Figure 1.
The original (the four dotted lines) and improved (the four solid lines) S-shaped families of transfer functions.
Figure 1.
The original (the four dotted lines) and improved (the four solid lines) S-shaped families of transfer functions.
Figure 2.
The original (the four dotted lines) and improved (the four solid lines) V-shaped families of transfer functions.
Figure 2.
The original (the four dotted lines) and improved (the four solid lines) V-shaped families of transfer functions.
Figure 3.
The original (the four dotted lines) and improved (the four solid lines) U-shaped families of transfer functions.
Figure 3.
The original (the four dotted lines) and improved (the four solid lines) U-shaped families of transfer functions.
Figure 4.
The original (the four dotted lines) and improved (the four solid lines) Z-shaped families of transfer functions.
Figure 4.
The original (the four dotted lines) and improved (the four solid lines) Z-shaped families of transfer functions.
Figure 5.
The curve of S1(x), V1(x), U1(x), and Z1(x) transfer functions.
Figure 5.
The curve of S1(x), V1(x), U1(x), and Z1(x) transfer functions.
Figure 6.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f1-f7.
Figure 6.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f1-f7.
Figure 7.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f8-f13.
Figure 7.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f8-f13.
Figure 8.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f14-f23.
Figure 8.
The optimal values of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO on f14-f23.
Figure 9.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f1-f7.
Figure 9.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f1-f7.
Figure 10.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f8-f13.
Figure 10.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f8-f13.
Figure 11.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f14-f23.
Figure 11.
The optimal values of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO on f14-f23.
Figure 12.
Thematic maps for the Indian Pines data set with 16 classes. (a) false-color composite; (b) ground truth data with 16 classes in different colors.
Figure 12.
Thematic maps for the Indian Pines data set with 16 classes. (a) false-color composite; (b) ground truth data with 16 classes in different colors.
Figure 13.
The OA, AA, Kappa values of BQUATE2-S1i-SVM, BQUATE2-V1i-SVM, BQUATE1-U1-SVM, BQUATE1-Z1-SVM, SVM, PCA-SVM, and LDA-SVM on Indian Pines.
Figure 13.
The OA, AA, Kappa values of BQUATE2-S1i-SVM, BQUATE2-V1i-SVM, BQUATE1-U1-SVM, BQUATE1-Z1-SVM, SVM, PCA-SVM, and LDA-SVM on Indian Pines.
Figure 14.
The classification maps of the different tested algorithms. (a) Ground truth (b) BQUATE2-S1i-SVM (c) BQUATE2-V1i-SVM (d) BQUATE1-U1-SVM (e) BQUATE1-Z1-SVM (f) SVM (g) PCA-SVM (h) LDA-SVM.
Figure 14.
The classification maps of the different tested algorithms. (a) Ground truth (b) BQUATE2-S1i-SVM (c) BQUATE2-V1i-SVM (d) BQUATE1-U1-SVM (e) BQUATE1-Z1-SVM (f) SVM (g) PCA-SVM (h) LDA-SVM.
Table 1.
The six schemes of Matrix B calculation in QUATRE algorithm.
Table 1.
The six schemes of Matrix B calculation in QUATRE algorithm.
Number | QUATRE/B | Equation |
---|
1 | QUATRE/best/1 | |
2 | QUATRE/rand/1 | |
3 | QUATRE/target/1 | |
4 | QUATRE/target/2 | |
5 | QUATRE/rand/2 | |
6 | QUATRE/best/2 | |
Table 2.
The expressions of the S-shaped families of transfer functions.
Table 2.
The expressions of the S-shaped families of transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 3.
The expressions of the V-shaped families of transfer functions.
Table 3.
The expressions of the V-shaped families of transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 4.
The expressions of the U-shaped families of transfer functions.
Table 4.
The expressions of the U-shaped families of transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 5.
The expressions of the Z-shaped families of transfer functions.
Table 5.
The expressions of the Z-shaped families of transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 6.
The expressions of the improved S-shaped transfer functions.
Table 6.
The expressions of the improved S-shaped transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 7.
