Product Supply Chain Network Using Hybrid Metaheuristic Algorithms
## 3 Solution Algorithms
### Hmpga-Vns Algorithm
The S/N ratio output is analyzed by Minitab software to identify the optimal levels for each algorithm, as illustrated in Figure 4. The larger values of the S/N ratio indicate more robust algorithms, and these levels are considered as the optimal ones. For GA, the optimal levels are 1, 2, 3, and 3 for the respective parameters. In addition to the S/N ratio, the RPD is employed as an additional measure for further analysis. Figure 5 presents the RPD results for each parameter level, indicating the best levels for the factors. These findings are consistent with the results obtained from the S/N ratio analysis. ### Experimental Results

Based on the findings from the previous section, we adjust the parameters of the different metaheuristic algorithms. To ensure the reliability of the results, we conduct five replications for each experiment due to the random nature of the algorithms. The relative performance of the algorithms is evaluated by examining the effect of various problem sizes on their robustness. To assess the robustness of the algorithm, the impact of different problem sizes on their comparative performance is investigated. Figure 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**L9** & **A** & **B** & **C** & **D** \\ \hline
2 & 1 & 2 & 2 & 2 \\
4 & 2 & 1 & 2 & 3 \\
5 & 2 & 2 & 3 & 1 \\
6 & 2 & 3 & 1 & 2 \\
7 & 3 & 1 & 3 & 2 \\
8 & 3 & 2 & 1 & 3 \\
9 & 3 & 3 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The orthogonal array L9 for GA. Figure 6 displays the inverse relationship between the algorithm's capability and the size of the 10 problems considered. Each point presented in Figure 6 represents the means obtained using some algorithm from replicate experiments of the corresponding instances size described above. The best-performing algorithms are expected to exhibit consistently lower values with higher capacities. The graph highlights the outstanding performance of the HMPGA-VNS algorithm, which outperforms the other algorithms in the entire series. Figure 4: Mean S/N ratios plot for each level of the factors (factors represented by capitalized letter in each subfigure are consistent with Table 4). Figure 5: Mean RPD plot for each level of the factors (factors represented by capitalized letter in each subfigure are consistent with Table 4). Furthermore, the performance of the various algorithms is further compared by analyzing the variance of the mean RPD of each algorithm for instances of different problem sizes. The analysis of variance (ANOVA) is utilized to obtain the means and least significant difference (LSD) intervals with a confidence level of 95% for each algorithm, as depicted in Figure 7. The statistical analysis indicates a significant difference in performance between HMPGA-VNS and all other algorithms. Remarkably, HMPGA-VNS outperforms all other algorithms, while the performance of the other algorithms, in terms of mean RPD, does not exhibit any significant difference. ### Sensitivity Analysis

This section aims to examine how the solution is affected by demand, product shelf life, and waste rate. To achieve this, the different values for these parameters in P10 are analyzed. Table 6 demonstrates that the objective function exhibits nearly linear behavior in response to changes in demand. Specifically, when the demand increases or decreases by 40%, the objective function correspondingly increases or decreases by 36.49%. Figure 6: Means plot for the interaction between each algorithm and instances. Figure 7: Means plot and LSD intervals for the Algorithms. In Table 7, the results of the sensitivity analysis for product shelf life in two to six periods are presented. It is observed that extending the product shelf life leads to a reduction in the total cost of the supply chain. Furthermore, Table 8 illustrates that reducing the waste rate can effectively minimize costs by decreasing transportation, production, and waste-related expenses.