## 6 Conclusions  
This paper proposes the HSADE algorithm to solve the realistic egg distribution problem in Thailand. The problem has dealt with the multi-product (egg sizes), multi-depot vehicle routing problem, with heterogeneous fleets, time window constraints and inventory restrictions to minimize the total cost. The MILP model of egg distribution in Thailand has been formalized. The differential evolution algorithm is selected as the core mechanic to develop the best algorithm to solve the large-sized test instance and the case study. The \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{4}{c}{**Relative Improvement (_RI_) \%**} \\ \cline{2-5}  & **DE** & **IDE** & **ISDE** & **HSADE** \\ \hline S1 & 1.45 & 1.45 & 1.45 & 1.45 \\ S2 & 1.01 & 1.01 & 1.01 & 1.01 \\ S3 & 3.85 & 3.85 & 3.85 & 3.85 \\ S4 & 3.02 & 3.02 & 3.02 & 3.02 \\ S5 & 6.66 & 6.66 & 6.66 & 6.66 \\ M1 & 6.87 & 8.94 & 7.90 & 10.16 \\ M2 & 7.34 & 6.81 & 9.39 & 11.03 \\ M3 & 9.71 & 12.69 & 13.58 & 14.81 \\ M4 & 12.81 & 14.91 & 14.52 & 15.84 \\ M5 & 5.02 & 8.42 & 10.06 & 12.04 \\ M6 & 5.86 & 8.45 & 10.62 & 12.36 \\ M7 & 8.17 & 10.35 & 11.78 & 13.22 \\ L1 & 24.77 & 26.60 & 27.17 & 28.04 \\ L2 & 18.71 & 21.68 & 22.31 & 24.13 \\ L3 & 14.55 & 17.68 & 18.70 & 20.00 \\ L4 & 24.56 & 26.03 & 26.30 & 27.78 \\ L5 & 15.24 & 19.94 & 20.04 & 22.14 \\ L6 & 13.26 & 16.94 & 17.58 & 19.11 \\ CS1 & 17.57 & 19.20 & 20.96 & 21.90 \\ Average & 10.55 & 12.35 & 12.99 & 14.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The relative improvement (_RI_) results for testing instances. Figure 9: The relative improvement (_RI_) results for testing instances. constructive heuristics adopt the initial solution to guide the solution through a customer clustering method. The hybrid and self-adaptive differential evolution were developed. The hybrid with neighborhood structure, including \(k\)-random inter-exchange and \(k\)-random insertion by probability, \(k\)-random intra-exchange, and \(k\)-random intra-insertion, were implemented to avoid trapping in a local optimum. The self-adaptive mutation strategy was developed with a new self-adaptive algorithm to change the mutation formula. The optimal solution for a small-sized instance and the lower bound solution for medium and large-sized problems are the criterion to measure the Heuristic Performance (_HP_) with our proposed algorithm. The current practice of egg distribution in Thailand has been developed to measure relative improvement (_RI_) to demonstrate the ability to improve our proposed algorithm from the current practice. For the computation result of our HSADE algorithm applied to egg distribution, LINGO solves the MILP model with a prespecified time limit for 19 instances. The test results show that our proposed algorithm can provide the optimal solution; the HSADE algorithm significantly outperforms LINGO both in solution quality and CPU time. The heuristic performance (_HP_) showed that the HSADE algorithm obtained a near-optimal solution ranging from 94.64% to 95.85% and the current practice obtained a solution ranging from 68.58% to 85.87% for medium and large-sized instances. The average heuristic performance (_HP_) of HSADE is 96.40% for all instances. Additionally, the relative improvement (_RI_) has been compared to the total cost of the solution obtained from the current practice with DE, IDE, ISDE, and HSADE algorithms. Those algorithms had average relative improvements equal to 10.55%, 12.35%, 12.99%, and 14.13%, respectively. The statistical results obtained using the Wilcoxon signed-rank test showed that compared the total cost of LINGO and our proposed algorithm. As a result, our proposed algorithm obtains solutions that are not significantly different from the optimal solution for the small-sized instances. Additionally, the statistical test for large-sized instances showed that the proposed HSADE algorithm was significantly better than the DE, IDE, and ISDE algorithms, respectively.