The expressions of the improved V-shaped transfer functions.
Table 7.
The expressions of the improved V-shaped transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 8.
The expressions of the improved U-shaped transfer functions.
Table 8.
The expressions of the improved U-shaped transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 9.
The expressions of the improved Z-shaped transfer functions.
Table 9.
The expressions of the improved Z-shaped transfer functions.
Name | Transfer Function |
---|
| |
| |
| |
| |
Table 10.
Unimodal benchmark functions.
Table 10.
Unimodal benchmark functions.
Name | Function | Search Space | D | |
---|
Shpere | | [−100,100] | 30 | 0 |
Schwefel’s function 2.21 | | [−10,10] | 30 | 0 |
Schwefel’s function 1.2 | | [−100,100] | 30 | 0 |
Schwefel’s function 2.22 | | [−100,100] | 30 | 0 |
Rosenbroke | | [−30,30] | 30 | 0 |
Step | | [−100,100] | 30 | 0 |
Dejong’s noisy | | [−1.28,1.28] | 30 | 0 |
Table 11.
Common multimodal benchmark functions.
Table 11.
Common multimodal benchmark functions.
Name | Function | Search Space | D | |
---|
Schwefel | | [−500,500] | 30 | −12,569 |
Rastringin | | [−5.12,5.12] | 30 | 0 |
Ackley | | [−32,32] | 30 | 0 |
| | | | |
Griewank | | [−600,600] | 30 | 0 |
Generalized penalized 1 | | [−50,50] | 30 | 0 |
| | | | |
| | | | |
| | | | |
| | | | |
Generalized penalized 2 | | [−50,50] | 30 | 0 |
| | | | |
| | | | |
| | | | |
Table 12.
Multimodal benchmark functions in low dimension.
Table 12.
Multimodal benchmark functions in low dimension.
Name | Function | Search Space | D | |
---|
Fifth of Dejong | | [−65,65] | 2 | 1 |
Kowalik | | [−5,5] | 4 | 0.00030 |
Six-hump camel back | | [−5,5] | 2 | −1.0316 |
Branins | | [−5,5] | 2 | 0.398 |
Goldstein-Price | | [−2,2] | 2 | 3 |
| | | | |
| | | | |
Hartman 1 | | [1,3] | 3 | −3.86 |
Hartman 2 | | [0,1] | 6 | −3.32 |
Shekel 1 | | [0,10] | 4 | −10.1532 |
Shekel 2 | | [0,10] | 4 | −10.4028 |
Shekel 3 | | [0,10] | 4 | −10.5363 |
Table 13.
The statistical results of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO.
Table 13.
The statistical results of BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE2-S2i, BQUATE2-V2i, and BPSO.
Function | BDE | ABGWO-V3a | BQUATE1-S2 | BQUATE1-V2 | BQUATE2-S2i | BQUATE2-V2i | BPSO |
---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD |
---|
f1 | 3.7333 | 1.8742 | 3.4333 | 1.3047 | 3.8333 | 0.5307 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 7.8333 | 1.1769 |
f2 | 3.5333 | 1.4559 | 2.7000 | 1.3170 | 3.6000 | 0.8137 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 8.1667 | 1.0532 |
f3 | 93.5333 | 69.4057 | 73.6667 | 63.7264 | 116.7000 | 38.7220 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 652.1333 | 178.1527 |
f4 | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 0.9667 | 0.1826 | 0.0000 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | 0.0000 |
f5 | 0.0000 | 0.0000 | 543.4667 | 140.4708 | 333.1667 | 79.2421 | 29.0000 | 0.0000 | 0.0000 | 0.0000 | 47.2000 | 63.5227 | 172.7667 | 233.0352 |
f6 | 13.3000 | 3.0783 | 13.9000 | 2.3134 | 14.6333 | 1.8705 | 7.5000 | 0.0000 | 7.5000 | 0.0000 | 7.5000 | 0.0000 | 24.2333 | 1.9989 |
f7 | 45.0334 | 18.4923 | 32.2667 | 16.4231 | 43.7976 | 7.8121 | 0.0001 | 0.0001 | 0.0022 | 0.0021 | 0.0376 | 0.0306 | 108.7332 | 13.3579 |
