## 4 Solution Strategies
### The Neighborhood Search by Probability
The second column shows instance names, and the third to sixth columns show the characteristics of the problems in which the number of depots, the number of customers, size of demand (egg trays) (egg trays 36 eggs), the number of vehicles of each depot, number of product types, and capacity size of the vehicles. Note that the size of demand is randomly generated using a uniform distribution U (min, max). The vehicles' capacity size, including two fleet sizes, is the small fleet size (S) or large fleet size (L). From Table 3, the number of depots is divided into three groups, which are small, medium, and large-scale test instances. There are two to three, four and six for small, medium, and large-sized instances, respectively. Sizes of demand (egg trays) for small, medium, and large-sized test instances are between 10 to 60 egg trays, 20 to 100 egg trays, and 40 to 150 egg trays. The number of customers for small, medium, and large-sized test instances is 12-20, 50-100, and 160-360 nodes, respectively. The number of vehicles in each depot for small, medium, and large-sized test instances are 4, 8-15, 40-65 vehicles, respectively. The number of product types for small, medium, and large-sized test instances are 2-4, 4-5, 6 product types, respectively. The capacity sizes of vehicles for small, medium, and large-sized test instances are 60/100, 80/120, and 150/200. Moreover, presently, the case study company has the customers' orders size of demand ranging from 30 to 300 for 500 \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Size** & **Instance** & **No. Depot** & **No. Customer** & \begin{tabular}{c} **Size of Demand** \\ **(Egg Trays)** \\ \end{tabular} & \begin{tabular}{c} **No. Vehicles** \\ **of Each** \\ **Depot** \\ \end{tabular} & \
\begin{tabular}{c} **No. Product** \\ **Types** \\ \end{tabular} &
\begin{tabular}{c} **Capacity** \\ **Size of** \\ **Vehicles S/L** \\ \end{tabular} \\ \hline Small & S1 & 2 & 12 & U (10,60) & 4 & 2 & 60/100 \\  & S2 & 2 & 12 & U (10,60) & 4 & 2 & 60/100 \\  & S3 & 3 & 15 & U (10,60) & 4 & 2 & 60/100 \\  & S4 & 3 & 15 & U (10,60) & 4 & 3 & 60/100 \\  & S5 & 3 & 20 & U (10,60) & 4 & 3 & 60/100 \\ Medium & M1 & 4 & 50 & U (20,100) & 8 & 4 & 80/120 \\  & M2 & 4 & 50 & U (20,100) & 8 & 4 & 80/120 \\  & M3 & 4 & 50 & U (20,100) & 10 & 4 & 80/120 \\  & M4 & 4 & 75 & U (20,100) & 10 & 4 & 80/120 \\  & M5 & 4 & 75 & U (20,100) & 15 & 5 & 80/120 \\  & M6 & 4 & 100 & U (20,100) & 15 & 5 & 80/120 \\  & M7 & 4 & 100 & U (20,100) & 15 & 5 & 80/120 \\ Large & L1 & 6 & 160 & U (40,150) & 40 & 6 & 150/200 \\  & L2 & 6 & 160 & U (40,150) & 45 & 6 & 150/200 \\  & L3 & 6 & 240 & U (40,150) & 50 & 6 & 150/200 \\  & L4 & 6 & 240 & U (40,150) & 55 & 6 & 150/200 \\  & L5 & 6 & 360 & U (40,150) & 60 & 6 & 150/200 \\  & L6 & 6 & 360 & U (40,150) & 65 & 6 & 150/200 \\  & CS1 & 8 & 500 & U (30,300) & 250 & 6 & 300/400 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The factors of data generated for each problem instance. customers per day. The case study company has 250 vehicles per eight depots with capacity sizes of vehicles 300/400 to transport the products. The number of product types is six. We set the computation time as the stopping criteria of our proposed method. The limited computation time of LINGO is set to 30 min, 1440 min and 4320 min for small, medium and large-sized instances, respectively. Our proposed method used a limited computation time of 5 min, 15 min and 30 min for small, medium and large-sized instances, respectively. The traditional DE, DE combined initial solution (IDE), and IDE combined self-adaptive (ISDE) were selected for comparison with the HSADE algorithm. The parameter values used in our implementation include scaling factor (\(F\)) = 2, \(Cmin\) = 0.5, \(Cmax\) = 1 [32] and the population is set to 25. The DE and IDE used the DE/rand/1 (Equation (30)) mutation strategy. The self-adaptive mutation strategy is set as Ts = 0.2 \(\times\) Tmax for using the single mutation strategy DE/rand/1 when T \(<\) Ts.