Acta Armamentarii ›› 2025, Vol. 46 ›› Issue (8): 240997-.doi: 10.12382/bgxb.2024.0997
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ZHANG Yue, ZHANG Ning*(), XU Xiping**(
), PAN Yue
Received:
2024-10-28
Online:
2025-08-28
Contact:
ZHANG Ning, XU Xiping
CLC Number:
ZHANG Yue, ZHANG Ning, XU Xiping, PAN Yue. UAV Trajectory Planning under Complex Constraints Based on GOTDBO Algorithm[J]. Acta Armamentarii, 2025, 46(8): 240997-.
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类型 | 序号 | 函数 | 最优值 |
---|---|---|---|
单峰 函数 | F1 | Shifted and Rotated Bent Cigar Function | 100 |
F2 | Shifted and Rotated Zakharov Function | 300 | |
多峰 函数 | F3 | Shifted and Rotated Rosenbrock's Function | 400 |
F4 | Shifted and Rotated Rastrigin's Function | 500 | |
F5 | Shifted and Rotated Expanded Scaffer's F6 Function | 600 | |
F6 | Shifted and Rotated Lunacek Bi-Rastrigin's function | 700 | |
F7 | Shifted and Rotated Non-Continious Rastrigin's function | 800 | |
F8 | Shifted and Rotated Levy Function | 900 | |
F9 | Shifted and Rotated Schwefel's Function | 1000 | |
混合 函数 | F10 | Hybrid Function 1(N=3) | 1100 |
F11 | Hybrid Function 2(N=3) | 1200 | |
F12 | Hybrid Function 3(N=3) | 1300 | |
F13 | Hybrid Function 4(N=3) | 1400 | |
F14 | Hybrid Function 5(N=3) | 1500 | |
F15 | Hybrid Function 6(N=3) | 1600 | |
F16 | Hybrid Function 6(N=4) | 1700 | |
F17 | Hybrid Function 6(N=5) | 1800 | |
F18 | Hybrid Function 6(N=6) | 1900 | |
F19 | Hybrid Function 6(N=7) | 2000 | |
组合 函数 | F20 | Composition Function 1(N=3) | 2100 |
F21 | Composition Function 2(N=3) | 2200 | |
F22 | Composition Function 3(N=4) | 2300 | |
F23 | Composition Function 4(N=4) | 2400 | |
F24 | Composition Function 5(N=5) | 2500 | |
F25 | Composition Function 6(N=5) | 2600 | |
F26 | Composition Function 7(N=6) | 2700 | |
F27 | Composition Function 8(N=6) | 2800 | |
F28 | Composition Function 9(N=3) | 2900 | |
F29 | Composition Function 10 (N=3) | 3000 | |
维度(D):[-100,100]D |
Table 1 Information of CEC2017 test function
类型 | 序号 | 函数 | 最优值 |
---|---|---|---|
单峰 函数 | F1 | Shifted and Rotated Bent Cigar Function | 100 |
F2 | Shifted and Rotated Zakharov Function | 300 | |
多峰 函数 | F3 | Shifted and Rotated Rosenbrock's Function | 400 |
F4 | Shifted and Rotated Rastrigin's Function | 500 | |
F5 | Shifted and Rotated Expanded Scaffer's F6 Function | 600 | |
