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Table12. The average makespan and average energy cost obtained by MOEA/D-MR, NSGA-II, SPEA2, and IMOEA/DTL.
Makespan (Minute)
Energy Cost (CNY)
Problems
MOEA/D-MR NSGA-II SPEA2 IMOEA/DTL MOEA/D-MR NSGA-II
SPEA2 IMOEA/DTL
Job1 Job2 Job3 Job4 Job5 Job6 Job7 Job8 Job9
10,049 11,817 14,104 16,030 18,534 19,603 21,236 23,006 27,008 26,571 28,920 30,127 32,440 35,034 35,787 40,290
10,064 11,864 14,139 16,089 18,537 19,680 21,348 23,044 27,075 26,585 28,914 30,167 32,451 35,093 35,835 40,241
10,053 11,881 14,175 16,128 18,567 19,642 21,337 23,063 27,079 26,584 29,001 30,219 32,510 35,078 35,768 40,253
9939
801,309 964,677
803,965 804,358 966,456 966,000
795,656 957,500
11,800 14,033 16,008 18,460 19,531 21,222 22,953 26,922 26,501 28,886 30,117 32,358 34,972 35,712 40,185
1,158,100 1,302,626 1,520,818 1,610,892 1,777,566 1,916,511 2,223,799 2,193,870 2,427,444 2,565,900 2,699,366 2,887,249 2,984,084 3,380,449
1,161,747 1,159,518 1,150,038 1,304,014 1,303,485 1,291,973 1,521,966 1,521,371 1,511,605 1,608,901 1,610,826 1,596,377 1,779,676 1,778,261 1,768,963 1,921,468 1,918,722 1,908,951 2,226,399 2,224,613 2,213,336 2,193,213 2,193,967 2,183,339 2,426,101 2,424,184 2,408,955 2,568,756 2,566,343 2,551,189 2,700,491 2,697,074 2,684,005 2,887,706 2,886,665 2,876,694 2,985,389 2,985,440 2,971,161 3,385,432 3,383,498 3,368,202
Job10 Job11 Job12 Job13 Job14 Job15 Job16
In China, most of the scheduling jobs of the tissue paper mills are completed by workers based on their experience. The quality of the scheduling depends on the experience of the workers. In this study, a real scheduling problem is solved by IMOEA/DTL, and the solution is compared with that obtained by workers. The solution obtained by workers has the makespan of 17,035 and the energy cost of 1,368,497. Table 13 indicates that the average makespan obtained by IMOEA/DTL is about 7.5% less than that obtained by the worker. The average energy cost obtained by IMOEA/DTL is about 1.5% less than that obtained by the worker. From Table 13, it can be seen that the minimum energy cost is 1,333,494, and the corresponding makespan is 16,754, which reduces by 2.6% and 1.6%, respectively. The minimum makespan is 15,367, and the corresponding energy cost is 1,361,331, which decrease by 9.8% and 0.5%, respectively. The largest energy cost is 1,375,361, which is 0.5% higher than the cost obtained by the worker, but the corresponding makespan is reduced by 9.5%. The largest makespan is 18,675, which is 8.8% higher than the cost obtained by the worker, but the corresponding energy cost is reduced by 2.5%. It can be concluded that IMOEA/DTL can reduce both the energy cost and the makespan. Although the maximum makespan and the maximum energy cost are larger than those obtained by the worker, the corresponding energy cost and makespan are smaller. Figure 7 shows the scatter plot for the solutions obtained by IMOEA/DTL and the worker. The energy cost obtained by IMOEA/DTL is lower than that obtained by the worker. The solutions of IMOEA/DTL with lower energy cost than that obtained by the worker account for about 98.56% of the total solutions of IMOEA/DTL. While the solutions of IMOEA/DTL with lower makespan than that obtained by the worker account for about 97.12% of the total solutions of IMOEA/DTL. About 95.68% of the total solutions obtained by IMOEA/DTL have lower energy cost and makespan than those obtained by the worker.
Table 13. The average, maximum, and minimum value of energy cost and makespan obtained by IMOEA/DTL.
Average Makespan (Minute)
Average Energy cost (CNY)
Maximum Makespan (Minute)
Minimum Energy Cost (CNY)
Minimum Makespan (Minute)
Maximum Energy Cost (CNY)
15,754
1,347,737
18,675
1,333,494
15,367
1,375,361
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