f8 | −25.2441 | 0.0000 | −22.6075 | 0.8765 | −18.2038 | 0.7808 | −19.5502 | 0.9293 | −25.2441 | 0.0000 | −25.2441 | 0.0000 | −17.1941 | 1.0525 |
f9 | 3.8667 | 1.5916 | 2.9000 | 1.2134 | 4.0000 | 0.5252 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 7.9667 | 0.9279 |
f10 | 1.2908 | 0.2408 | 1.2618 | 0.2606 | 1.3185 | 0.1427 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 1.9306 | 0.1250 |
f11 | 0.1725 | 0.0507 | 0.1254 | 0.0504 | 0.1020 | 0.0218 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.2978 | 0.0443 |
f12 | 2.3200 | 0.2834 | 2.1036 | 0.2164 | 2.2528 | 0.1022 | 1.6690 | 0.0000 | 1.6690 | 0.0000 | 1.6690 | 0.0000 | 3.0290 | 0.2758 |
f13 | 0.0000 | 0.0000 | 0.3133 | 0.1383 | 0.8500 | 0.0900 | 0.6867 | 0.0860 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.9300 | 0.1264 |
f14 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 |
f15 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 |
f16 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
f17 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 |
f18 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 |
f19 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 |
f20 | −0.1556 | 0.0280 | −0.1440 | 0.0433 | -0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 |
f21 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −1.9948 | 1.8770 |
f22 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −3.1387 | 2.1192 |
f23 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −2.6071 | 2.0951 |
count | 6 + 6 | 3 + 6 | 4 + 6 | 14 + 6 | 15 + 6 | 14 + 6 | 1 + 6 |
Table 14.
The statistical results of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO.
Table 14.
The statistical results of BDE, ABGWO-V3a, BQUATE1-U2, BQUATE1-Z2, BQUATE2-U2i, BQUATE2-Z2i, and BPSO.
Function | BDE | ABGWO-V3a | BQUATE1-U2 | BQUATE1-Z2 | BQUATE2-U2i | BQUATE2-Z2i | BPSO |
---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD |
---|
f1 | 3.7333 | 1.8742 | 3.4333 | 1.3047 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1000 | 0.3051 | 7.8333 | 1.1769 |
f2 | 3.5333 | 1.4559 | 2.7000 | 1.3170 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1000 | 0.3051 | 8.1667 | 1.0532 |
f3 | 93.5333 | 69.4057 | 73.6667 | 63.7264 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.6000 | 1.0700 | 652.1333 | 178.1527 |
f4 | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 0.0000 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | 0.0000 |
f5 | 0.0000 | 0.0000 | 543.4667 | 140.4708 | 29.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 172.7667 | 233.0352 |
f6 | 13.3000 | 3.0783 | 13.9000 | 2.3134 | 7.5000 | 0.0000 | 7.5000 | 0.0000 | 7.5000 | 0.0000 | 7.5667 | 0.3651 | 24.2333 | 1.9989 |
f7 | 45.0334 | 18.4923 | 32.2667 | 16.4231 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0031 | 0.0031 | 1.2172 | 1.1935 | 108.7332 | 13.3579 |
f8 | −25.2441 | 0.0000 | −22.6075 | 0.8765 | −19.1294 | 0.9358 | −25.2441 | 0.0000 | −25.2441 | 0.0000 | −25.2441 | 0.0000 | −17.1941 | 1.0525 |
f9 | 3.8667 | 1.5916 | 2.9000 | 1.2134 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1000 | 0.3051 | 7.9667 | 0.9279 |
