## 4 Results and Discussion
### Research for Parameters of MODE  
There are some important parameters of MODE like population size, iteration number, crossover probability, and mutation probability. In order to study the impacts of population size and iteration number on the execution time, they were set as different values. The results are shown in Figure 4.  
From Figure 4, it is apparent that population size and iteration number have great influences on the execution time. With the increase of population size, the execution time increased lightly at first stage, then there was a significant decline, afterwards it increased again. When the population size becomes larger, on the one hand, the calculation speed slows down; on the other hand, the global search ability of the algorithms becomes stronger, the optimal solution can be found in less generations. When the population size is 100, the execution time is least. As for the iteration number, the execution time became larger when it increases. Nevertheless, the smaller the iteration number, the less accurate the results. In order to take both execution time and accuracy into account, the iteration number was set as 500. To verify the above analysis of population size and iteration number, we performed 10 runs for each value of population size and iteration number to count the run time. Besides, the hypervolume of each Pareto solution set was also calculated. The reference point is (41,739, 3281,867.2). The results are shown in Tables 4 and 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Value** & **50** & **70** & **100** & **110** & **150** & **200** & **250** \\ \hline Max run time(s) & 6059.25 & 6010 & 4139.3 & 4311.8 & 5395 & 6582.5 & 10,645 \\ Min run time(s) & 1221.25 & 1395 & 1663 & 1745.8 & 1942.3 & 2196.3 & 3665 \\ Average run time(s) & 3177.5 & 3380 & 2323.8 & 2555 & 3211.8 & 3810 & 6537.5 \\ Max hypervolume & 966.2 & 1053.6 & 1140 & 1095.1 & 1103.2 & 1150.3 & 1223 \\ Min hypervolume & 817 & 818.9 & 859.3 & 863 & 834.5 & 853.5 & 869.3 \\ Average hypervolume & 862 & 906.4 & 946.4 & 947.9 & 957.14 & 965.2 & 987.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Run time and hypervolume under different population sizes. Figure 4: Execution time of different population size and iteration number. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Region** & \(P_{Gj}^{max}\) & \(P_{Gj}^{min}\) & \(n\) & \(m\) & \(l\) & \(\Lambda_{G}\) \\ \hline Binhai & 1000 MW & 400 MW & 0.00611 & 38 & 380 & 1200 \\ Dafeng & 1000 MW & 400 MW & 0.00713 & 42.45 & 363 & 1100 \\ Chenjia & 660 MW & 265 MW & 0.00711 & 45.31 & 360 & 1080 \\ Sheyang & 660 MW & 265 MW & 0.00898 & 46.57 & 350 & 880 \\ Funing & 268 MW & 135 MW & 0.00935 & 40.89 & 420 & 760 \\ Yancheng & 135 MW & 70 MW & 0.00828 & 39 & 390 & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of conventional units. Hypervolume can be used to assess the overall performance of Pareto solution set. And the bigger the hypervolume, the better the solution. With the increase of population size or iteration number, the corresponding hypervolume became larger as well. Because it is more likely to find the global optimal solution with larger population sizes or more iterations numbers. From Tables 4 and 5, it can be known that there are some deviations in the execution time and solutions obtained by the same parameters. It is because the initial population of MODE is chosen randomly. Different crossover probabilities or mutation probabilities correspond to different optimization paths, and different optimization paths correspond to different calculation time or optimal solution. In order to explore the influences of crossover probability and mutation probability, we also performed 10 runs for each value of them. The results are shown in Table 6.  
It can be seen that the influences of crossover probability and mutation probability on the execution time and solutions are lighter than the influences of population size and iteration number.