Table 6 SD metric evaluation across algorithms using DTLZ problems.

From: Sperm swarm optimization for many objective power flow problems with enhanced performance evaluation in power systems

Problem

Objectives (M)

Decision Variables (D)

MaOSSO

NSGAIII

RVEA

NMPSO

MOEA/D-DE

DTLZ1

5

9

5.6789e−3 (1.23e−3)

9.1236e−3 (2.45e−3)

1.2734e−2 (1.68e−3)

7.4329e−3 (1.55e−3)

3.6512e−2 (4.78e−3)

8

12

9.8723e−3 (1.98e−3)

2.7635e−2 (3.12e−3)

2.5712e−2 (2.71e−3)

1.3925e−2 (2.18e−3)

8.2387e−2 (1.45e−2)

10

14

1.2128e−2 (1.03e−3)

3.1827e−2 (4.09e−3)

3.5684e−2 (2.87e−3)

1.5426e−2 (3.21e−3)

1.2873e−1 (2.10e−2)

DTLZ2

5

14

3.7651e−4 (6.71e−5)

5.1234e−4 (7.23e−5)

5.4367e−4 (8.12e−5)

5.0329e−4 (6.72e−5)

6.3842e−4 (7.89e−5)

8

17

6.1253e−4 (8.92e−5)

8.7346e−4 (1.15e−4)

9.4582e−4 (1.23e−4)

7.3452e−4 (9.81e−5)

1.1024e−3 (1.56e−4)

10

19

7.8941e−4 (1.23e−4)

1.1245e−3 (1.48e−4)

1.2458e−3 (1.76e−4)

8.9425e−4 (1.32e−4)

1.5032e−3 (2.04e−4)

DTLZ3

5

14

2.0156e−2 (4.12e−3)

3.9235e−2 (6.87e−3)

4.7682e−2 (5.12e−3)

2.9348e−2 (4.87e−3)

1.8125e−1 (2.54e−2)

8

17

3.2461e−2 (6.28e−3)

5.7124e−2 (7.64e−3)

6.8435e−2 (9.23e−3)

4.2157e−2 (5.12e−3)

2.4523e−1 (3.45e−2)

10

19

4.8127e−2 (7.34e−3)

6.1285e−2 (8.92e−3)

7.6582e−2 (1.02e−2)

5.9432e−2 (7.14e−3)

3.1142e−1 (4.32e−2)

DTLZ4

5

14

4.5167e−3 (6.25e−4)

5.7429e−3 (7.84e−4)

6.1284e−3 (8.12e−4)

5.9328e−3 (7.21e−4)

7.1423e−3 (8.87e−4)

8

17

6.3218e−4 (7.14e−5)

8.2157e−4 (9.45e−5)

8.9324e−4 (1.12e−4)

7.5249e−4 (8.12e−5)

1.1237e−3 (1.25e−4)

10

19

7.8451e−4 (1.05e−4)

1.0253e−3 (1.28e−4)

1.1428e−3 (1.48e−4)

9.6452e−4 (1.14e−4)

1.5826e−3 (2.12e−4)

DTLZ5

5

14

5.6231e−3 (6.91e−4)

7.3412e−3 (8.45e−4)

8.2341e−3 (9.87e−4)

6.7843e−3 (7.45e−4)

9.1345e−3 (1.12e−3)

8

17

7.4328e−4 (9.34e−5)

9.8124e−4 (1.23e−4)

1.0235e−3 (1.48e−4)

8.4123e−4 (1.05e−4)

1.2345e−3 (1.56e−4)

10

19

8.6452e−4 (1.14e−4)

1.2341e−3 (1.78e−4)

1.4124e−3 (2.03e−4)

1.0345e−3 (1.56e−4)

1.6542e−3 (2.48e−4)

DTLZ6

5

14

1.2342e−2 (2.45e−3)

1.8456e−2 (3.14e−3)

2.0348e−2 (4.12e−3)

1.5432e−2 (3.12e−3)

2.4312e−2 (5.23e−3)

8

17

2.8431e−2 (4.78e−3)

3.6241e−2 (5.12e−3)

4.1243e−2 (6.21e−3)

3.2154e−2 (4.54e−3)

5.1243e−2 (7.83e−3)

10

19

3.4521e−2 (5.87e−3)

4.8123e−2 (6.94e−3)

5.7423e−2 (8.12e−3)

4.9321e−2 (6.45e−3)

6.8324e−2 (9.34e−3)

DTLZ7

5

24

4.1232e−3 (7.81e−4)

5.2145e−3 (9.21e−4)

5.7348e−3 (1.12e−3)

4.8123e−3 (8.45e−4)

6.2148e−3 (1.28e−3)

8

27

5.7345e−3 (9.34e−4)

7.8124e−3 (1.23e−3)

8.2341e−3 (1.45e−3)

6.7124e−3 (1.05e−3)

9.1243e−3 (1.56e−3)

10

29

6.4234e−3 (1.05e−3)

9.1245e−3 (1.56e−3)

1.0345e−2 (1.78e−3)

7.9432e−3 (1.34e−3)

1.2143e−2 (2.12e−3)

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