f10 | 1.2908 | 0.2408 | 1.2618 | 0.2606 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0717 | 0.2188 | 1.9306 | 0.1250 |
f11 | 0.1725 | 0.0507 | 0.1254 | 0.0504 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0078 | 0.0092 | 0.2978 | 0.0443 |
f12 | 2.3200 | 0.2834 | 2.1036 | 0.2164 | 1.6690 | 0.0000 | 1.6690 | 0.0000 | 1.6690 | 0.0000 | 1.7043 | 0.0607 | 3.0290 | 0.2758 |
f13 | 0.0000 | 0.0000 | 0.3133 | 0.1383 | 0.7500 | 0.1196 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.9300 | 0.1264 |
f14 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 | 12.6705 | 0.0000 |
f15 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 | 0.1484 | 0.0000 |
f16 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
f17 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 | 27.7029 | 0.0000 |
f18 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 | 600.0000 | 0.0000 |
f19 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 | −0.3348 | 0.0000 |
f20 | −0.1556 | 0.0280 | −0.1440 | 0.0433 | −0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 | −0.1657 | 0.0000 |
f21 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −4.9161 | 0.7619 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −5.0552 | 0.0000 | −1.9948 | 1.8770 |
f22 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −5.0877 | 0.0000 | −3.1387 | 2.1192 |
f23 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −4.7105 | 1.2754 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −5.1285 | 0.0000 | −2.6071 | 2.0951 |
count | 6 + 6 | 3 + 6 | 12 + 6 | 16 + 6 | 15 + 6 | 7 + 6 | 1 + 6 |
Table 15.
The t-test results of the compared algorithms (QUATRE1-S2, QUATRE1-V2, QUATRE1-U2, QUATRE1-Z2, QUATRE2-S2i, QUATRE2-V2i, QUATRE2-U2i, and QUATRE2-Z2i) on ABGWO-V3a.
Table 15.
The t-test results of the compared algorithms (QUATRE1-S2, QUATRE1-V2, QUATRE1-U2, QUATRE1-Z2, QUATRE2-S2i, QUATRE2-V2i, QUATRE2-U2i, and QUATRE2-Z2i) on ABGWO-V3a.
Function | QUATRE1-S2 | QUATRE1-V2 | QUATRE1-U2 | QUATRE1-Z2 | QUATRE2-S2i | QUATRE2-V2i | QUATRE2-U2i | QUATRE2-Z2i |
---|
f1 | = | + | + | + | + | + | + | + |
f2 | – | + | + | + | + | + | + | + |
f3 | – | + | + | + | + | + | + | + |
f4 | = | = | = | = | = | = | = | = |
f5 | + | + | + | + | + | + | + | + |
f6 | = | + | + | + | + | + | + | + |
f7 | – | + | + | + | + | + | + | + |
f8 | – | – | – | + | + | + | + | + |
f9 | – | + | + | + | + | + | + | + |
f10 | = | + | + | + | + | + | + | + |
f11 | = | + | + | + | + | + | + | + |
f12 | – | + | + | + | + | + | + | + |
f13 | – | – | – | + | + | + | + | + |
f14 | = | = | = | = | = | = | = | = |
f15 | = | = | = | = | = | = | = | = |
f16 | = | = | = | = | = | = | = | = |
f17 | = | = | = | = | = | = | = | = |
f18 | = | = | = | = | = | = | = | = |
f19 | = | = | = | = | = | = | = | = |
f20 | + | + | + | + | + | + | + | + |
f21 | = | = | = | = | = | = | = | = |
f22 | = | = | = | = | = | = | = | = |
f23 | = | = | = | = | = | = | = | = |
Table 16.
The t-test results of the compared algorithms (QUATRE1-S2, QUATRE1-V2, QUATRE1-U2, QUATRE1-Z2, QUATRE2-S2i, QUATRE2-V2i, QUATRE2-U2i, and QUATRE2-Z2i) on BDE.
Table 16.
The t-test results of the compared algorithms (QUATRE1-S2, QUATRE1-V2, QUATRE1-U2, QUATRE1-Z2, QUATRE2-S2i, QUATRE2-V2i, QUATRE2-U2i, and QUATRE2-Z2i) on BDE.