F6 | Shifted and Rotated Lunacek Bi-Rastrigin's function | 700 | |
F7 | Shifted and Rotated Non-Continious Rastrigin's function | 800 | |
F8 | Shifted and Rotated Levy Function | 900 | |
F9 | Shifted and Rotated Schwefel's Function | 1000 | |
混合 函数 | F10 | Hybrid Function 1(N=3) | 1100 |
F11 | Hybrid Function 2(N=3) | 1200 | |
F12 | Hybrid Function 3(N=3) | 1300 | |
F13 | Hybrid Function 4(N=3) | 1400 | |
F14 | Hybrid Function 5(N=3) | 1500 | |
F15 | Hybrid Function 6(N=3) | 1600 | |
F16 | Hybrid Function 6(N=4) | 1700 | |
F17 | Hybrid Function 6(N=5) | 1800 | |
F18 | Hybrid Function 6(N=6) | 1900 | |
F19 | Hybrid Function 6(N=7) | 2000 | |
组合 函数 | F20 | Composition Function 1(N=3) | 2100 |
F21 | Composition Function 2(N=3) | 2200 | |
F22 | Composition Function 3(N=4) | 2300 | |
F23 | Composition Function 4(N=4) | 2400 | |
F24 | Composition Function 5(N=5) | 2500 | |
F25 | Composition Function 6(N=5) | 2600 | |
F26 | Composition Function 7(N=6) | 2700 | |
F27 | Composition Function 8(N=6) | 2800 | |
F28 | Composition Function 9(N=3) | 2900 | |
F29 | Composition Function 10 (N=3) | 3000 | |
维度(D):[-100,100]D |
算法 | 参数设定 |
---|---|
DBO[ | 自然系数α∈(0.1,0.9),偏转系数β属于(0.1~1.0),蜣螂偏转角θ∈(0°,180°),随机数r∈(0.1,1.0) |
SABO[ | 电荷因子C从0.5~2.0,动力因子D1从2线性递减至0,吸引力系数k∈(0.1,0.9) |
GWO[ | 参数α从2线性递减至0 |
WOA[ | α从2线性递减至0,b=1 |
NGO[ | 自然系数α∈(0.1,0.9),生长率β∈(0.1,1.0) |
HHO[ | t=0,吸引力因子A∈(0.1,1.0),竞争因子C∈(0.1,1.0) |
Table 2 Parameter values for the optimization algorithms
算法 | 参数设定 |
---|---|
DBO[ | 自然系数α∈(0.1,0.9),偏转系数β属于(0.1~1.0),蜣螂偏转角θ∈(0°,180°),随机数r∈(0.1,1.0) |
SABO[ | 电荷因子C从0.5~2.0,动力因子D1从2线性递减至0,吸引力系数k∈(0.1,0.9) |
GWO[ | 参数α从2线性递减至0 |
WOA[ | α从2线性递减至0,b=1 |
NGO[ | 自然系数α∈(0.1,0.9),生长率β∈(0.1,1.0) |
HHO[ | t=0,吸引力因子A∈(0.1,1.0),竞争因子C∈(0.1,1.0) |
函数 | 指标 | GOTDBO | DBO | SABO | GWO | NGO | WOA | HHO |
---|---|---|---|---|---|---|---|---|
F1 | Avg | 3.84×103 | 5.47×107 | 7.30×109 | 1.73×109 | 2.29×105 | 4.82×108 | 2.29×107 |
Std | 5.23×103 | 6.96×107 | 2.71×109 | 1.56×109 | 2.56×105 | 2.30×108 | 6.23×106 | |
F2 | Avg | 2.35×104 | 9.80×104 | 5.66×104 | 4.30×104 | 5.37×104 | 2.52×105 | 2.87×104 |
Std | 6.52×103 | 3.23×104 | 6.55×103 | 1.05×104 | 5.77×103 | 7.38×104 | 6.15×103 | |
F3 | Avg | 4.95×102 | 5.85×102 | 1.19×103 | 5.70×102 | 5.06×102 | 6.75×102 | 5.50×102 |
Std | 2.00×101 | 9.59×101 | 3.99×102 | 3.77×101 | 1.72×101 | 8.77×101 | 3.38×101 | |
