## 4 Computational Experiments
### The First Set of Experiments  
For the first set of experiments, six instances (instances 506, 709, 781, 809, 897, and 909) with 80 jobs were used to investigate the effects of the parameters. The parameter  
Figure 5: The procedure for the evolution of the emerging market population in the DILA.  
of controlled probability has 17 separate levels (see Table 2). The single-stage type has 11 levels, and the two-stage type has six levels. The parameter of the phase termination time has three levels: 1, 2, and 3 s. Therefore, there are a total of 51 different combinations of the two major parameters. The remaining parameters of the DILA were set as follows: the fixed length for the MPMX crossover was set to 15, the DC size for the DC procedure was set to 4, the neighborhood structure was set to \(\mathit{INS}(1)+\mathit{INS}(2)+\ldots+\mathit{INS}(8)\), the initial population size was set to 30, and the maximum execution time was set to 40 s. Then, the DILA was applied to each of the 51 combinations to solve the six instances five times each.  
Analysis of variance (ANOVA) was used to analyze the RDI produced by the DILA runs of all the 51 combinations for the six instances. Table 3 presents the results of the ANOVA, showing that the parameter of controlled probability significantly affects the performance of the DILA. Therefore, we applied [PERSON]'s test to test if the performance of any two controlled probabilities is significantly different. Table 4 presents the results of [PERSON]'s test. Note that the different letters indicate the performance of the DILA with the indicated levels being significantly different. The results in Table 4 show that the following combinations of the controlled probabilities produce the best mean RDI: stage 1: (\(p_{a}^{1}=0.5\), \(p_{r}^{1}=0.2\)); stage 2: (\(p_{a}^{2}=0.8\), \(p_{r}^{2}=0.2\)). Furthermore, the results show that the single-stage type produces the six worst mean RDIs. Table 3, the ANOVA table, also shows that the phase termination time does not significantly affect the output. This means that the three levels do not affect the DILA differently. However, the phase termination time of 2 s produces the best mean RDI. Based on the results, these analyses suggest that the best parameters are as follows: controlled probability: stage 1 = (0.50, 0.20) and stage 2 = (0.80, 0.20) and phase termination time: 2 s.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of MAF and MRF** & **Controlled Probability (\(\boldsymbol{p_{a^{\prime}}}\), \(\boldsymbol{p_{r}}\))** \\ \hline \hline  & (0.00, 0.00) \\  & (0.20, 0.20) \\  & (0.20, 0.40) \\  & (0.20, 0.60) \\  & (0.20, 0.80) \\ Single Stage & (0.50, 0.20) \\  & (0.50, 0.50) \\  & (0.80, 0.20) \\  & (1.00, 0.00) \\  & (0.00, 1.00) \\ \hline \hline  & Stage 1= (0.20, 0.20), stage 2 = (0.50, 0.20) \\  & Stage 1= (0.20, 0.20), stage 2 = (0.80, 0.20) \\ Two Stage & Stage 1= (0.50, 0.20), stage 2 = (0.20, 0.20) \\  & Stage 1= (0.80, 0.20), stage 2 = (0.20, 0.20) \\  & Stage 1= (0.80, 0.20), stage 2 = (0.50, 0.20) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The values of the controlled probability.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & \begin{tabular}{c} **Type III Sum of** \\ **Squares** \\ \end{tabular} & \begin{tabular}{c} **df** \\ **df** \\ **Square** \\ \end{tabular} & \
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} &
\begin{tabular}{c} **F** \\ **Size** \\ \end{tabular} \\ \hline Corrected model & 20.936  & 23 & 0.91 & 76.385 & 0 \\ Intercept & 19.095 & 1 & 19.095 & 1602.365 & 0 \\ Instances & 20.603 & 5 & 4.121 & 345.773 & 0 \\ Controlled probability & 0.328 & 16 & 0.02 & 1.719 & 0.043 \\ \hline \hline \end{tabular}
\end{table}
Table 3: ANOVA table for testing the significance of the major parameters of DILA.