Figure 1
Echo State Network diagram.
Figure 2
Grey wolf’s initial position.
Figure 3
Grey wolf location update.
| Algorithm GWO_ESN |
| Optimize W out |
| function GWO_ESN (Xi, a, A, C, N, Win, W, Wback) |
| position = initialization (m, dim); |
| Wout=position |
| do |
| fitness =ESN (U, Y, M, Wout); |
| If fitness< Xα |
| fitness = Xα |
| X1=position |
| end |
| if fitness>Xα&&fitness< Xβ |
| fitness = Xβ |
| X2=position |
| end |
| if fitness>Xα&&fitness> Xβ&& fitness> Xδ |
| fitness = Xδ |
| X3=position |
| end |
| t=0 |
| for X1, X2, X3 |
| update by Equation (12 13 14) |
| end for |
| update a, A, and C |
| update Xα Xβ Xδ |
| t=t+1 |
| until (t > Max_iteration) |
| Wout=3/sum (X1+X2 +X3) |
| return Wout |
| end function |
Table 1
Data set information.
| No. | Datasets | Data Length | Training set | Testing set |
|---|---|---|---|---|
| 1 | Separation of EEG data | 5001*1 | 2000 | 500 |
| 2 | Railway passenger traffic | 34*8 | 16 | 16 |
| 3 | Food production 1 | 27*8 | 13 | 13 |
| 4 | Food production 1 | 10*10 | 5 | 5 |
| 5 | The Shanghai Composite Index | 400*7 | 200 | 199 |
| 6 | Mackey-Glass | 400*1 | 200 | 199 |
| 7 | Lorenz | 600*1 | 300 | 299 |
Figure 4
Comparison of different model predictions.
Table 2
Mean square error comparison.
| Number | BP | Elman | ESN | RLS_ESN | PSO_ESN | GWO_ESN |
|---|---|---|---|---|---|---|
| 1 | 0.0357 | 0.0164 | 0.0250 | 0.0303 | 0.0217 | 0.0019 |
| 2 | 0.0413 | 0.0058 | 0.0306 | 0.0224 | 0.0272 | 6.2226e–5 |
| 3 | 0.0240 | 0.0253 | 0.0221 | 0.0189 | 0.0189 | 0.0013 |
| 4 | 0.0464 | 0.1284 | 0.0207 | 0.1023 | 0.0266 | 3.84e–6 |
| 5 | 0.2834 | 0.0887 | 0.0086 | 0.0005 | 0.1241 | 1.6817e–6 |
| 6 | 0.0362 | 0.0214 | 0.0122 | 0.0056 | 0.0435 | 0.0011 |
| 7 | 0.0413 | 0.0326 | 0.0237 | 0.0147 | 0.1267 | 2.65e–4 |
Table 3
Running time comparison(s).
| Number | BP | Elman | ESN | RLS_ESN | PSO_ESN | GWO_ESN |
|---|---|---|---|---|---|---|
| 1 | 5.0357 | 8.9908 | 3.1273 | 6.0547 | 240.4544 | 30.3024 |
| 2 | 4.1332 | 4.8048 | 2.0346 | 4.3509 | 80.0272 | 20.3445 |
| 3 | 3.0233 | 3.4559 | 0.2234 | 2.0465 | 100.3323 | 14.3445 |
| 4 | 2.1347 | 5.5456 | 0.4563 | 2.1342 | 90.2314 | 10.8436 |
| 5 | 3.4536 | 6.1877 | 1.1386 | 3.2432 | 130.3213 | 34.2564 |
| 6 | 4.5434 | 7.2331 | 2.0454 | 4.0989 | 205.4512 | 38.0921 |
| 7 | 4.6564 | 6.7789 | 1.8732 | 3.9807 | 180.3455 | 45.6733 |