## 4 Solution Strategies
### The Neighborhood Search by Probability
If T \(\geq\) Ts, then the self-adaptive mutation strategy is used to change the mutation strategies of the vectors. The current practice in egg distribution is based on a greedy algorithm. The computational results are shown in Table 4, and the statistical test has been performed using the Wilcoxon signed-rank test shown in Table 5. The HSADE yields a better solution than all other proposed algorithms, including the current practice, DE, IDE and ISDE. The statistical test indicates that the solutions obtained from our proposed algorithm were significantly different at a \(p\)-value \(\leq\) 0.05 compared to those obtained from the LINGO for 19 instances (Table 5, second row). However, our proposed solution for small-sized instances was not significantly different compared to the LINGO. In Table 5, the fifth column for the HSADE shows that the solutions were significantly different, compared with all algorithms. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Instance**} & \multicolumn{2}{c}{**LINGO**} & \multirow{2}{*}{**Current**} & \multicolumn{5}{c}{**The Proposed Method (Best)**} \\ \cline{2-2} \cline{4-7}  & **Total Cost** & & & **Practice** & **DE** & **IDE** & **ISDE** & **HSADE** \\ \hline S1 & 1836 & 1863 & 1836 & 1836 & 1836 & 1836 \\ S2 & 1880 & 1899 & 1880 & 1880 & 1880 & 1880 \\ S3 & 1750 & 1820 & 1750 & 1750 & 1750 & 1750 \\ S4 & 2056 & 2120 & 2056 & 2056 & 2056 & 2056 \\ S5 & 2344 & 2511 & 2344 & 2344 & 2344 & 2344 \\ M1 & 2740 & 3191 & 2972 & 2906 & 2939 & 2867 \\ M2 & 5652 & 6628 & 6142 & 6177 & 6006 & 5897 \\ M3 & 6233 & 7726 & 6976 & 6746 & 6677 & 6582 \\ M4 & 6657 & 8318 & 7253 & 7078 & 7111 & 7001 \\ M5 & 8315 & 9973 & 9473 & 9134 & 8970 & 8773 \\ M6 & 15,001 & 17,961 & 16,909 & 16,445 & 16,054 & 15,742 \\ M7 & 19,692 & 23,972 & 22,014 & 21,491 & 21,149 & 20,805 \\ L1 & 76,850 & 112,064 & 84,311 & 82,263 & 81,618 & 80,645 \\ L2 & 124,300 & 171,747 & 139,627 & 134,522 & 133,432 & 130,321 \\ L3 & 161,918 & 213,755 & 182,669 & 175,969 & 173,796 & 171,020 \\ L4 & 190,615 & 277,488 & 209,356 & 205,258 & 204,531 & 200,409 \\ L5 & 240,685 & 324,516 & 275,091 & 259,837 & 259,487 & 252,696 \\ L6 & 281,520 & 367,720 & 318,981 & 305,452 & 303,086 & 297,469 \\ CS1 & 400,924 & 539,238 & 444,532 & 435,715 & 426,236 & 421,168 \\ \hline \end{tabular}
\end{table} 
Table 4: Computational results showing the total cost. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Current**} & \multirow{2}{*}{**DE**} & \multirow{2}{*}{**IDE**} & \multirow{2}{*}{**ISDE**} & \multirow{2}{*}{**HSADE**} \\ \cline{2-2} \cline{4-7}  & **Practice** & & & & & \\ \hline LINGO & 0.0001 & 0.001 & 0.001 & 0.001 & 0.001 \\ DE & & & 0.001 & 0.001 & 0.001 \\ IDE & & & & 0.002 & 0.001 \\ ISDE & & & & & 0.001 \\ \hline \end{tabular}
\end{table} 
Table 5: Statistical test results of the total cost obtained from Table 4.  
Additionally, the heuristic performance (_HP_) percentage was measured using the solution obtained from all compared algorithms by comparing it with the optimal solution obtained from the LINGO. The results show that the HSADE algorithm provided 100% _HP_ for the small-sized instance. Based on the medium-sized instance, the range of _HP_ of the HSADE algorithm is 94.66% to 95.85% (with an average of 95.14%), compared to the lower bound solution. Similarly to the medium-sized instances, the large-sized instances demonstrate a range of _HP_ of 94.64% to 95.38% (with an average of 95.06%). The _HP_ of the HSADE algorithm compared with the case study was 95.20%. The average _HP_s of current practice, DE, IDE, ISDE and HSADE algorithms are 82.92%, 92.48%, 94.40%, 95.11% and 96.40%, respectively (Table  
The relative improvement (_RI_) results are shown in Table 7. The total costs of the solutions obtained from the current practice were compared with the DE, IDE, ISDE and HSADE algorithms. The results show that the HSADE algorithm outperforms all other algorithms (Figure 9).