Table 7 Standard deviation of repetitive cases.
Algorithm | Function dimension | ||||||
|---|---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 15 | 20 | |
(a) Ackley function | |||||||
MA | 2.6E-01 | 7.9E-01 | 7.7E-01 | 7.4E-01 | 7.3E-01 | 7.4E-01 | 5.8E-01 |
PSO | 5.4E-02 | 1.8E-01 | 8.3E-01 | 1.0E + 00 | 9.2E-01 | 6.4E-01 | 5.1E-01 |
GA | 5.4E-05 | 1.7E-03 | 7.7E-03 | 1.8E-02 | 2.5E-01 | 1.1E + 00 | 9.9E-01 |
FA | 1.2E + 00 | 1.6E + 00 | 1.5E + 00 | 1.4E + 00 | 1.3E + 00 | 9.5E-01 | 8.4E-01 |
SCA | 1.8E + 00 | 1.1E + 00 | 9.0E-01 | 6.7E-01 | 7.2E-01 | 5.1E-01 | 3.6E-01 |
HSI-MA | 2.3E-09 | 9.1E-07 | 1.6E-05 | 5.6E-05 | 1.4E-04 | 1.6E-01 | 5.6E-01 |
(b) Rastrigin Function | |||||||
MA | 3.6E-01 | 8.4E-01 | 1.6E + 00 | 2.3E + 00 | 2.3E + 00 | 5.7E + 00 | 1.0E + 01 |
PSO | 2.1E-01 | 2.1E + 00 | 4.9E + 00 | 6.8E + 00 | 7.9E + 00 | 1.3E + 01 | 1.2E + 01 |
GA | 7.0E-07 | 3.6E-01 | 1.1E + 00 | 1.9E + 00 | 2.2E + 00 | 6.2E + 00 | 1.4E + 01 |
FA | 2.6E + 00 | 6.8E + 00 | 1.1E + 01 | 1.3E + 01 | 1.7E + 01 | 2.0E + 01 | 2.5E + 01 |
SCA | 4.5E + 00 | 7.7E + 00 | 1.0E + 01 | 1.3E + 01 | 1.3E + 01 | 1.7E + 01 | 2.2E + 01 |
HSI-MA | 1.4E-13 | 7.4E-08 | 3.0E-01 | 6.7E-01 | 9.3E-01 | 2.3E + 00 | 5.0E + 00 |
(c) Drop-wave function | |||||||
MA | 4.4E-02 | 7.2E-02 | 8.8E-02 | 9.3E-02 | 1.1E-01 | 1.1E-01 | 1.1E-01 |
PSO | 1.0E-02 | 1.2E-16 | 6.2E-02 | 9.7E-02 | 1.1E-01 | 1.1E-01 | 9.1E-02 |
GA | 3.0E-02 | 4.1E-02 | 9.5E-02 | 1.6E-01 | 1.9E-01 | 8.2E-02 | 2.4E-02 |
FA | 7.9E-02 | 1.9E-01 | 1.2E-01 | 8.6E-02 | 2.8E-02 | 1.3E-02 | 5.8E-03 |
SCA | 2.0E-01 | 1.5E-01 | 1.1E-01 | 3.3E-02 | 2.2E-02 | 8.2E-03 | 4.9E-03 |
HSI-MA | 2.8E-13 | 1.8E-02 | 2.8E-02 | 5.5E-02 | 7.9E-02 | 1.2E-01 | 1.1E-01 |
(d) Griewank function | |||||||
MA | 5.1E-08 | 4.3E-07 | 4.1E-04 | 4.2E-04 | 1.0E-06 | 1.4E-06 | 1.7E-06 |
PSO | 3.1E-03 | 9.7E-03 | 1.9E-02 | 3.7E-02 | 1.3E-02 | 2.4E-02 | 3.3E-02 |
