Table 4 Comparison of %GAP of HES with other benchmark problems.

From: A hybrid evolution strategies algorithm for non-permutation flow shop scheduling problems

Instance

DMU

MHD-ACS

NNP-ACS

IG

HIGA

HES

%GAP

%GAP

%GAP

%GAP

%GAP

%GAP

DMU_20_15_3

32.29%

31.78%

20.66%

16.73%

14.04%

14.04%

DMU_20_15_6

30.81%

27.65%

24.68%

19.57%

20.20%

20.20%

DMU_20_15_4

26.09%

26.33%

23.19%

18.72%

17.02%

17.02%

DMU_20_15_10

25.79%

24.71%

22.11%

18.36%

17.34%

17.34%

DMU_20_15_5

25.16%

23.35%

17.26%

11.91%

11.85%

11.85%

DMU_20_20_1

27.67%

27.62%

26.85%

20.71%

19.62%

19.62%

DMU_20_20_3

27.17%

25.68%

24.91%

17.94%

20.28%

20.28%

DMU_20_20_9

26.70%

26.14%

20.96%

16.30%

14.04%

14.04%

DMU_20_20_2

25.90%

24.89%

21.90%

16.10%

16.72%

16.72%

DMU_20_20_10

23.38%

23.33%

19.12%

14.62%

17.68%

17.68%

DMU_30_15_3

30.00%

29.60%

22.56%

14.48%

12.21%

12.21%

DMU_30_15_4

30.00%

29.51%

23.36%

14.88%

15.17%

15.17%

DMU_30_15_9

26.28%

26.18%

22.13%

14.20%

15.39%

15.39%

DMU_30_15_8

24.83%

24.57%

16.26%

11.40%

9.82%

9.82%

DMU_30_15_6

23.02%

23.06%

21.82%

15.08%

15.99%

15.99%

DMU_30_20_3

28.65%

24.57%

20.56%

13.13%

11.46%

11.46%

DMU_30_20_1

26.51%

25.50%

29.48%

19.51%

19.55%

19.55%

DMU_30_20_6

24.72%

23.80%

20.68%

16.39%

14.21%

14.21%

DMU_30_20_10

24.41%

20.90%

20.19%

13.04%

13.02%

13.02%

DMU_30_20_2

22.39%

22.77%

22.81%

15.18%

11.98%

11.98%

DMU_40_15_5

25.65%

25.40%

17.28%

7.81%

9.80%

9.80%

DMU_40_15_9

24.07%

23.27%

21.98%

12.23%

15.08%

15.08%

DMU_40_15_2

22.99%

23.48%

19.13%

11.97%

12.95%

12.95%

DMU_40_15_10

22.32%

19.94%

14.60%

5.63%

8.31%

8.31%

DMU_40_15_8

21.65%

21.43%

17.04%

9.25%

10.90%

10.90%

DMU_40_20_3

25.66%

25.28%

26.61%

15.12%

26.49%

26.49%

DMU_40_20_9

25.51%

24.97%

23.17%

11.49%

20.42%

20.42%

DMU_40_20_6

24.69%

24.81%

24.46%

14.71%

20.63%

20.63%

DMU_40_20_7

23.31%

22.98%

20.02%

9.98%

17.86%

17.86%

DMU_40_20_5

20.10%

20.06%

21.88%

9.28%

20.13%

20.13%

DMU_50_15_6

21.99%

21.32%

20.17%

8.98%

12.58%

12.58%

DMU_50_15_5

20.83%

17.95%

15.14%

10.59%

8.59%

8.59%

DMU_50_15_1

19.65%

19.43%

16.25%

6.36%

9.58%

9.58%

DMU_50_15_8

19.58%

19.74%

16.41%

8.38%

11.19%

11.19%

DMU_50_15_2

18.66%

18.08%

15.56%

8.30%

10.67%

10.67%

DMU_50_20_2

31.13%

31.10%

25.16%

17.11%

18.64%

18.64%

DMU_50_20_1

26.77%

26.50%

19.71%

9.23%

8.42%

8.42%

DMU_50_20_7

24.59%

24.70%

23.89%

14.74%

11.01%

11.01%

DMU_50_20_8

24.55%

23.76%

22.23%

9.16%

7.47%

7.47%

DMU_50_20_4

24.35%

24.48%

25.01%

15.61%

12.74%

12.74%