Research Article
An Improved Real-Coded Population-Based Extremal Optimization Method for Continuous Unconstrained Optimization Problems
Table 2
Comparative performances of IRPEO with the GAs [
24] and PEO [
22] for test functions.
| | Problems | Optimum | Algorithm | | (rank) | | SD (rank) | Final rank |
| | 0 (min) | IRPEO | | | | | 1 | | GA-ADM [24] | / | (7) | / | (6) | 7 | | GA-RM [24] | / | (4) | / | (3) | 4 | | GA-PLM [24] | / | (2) | / | (2) | 2 | | GA-NUM [24] | / | (3) | / | (4) | 3 | | GA-MNUM [24] | / | (6) | / | (7) | 6 | | GA-PM [24] | / | (8) | / | (8) | 8 | | PEO [22] | | (5) | | (5) | 5 |
| | 3 (max) | IRPEO | 3.00000 | 3.00000 | 3.00000 | | 1 | | GA-ADM [24] | / | 3.00000 (1) | / | (2) | 2 | | GA-RM [24] | / | 2.99995 (4) | / | (4) | 4 | | GA-PLM [24] | / | 2.99998 (3) | / | (3) | 3 | | GA-NUM [24] | / | 2.99985 (5) | / | (5) | 5 | | GA-MNUM [24] | / | 2.98028 (7) | / | (7) | 7 | | GA-PM [24] | / | 2.99358 (6) | / | (6) | 6 |
| | 1 (max) | IRPEO | 1.000000 | 1.000000 | 1.000000 | | 1 | | GA-ADM [24] | / | 1.000000 (1) | / | (2) | 2 | | GA-RM [24] | / | 0.999994 (5) | / | (4) | 5 | | GA-PLM [24] | / | 0.999996 (4) | / | (3) | 4 | | GA-NUM [24] | / | 0.999986 (6) | / | (5) | 6 | | GA-MNUM [24] | / | 0.999997 (3) | / | (7) | 3 | | GA-PM [24] | / | 0.999560 (7) | / | (6) | 7 |
| | 0 (min) | IRPEO | | | | | 1 | | GA-ADM [24] | / | (2) | / | (5) | 2 | | GA-RM [24] | / | (4) | / | (7) | 4 | | GA-PLM [24] | / | (3) | / | (6) | 3 | | GA-NUM [24] | / | (5) | / | (3) | 5 | | GA-MNUM [24] | / | (6) | / | (2) | 6 | | GA-PM [24] | / | (7) | / | (4) | 7 |
| | 0 (min) | IRPEO | | | | | 1 | | GA-ADM [24] | / | (7) | / | (6) | 7 | | GA-RM [24] | / | (3) | / | (3) | 3 | | GA-PLM [24] | / | (2) | / | (2) | 2 | | GA-NUM [24] | / | (4) | / | (4) | 4 | | GA-MNUM [24] | / | (8) | / | (8) | 8 | | GA-PM [24] | / | (6) | / | (7) | 6 | | PEO [22] | | (5) | | (5) | 5 |
| | 0 (min) | IRPEO | | | | | 1 | | GA-ADM [24] | / | (4) | / | (4) | 4 | | GA-RM [24] | / | (7) | / | (6) | 7 | | GA-PLM [24] | / | (5) | / | (5) | 5 | | GA-NUM [24] | / | (6) | / | (7) | 6 | | GA-MNUM [24] | / | (3) | / | (3) | 3 | | GA-PM [24] | / | (8) | / | (8) | 8 | | PEO [22] | | (2) | | (2) | 2 |
| | 0 (min) | IRPEO | | (3) | | (3) | 3 | | GA-ADM [24] | / | (1) | / | (1) | 1 | | GA-RM [24] | / | (5) | / | (5) | 5 | | GA-PLM [24] | / | (4) | / | (4) | 4 | | GA-NUM [24] | / | (6) | / | (6) | 6 | | GA-MNUM [24] | / | (1) | / | (1) | 1 | | GA-PM [24] | / | (7) | / | (7) | 7 |
| | 0 (min) | IRPEO | | (3) | | (3) | 3 | | GA-ADM [24] | / | (1) | / | (1) | 1 | | GA-RM [24] | / | (6) | / | (5) | 6 | | GA-PLM [24] | / | (4) | / | (4) | 4 | | GA-NUM [24] | / | (5) | / | (6) | 5 | | GA-MNUM [24] | / | (1) | / | (1) | 1 | | GA-PM [24] | / | (7) | / | (7) | 7 |
| | 0 (min) | IRPEO | | (3) | | (3) | 3 | | GA-ADM [24] | / | (1) | / | (1) | 1 | | GA-RM [24] | / | (6) | / | (6) | 6 | | GA-PLM [24] | / | (4) | / | (4) | 4 | | GA-NUM [24] | / | (5) | / | (5) | 5 | | GA-MNUM [24] | / | (1) | / | (1) | 1 | | GA-PM [24] | / | (7) | / | (7) | 7 |
| | 0 (min) | IRPEO | | (3) | | (3) | 3 | | GA-ADM [24] | / | (1) | / | (1) | 1 | | GA-RM [24] | / | (5) | / | (5) | 5 | | GA-PLM [24] | / | (4) | / | (4) | 4 | | GA-NUM [24] | / | (6) | / | (6) | 6 | | GA-MNUM [24] | / | (1) | / | (1) | 1 | | GA-PM [24] | / | (7) | / | (7) | 7 |
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