Function | QUATRE1-S2 | QUATRE1-V2 | QUATRE1-U2 | QUATRE1-Z2 | QUATRE2-S2i | QUATRE2-V2i | QUATRE2-U2i | QUATRE2-Z2i |
---|
f1 | = | + | + | + | + | + | + | + |
f2 | = | + | + | + | + | + | + | + |
f3 | = | + | + | + | + | + | + | + |
f4 | = | = | = | = | = | = | = | = |
f5 | – | – | – | = | = | – | = | = |
f6 | = | + | + | + | + | + | + | + |
f7 | = | + | + | + | + | + | + | + |
f8 | – | – | – | = | = | = | = | = |
f9 | = | + | + | + | + | + | + | + |
f10 | = | + | + | + | + | + | + | + |
f11 | + | + | + | + | + | + | + | + |
f12 | = | + | + | + | + | + | + | + |
f13 | – | – | – | = | = | = | = | = |
f14 | = | = | = | = | = | = | = | = |
f15 | = | = | = | = | = | = | = | = |
f16 | = | = | = | = | = | = | = | = |
f17 | = | = | = | = | = | = | = | = |
f18 | = | = | = | = | = | = | = | = |
f19 | = | = | = | = | = | = | = | = |
f20 | = | = | = | = | = | = | = | = |
f21 | = | = | = | = | = | = | = | = |
f22 | = | = | = | = | = | = | = | = |
f23 | = | = | = | = | = | = | = | = |
Table 17.
The time consumption of the algorithms(BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE1-U2, BQUATE1-Z2, BQUATE2-S4i, BQUATE2-V4i, BQUATE2-U4i, and BQUATE2-Z4i).
Table 17.
The time consumption of the algorithms(BDE, ABGWO-V3a, BQUATE1-S2, BQUATE1-V2, BQUATE1-U2, BQUATE1-Z2, BQUATE2-S4i, BQUATE2-V4i, BQUATE2-U4i, and BQUATE2-Z4i).
Function | BDE | ABGWO-V3a | BQUATE1-S2 | BQUATE1-V2 | BQUATE1-U2 | BQUATE1-Z2 | BQUATE2-S4i | BQUATE2-V4i | BQUATE2-U4i | BQUATE2-Z4i |
---|
f1 | 0.62744 | 16.2509 | 3.4680 | 3.4155 | 5.3539 | 3.6765 | 6.7833 | 6.3142 | 5.9397 | 6.6418 |
f2 | 0.70993 | 16.7380 | 2.5546 | 3.2635 | 5.2737 | 3.7985 | 6.6544 | 6.3128 | 6.0067 | 6.5947 |
f3 | 2.1763 | 17.2174 | 3.1963 | 3.8897 | 6.1809 | 4.6047 | 7.6322 | 7.0619 | 6.1531 | 7.3415 |
f4 | 0.6807 | 16.7796 | 2.6008 | 3.3246 | 5.3231 | 3.9412 | 6.8011 | 6.2822 | 5.6701 | 6.5871 |
f5 | 0.8110 | 17.6103 | 2.7293 | 3.3003 | 5.4441 | 4.2954 | 6.9998 | 6.3329 | 5.7365 | 6.5454 |
f6 | 0.7057 | 15.4679 | 2.5756 | 3.2538 | 5.3656 | 4.4473 | 7.2255 | 6.2649 | 5.6854 | 6.6404 |
f7 | 0.7183 | 15.7941 | 2.5958 | 3.2864 | 5.4784 | 4.2904 | 6.7943 | 6.2623 | 5.6009 | 6.6486 |
f8 | 0.7162 | 14.9921 | 2.5957 | 3.4029 | 5.4349 | 4.3990 | 7.5326 | 6.2789 | 5.7329 | 6.4835 |
