## 5 Computational Framework and Result  
The proposed metaheuristics were coded in C++ and simulated on a computer with Intel (R) Core i7-3520M CPU @ 2.90 GHz Ram 8.00 GB. We tested our algorithms on four test instances: small, medium, large, and case study. The simulation was executed five times, and the best solution among all was selected. Details of the test instances are shown in Table 7.  
Table 7 shows that we tested 37 sample data (12 small, 12 medium, and 12 large sample data, and 1 case study). For small test instances, the proposed methods were tested and compared with the optimal solution obtained from Lingo V.11 (mathematical method). For the medium and large samples, the proposed method was compared with the lower bound that was obtained by Lingo v.11 within 72 h of computation. \(P_{jm}\) is the processing time of job \(j\) of machine \(m\) (in minutes). \(E_{jm}\) is the energy used to produce job \(j\) on machine \(m\) and then converted into money units (THB). \(B\) is a constant number (THB), which is the production-overhead cost per hour of production in the factory. The proposed method was compared with the result of a traditional DE algorithm and the current practice method (CU). Details of the investigated algorithms are shown in Table 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Group Test Instance** & **Number of Test Instances** & \(P_{jm}\) **Number of** **(m)** & **Number of Jobs** & **Number of Machines** & \(E_{jm}\) **(THB)** & \(T^{\text{MAX}}\) & \(B\) & \(L^{\text{MAX}}\) \\ \hline Small & 12 & 4–30 & 5–30 & 2–5 & 30–75 & 20–30\% & 10–50 & 10–100 \\ Medium & 12 & 4–20 & 40–52 & 3–5 & 30–75 & 20–30\% & 10–50 & 10–100 \\ Large & 12 & 4–20 & 80–134 & 5–8 & 30–75 & 20–30\% & 10–50 & 10–100 \\ Case study & 1 & 4–20 & 201 & 11 & 30–75 & 20–30\% & 10–50 & 10–100 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Test-instance details. +++ ==ERROR: No output for this page==
Table 8 shows that six algorithms were tested in the provided sample datasets. The performance of VaNAS and other proposed methods was compared with that of a traditional DE. The first experiment was executed with the small and medium test instances. The stopping criterion for Lingo was the time period when it found the optimal solution; then, it collected the best solution and computation time. The stopping criteria for all proposed methods were set as 10% of the lowest computation time of Lingo. In this case, Lingo's lowest computation time to find the optimal solution was 651 s; thus, the stopping criteria of all proposed methods were set to 65 s. The percentage difference of all proposed methods with the obtained result from Lingo was found using Equation (26). Five replications were executed for each proposed method, and the best solution among the five runs is shown in Table 9. The statistical test is shown in Table 10.  
\[\%diff=\frac{\left(F_{opt}-F_{H}\right)}{F_{Opt}}\times 100\%\] (26)  
where \(F_{opt}\) is the solution obtained by Lingo during the predefined computation time, and \(F_{H}\) is the solution obtained by the proposed methods. The solutions are shown in Tables 9-14. \begin{table} \
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm** & **Detail** \\ \hline DE & Traditional DE \\ \hline CU & Current practice procedure \\ \hline VaNAS & Variable neighborhood strategy adaptive search \\ \hline SDR & Solution destroy and repair methods \\ \hline TTM & Track-transition methods \\ \hline MF & Multiplier factor \\ \hline \hline \end{tabular} \end{table} 
Table 8: Proposed-method details.