GA | 3.0E-02 | 4.1E-02 | 9.5E-02 | 1.6E-01 | 1.9E-01 | 8.2E-02 | 2.4E-02 |
FA | 6.5E-03 | 9.0E-02 | 1.5E-01 | 2.1E-01 | 1.9E-01 | 1.1E-01 | 5.8E-02 |
SCA | 4.4E-01 | 1.9E-01 | 1.7E-01 | 1.1E-01 | 4.9E-02 | 2.3E-02 | 7.0E-03 |
HSI-MA | 2.2E-17 | 1.3E-12 | 8.8E-11 | 9.7E-10 | 3.2E-09 | 1.5E-08 | 3.9E-08 |
(e) Levy function | |||||||
MA | 1.4E-08 | 3.9E-02 | 8.5E-02 | 9.8E-02 | 1.1E-01 | 1.7E-01 | 1.7E-01 |
PSO | 3.0E-17 | 1.5E-02 | 1.1E-01 | 1.6E-01 | 4.8E-01 | 1.2E + 00 | 1.7E + 00 |
GA | 1.0E-08 | 1.2E-06 | 5.1E-05 | 1.6E-04 | 3.2E-04 | 5.4E-01 | 1.5E + 00 |
FA | 3.3E-03 | 4.3E-01 | 9.4E-01 | 1.3E + 00 | 1.6E + 00 | 2.9E + 00 | 4.2E + 00 |
SCA | 3.0E-01 | 6.4E-01 | 1.2E + 00 | 2.2E + 00 | 2.4E + 00 | 3.8E + 00 | 4.2E + 00 |
HSI-MA | 3.8E-16 | 3.7E-13 | 9.7E-11 | 2.0E-09 | 1.1E-08 | 1.7E-07 | 9.7E-07 |
(f) Weierstrass function | |||||||
MA | 1.9E-02 | 7.2E-01 | 9.1E-01 | 1.0E + 00 | 1.3E + 00 | 1.6E + 00 | 1.9E + 00 |
PSO | 3.3E-02 | 4.2E-01 | 9.0E-01 | 1.0E + 00 | 1.5E + 00 | 1.7E + 00 | 2.4E + 00 |
GA | 6.3E-03 | 7.1E-01 | 1.8E + 00 | 2.0E + 00 | 2.0E + 00 | 2.5E + 00 | 2.8E + 00 |
FA | 3.5E-01 | 8.0E-01 | 1.3E + 00 | 1.5E + 00 | 1.6E + 00 | 1.8E + 00 | 2.0E + 00 |
SCA | 5.0E-01 | 7.2E-01 | 9.0E-01 | 9.0E-01 | 1.2E + 00 | 1.6E + 00 | 1.6E + 00 |
HSI-MA | 1.8E-03 | 7.5E-02 | 2.8E-01 | 4.4E-02 | 6.5E-01 | 1.1E + 00 | 1.5E + 00 |
(g) Sphere Function | |||||||
MA | 4.6E-08 | 3.7E-07 | 1.1E-06 | 2.0E-06 | 3.1E-06 | 8.3E-06 | 1.2E-05 |
PSO | 1.1E-03 | 6.9E-04 | 1.9E-03 | 7.5E-03 | 1.7E-05 | 3.5E-02 | 2.2E-01 |
GA | 7.1E-09 | 1.4E-06 | 1.1E-05 | 1.3E-04 | 7.6E-04 | 1.5E-02 | 2.3E-01 |
FA | 6.2E-03 | 8.7E-01 | 2.9E + 00 | 5.6E + 00 | 8.9E + 00 | 1.5E + 01 | 1.5E + 01 |
SCA | 7.0E-01 | 3.3E + 00 | 5.6E + 00 | 6.6E + 00 | 9.1E + 00 | 9.5E + 00 | 1.3E + 01 |
HSI-MA | 2.1E-17 | 5.3E-14 | 2.6E-11 | 5.4E-10 | 3.5E-09 | 6.0E-08 | 2.3E-07 |