f9 | 0.7161 | 17.7780 | 2.5965 | 3.2933 | 5.3374 | 4.0391 | 8.2188 | 6.3012 | 6.6056 | 6.6817 |
f10 | 0.7351 | 15.4774 | 2.6108 | 3.2774 | 5.4029 | 3.7106 | 7.8801 | 6.3021 | 6.4067 | 6.6676 |
f11 | 0.7716 | 14.5106 | 2.6574 | 3.2962 | 5.3558 | 3.7291 | 8.3399 | 6.5746 | 6.3531 | 6.6952 |
f12 | 1.2479 | 14.7338 | 3.0666 | 3.5307 | 5.6124 | 4.0569 | 7.9435 | 6.4522 | 6.6786 | 7.2990 |
f13 | 1.2632 | 14.7007 | 3.1742 | 3.6226 | 5.9234 | 4.0865 | 8.1302 | 6.4171 | 6.5651 | 6.8091 |
f14 | 0.6115 | 1.8261 | 1.4992 | 1.0958 | 1.4449 | 1.2067 | 1.8882 | 1.5145 | 1.5213 | 1.5724 |
f15 | 0.6694 | 2.0374 | 0.5284 | 0.6029 | 1.1020 | 0.7056 | 1.3289 | 1.0319 | 1.0575 | 1.0909 |
f16 | 0.5553 | 1.0338 | 0.4202 | 0.3506 | 0.6607 | 0.4244 | 0.9298 | 0.5916 | 0.6031 | 0.6352 |
f17 | 0.5428 | 1.0266 | 0.3377 | 0.3545 | 0.5409 | 0.4188 | 0.5847 | 0.5956 | 0.5930 | 0.6113 |
f18 | 0.5592 | 1.0166 | 1.5641 | 0.3535 | 0.5985 | 0.4313 | 0.5706 | 0.5909 | 0.5966 | 0.6220 |
f19 | 0.7770 | 1.6017 | 1.1716 | 0.5437 | 1.0079 | 0.6612 | 0.8813 | 0.9154 | 0.9052 | 0.9389 |
f20 | 0.7973 | 3.0584 | 2.4736 | 0.8634 | 1.4021 | 1.0917 | 1.4618 | 1.5124 | 1.5285 | 1.5924 |
f21 | 0.8798 | 2.1233 | 1.6826 | 0.6974 | 1.0730 | 0.8095 | 1.1294 | 1.1596 | 1.1616 | 1.2014 |
f22 | 0.9692 | 2.1611 | 1.3334 | 0.7354 | 1.2336 | 0.8218 | 1.1837 | 1.2024 | 1.2066 | 1.2449 |
f23 | 1.0245 | 2.2511 | 1.1589 | 0.8068 | 1.1845 | 0.8869 | 1.4182 | 1.2899 | 1.2973 | 1.3347 |
Table 18.
The classification performance of BQUATE2-S1i-SVM, BQUATE2-V1i-SVM, BQUATE1-U1-SVM, BQUATE1-Z1-SVM, SVM, PCA-SVM, and LDA-SVM on Indian Pines
Table 18.
The classification performance of BQUATE2-S1i-SVM, BQUATE2-V1i-SVM, BQUATE1-U1-SVM, BQUATE1-Z1-SVM, SVM, PCA-SVM, and LDA-SVM on Indian Pines
Accurate | BQUATE2-S1i-SVM | BQUATE2-V1i-SVM | BQUATE1-U1-SVM | BQUATE1-Z1-SVM | SVM | PCA-SVM | LDA-SVM |
---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD |
---|
Alfalfa | 0.5281 | 0.1412 | 0.4837 | 0.1407 | 0.5484 | 0.1489 | 0.5368 | 0.1400 | 0.4913 | 0.1319 | 0.6820 | 0.0403 | 0.7228 | 0.1128 |
Corn-no till | 0.7477 | 0.0447 | 0.7496 | 0.0406 | 0.7408 | 0.0401 | 0.7457 | 0.0374 | 0.6766 | 0.0420 | 0.6065 | 0.0399 | 0.7836 | 0.0389 |
Corn-min till | 0.6954 | 0.1016 | 0.7006 | 0.0855 | 0.7016 | 0.0886 | 0.7060 | 0.0836 | 0.5952 | 0.0443 | 0.3659 | 0.0801 | 0.6062 | 0.0400 |
