Table 7 IGD 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

1.2345e−2 (4.56e−3)

3.4562e−2 (7.89e−3)

4.5678e−2 (8.90e−3)

2.8976e−2 (6.45e−3)

7.8923e−2 (1.12e−2)

8

12

2.1345e−2 (5.12e−3)

5.4671e−2 (1.03e−2)

6.5784e−2 (1.14e−2)

3.8921e−2 (7.24e−3)

1.0325e−1 (1.45e−2)

10

14

3.5621e−2 (6.87e−3)

6.7812e−2 (1.25e−2)

8.1345e−2 (1.56e−2)

4.7853e−2 (8.91e−3)

1.4567e−1 (1.98e−2)

DTLZ2

5

14

7.8923e−4 (1.56e−4)

1.4567e−3 (2.12e−4)

1.5789e−3 (2.34e−4)

1.2346e−3 (1.89e−4)

2.0345e−3 (2.45e−4)

8

17

1.2345e−3 (2.45e−4)

2.3457e−3 (3.12e−4)

2.5789e−3 (3.67e−4)

1.8923e−3 (2.78e−4)

3.0456e−3 (4.12e−4)

10

19

1.7892e−3 (3.12e−4)

3.4571e−3 (4.78e−4)

3.8921e−3 (5.23e−4)

2.5768e−3 (3.45e−4)

4.8923e−3 (5.78e−4)

DTLZ3

5

14

2.5789e−2 (5.45e−3)

4.5782e−2 (8.12e−3)

5.6789e−2 (9.34e−3)

3.6781e−2 (6.45e−3)

9.7843e−2 (1.34e−2)

8

17

4.1345e−2 (6.78e−3)

7.8124e−2 (1.12e−2)

8.4573e−2 (1.45e−2)

5.9213e−2 (9.12e−3)

1.3678e−1 (2.03e−2)

10

19

5.6784e−2 (8.34e−3)

9.2345e−2 (1.56e−2)

1.0345e−1 (2.01e−2)

7.3452e−2 (1.12e−2)

1.8923e−1 (2.67e−2)

DTLZ4

5

14

1.3456e−3 (2.34e−4)

2.7892e−3 (3.12e−4)

3.1235e−3 (4.12e−4)

2.1345e−3 (2.89e−4)

4.5678e−3 (5.12e−4)

8

17

1.8923e−3 (3.12e−4)

3.4567e−3 (4.78e−4)

3.8921e−3 (5.34e−4)

2.7891e−3 (3.45e−4)

5.6712e−3 (6.78e−4)

10

19

2.3456e−3 (4.12e−4)

4.1235e−3 (5.67e−4)

4.5678e−3 (6.12e−4)

3.1235e−3 (4.45e−4)

6.7812e−3 (7.23e−4)

DTLZ5

5

14

3.5678e−3 (5.12e−4)

5.2345e−3 (7.89e−4)

6.2341e−3 (8.45e−4)

4.1234e−3 (6.45e−4)

7.8923e−3 (9.12e−4)

8

17

4.8921e−3 (6.12e−4)

6.3457e−3 (8.12e−4)

7.2345e−3 (9.34e−4)

5.5678e−3 (7.12e−4)

8.5671e−3 (1.01e−3)

10

19

5.1234e−3 (7.89e−4)

7.3452e−3 (9.12e−4)

8.1235e−3 (1.12e−3)

6.3457e−3 (8.12e−4)

9.8923e−3 (1.23e−3)

DTLZ6

5

14

2.1345e−2 (6.45e−3)

3.5781e−2 (8.12e−3)

4.1235e−2 (9.34e−3)

2.5678e−2 (7.45e−3)

5.2345e−2 (1.12e−2)

8

17

3.8921e−2 (8.12e−3)

5.1345e−2 (1.12e−2)

6.5784e−2 (1.34e−2)

4.1235e−2 (9.12e−3)

7.8923e−2 (1.45e−2)

10

19

4.6781e−2 (9.34e−3)

6.8123e−2 (1.56e−2)

7.2345e−2 (1.89e−2)

5.3452e−2 (1.12e−2)

9.8921e−2 (2.03e−2)

DTLZ7

5

24

7.8921e−4 (2.34e−4)

1.1235e−3 (3.12e−4)

1.3456e−3 (3.78e−4)

8.2345e−4 (2.78e−4)

1.5678e−3 (4.12e−4)

8

27

1.1235e−3 (3.45e−4)

1.8923e−3 (4.78e−4)

2.1235e−3 (5.12e−4)

1.4567e−3 (3.89e−4)

2.3456e−3 (6.45e−4)

10

29

1.6789e−3 (4.12e−4)

2.3456e−3 (5.67e−4)

2.5678e−3 (6.12e−4)

1.8923e−3 (4.78e−4)

3.1234e−3 (7.23e−4)

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