Corn | 0.4708 | 0.0757 | 0.4636 | 0.0552 | 0.4780 | 0.0685 | 0.4710 | 0.0594 | 0.4530 | 0.0526 | 0.3118 | 0.0575 | 0.4452 | 0.0341 |
Grass/pasture | 0.8923 | 0.0303 | 0.8909 | 0.0265 | 0.8883 | 0.0295 | 0.8863 | 0.0276 | 0.8561 | 0.0265 | 0.8380 | 0.0302 | 0.8804 | 0.0169 |
Grass/trees | 0.9217 | 0.0184 | 0.9192 | 0.0139 | 0.9172 | 0.0156 | 0.9231 | 0.0180 | 0.9087 | 0.0156 | 0.9272 | 0.0324 | 0.9605 | 0.0170 |
Grass/pasture-mowed | 0.7663 | 0.1371 | 0.8224 | 0.1325 | 0.8261 | 0.1291 | 0.7637 | 0.1574 | 0.6573 | 0.1286 | 0.3899 | 0.0549 | 0.5845 | 0.1107 |
Hay-windrowed | 0.9915 | 0.0049 | 0.9912 | 0.0029 | 0.9933 | 0.0035 | 0.9908 | 0.0057 | 0.9925 | 0.0039 | 0.9938 | 0.0049 | 0.9949 | 0.0045 |
Oats | 0.4923 | 0.0940 | 0.4808 | 0.1046 | 0.4912 | 0.0916 | 0.4931 | 0.1025 | 0.4082 | 0.0677 | 0.3652 | 0.1060 | 0.6181 | 0.1453 |
Soybean-no till | 0.6434 | 0.0359 | 0.6432 | 0.0365 | 0.6477 | 0.0363 | 0.6463 | 0.0370 | 0.6373 | 0.0443 | 0.5449 | 0.0569 | 0.6072 | 0.0346 |
Soybean-min till | 0.8350 | 0.0250 | 0.8328 | 0.0245 | 0.8286 | 0.0258 | 0.8337 | 0.0262 | 0.8161 | 0.0280 | 0.7026 | 0.0480 | 0.8039 | 0.0178 |
Soybean-clean till | 0.6566 | 0.0528 | 0.6578 | 0.0550 | 0.6540 | 0.0530 | 0.6635 | 0.0538 | 0.6012 | 0.0411 | 0.5602 | 0.0567 | 0.6359 | 0.0758 |
Wheat | 0.9110 | 0.0433 | 0.9138 | 0.0397 | 0.9093 | 0.0424 | 0.9067 | 0.0450 | 0.9018 | 0.0493 | 0.8012 | 0.0438 | 0.9862 | 0.0061 |
Woods | 0.9436 | 0.0165 | 0.9409 | 0.0183 | 0.9419 | 0.0170 | 0.9418 | 0.0180 | 0.9405 | 0.0165 | 0.9325 | 0.0103 | 0.9753 | 0.0086 |
Bldg-Grass-Tree-Drives | 0.6699 | 0.0845 | 0.6571 | 0.0856 | 0.6547 | 0.0818 | 0.6637 | 0.0745 | 0.6052 | 0.0794 | 0.6559 | 0.0879 | 0.6724 | 0.0379 |
Stones-steel towers | 0.8387 | 0.0424 | 0.8486 | 0.0540 | 0.8391 | 0.0589 | 0.8414 | 0.0529 | 0.8176 | 0.0685 | 0.7817 | 0.1337 | 0.9727 | 0.0205 |
OA | 0.7815 | 0.0146 | 0.7805 | 0.0151 | 0.7799 | 0.0147 | 0.7827 | 0.0141 | 0.7473 | 0.0112 | 0.6717 | 0.0205 | 0.7739 | 0.0085 |
AA | 0.7503 | 0.0160 | 0.7498 | 0.0158 | 0.7538 | 0.0169 | 0.7508 | 0.0158 | 0.7099 | 0.0121 | 0.6537 | 0.0192 | 0.7656 | 0.0134 |
Kappa | 0.7522 | 0.0158 | 0.7510 | 0.0163 | 0.7504 | 0.0160 | 0.7535 | 0.0153 | 0.7139 | 0.0121 | 0.6289 | 0.0219 | 0.7442 | 0.0090 |