F4 | Avg | 6.35×102 | 6.93×102 | 7.52×102 | 5.92×102 | 6.61×102 | 7.97×102 | 7.48×102 |
Std | 3.04×101 | 4.47×101 | 3.00×101 | 2.08×101 | 2.48×101 | 5.67×101 | 3.93×101 | |
F5 | Avg | 6.01×102 | 6.27×102 | 6.41×102 | 6.06×102 | 6.07×102 | 6.74×102 | 6.63×102 |
Std | 1.18×101 | 1.12×101 | 1.28×101 | 2.26×100 | 5.45×100 | 1.07×100 | 8.38×100 | |
F6 | Avg | 8.90×102 | 9.11×102 | 1.01×103 | 8.59×102 | 9.29×102 | 1.25×103 | 1.26×103 |
Std | 4.44×101 | 6.10×101 | 2.80×101 | 3.88×101 | 3.36×101 | 8.18×101 | 5.86×101 | |
F7 | Avg | 8.15×102 | 9.89×102 | 1.04×103 | 8.82×102 | 9.39×102 | 1.01×103 | 9.59×102 |
Std | 2.81×101 | 5.27×101 | 2.71×101 | 2.81×101 | 1.96×101 | 5.03×101 | 2.15×101 | |
F8 | Avg | 2.12×103 | 6.25×103 | 3.90×103 | 1.49×103 | 2.89×103 | 9.03×103 | 7.10×103 |
Std | 1.02×103 | 1.73×103 | 1.56×103 | 3.93×102 | 4.27×102 | 3.83×103 | 7.19×102 | |
F9 | Avg | 5.03×103 | 5.13×103 | 8.69×103 | 4.29×103 | 5.14×103 | 6.51×103 | 5.78×103 |
Std | 7.10×102 | 6.78×102 | 3.35×102 | 8.75×102 | 3.50×102 | 7.64×102 | 6.81×102 | |
F10 | Avg | 1.18×103 | 1.53×103 | 4.06×103 | 1.48×103 | 1.22×103 | 4.61×103 | 1.26×103 |
Std | 5.57×101 | 2.10×102 | 1.15×103 | 4.23×102 | 2.55×101 | 2.40×103 | 4.92×101 | |
F11 | Avg | 5.31×105 | 4.61×107 | 4.73×108 | 3.88×107 | 7.65×105 | 1.70×108 | 2.13×107 |
Std | 5.28×105 | 6.84×107 | 4.17×108 | 5.01×107 | 4.65×105 | 1.14×108 | 1.16×107 | |
F12 | Avg | 9.27×103 | 4.95×106 | 2.13×107 | 9.32×106 | 1.47×104 | 4.15×105 | 5.84×105 |
Std | 7.25×103 | 1.38×107 | 2.62×107 | 3.54×107 | 9.02×103 | 3.76×105 | 4.09×105 | |
F13 | Avg | 4.61×103 | 1.20×105 | 5.63×105 | 2.84×105 | 8.58×103 | 2.18×106 | 4.46×105 |
Std | 7.33×104 | 1.30×105 | 2.84×105 | 4.48×105 | 4.54×103 | 2.25×106 | 4.07×105 | |
F14 | Avg | 3.46×103 | 6.57×104 | 1.34×106 | 3.50×105 | 5.19×103 | 2.12×105 | 7.49×104 |
Std | 1.57×103 | 4.86×104 | 1.95×106 | 7.48×105 | 2.76×103 | 2.03×105 | 5.60×104 | |
F15 | Avg | 2.65×103 | 2.97×103 | 4.07×103 | 2.50×103 | 2.56×103 | 4.04×103 | 3.34×103 |
Std | 2.83×102 | 3.47×102 | 2.55×102 | 2.79×102 | 1.59×102 | 7.16×102 | 3.12×102 | |
F16 | Avg | 1.58×103 | 2.40×103 | 2.97×103 | 2.02×103 | 1.98×103 | 2.65×103 | 2.67×103 |
Std | 1.36×102 | 3.07×102 | 1.76×102 | 1.65×102 | 6.51×101 | 2.74×102 | 2.26×102 | |
F17 | Avg | 1.25×105 | 1.00×106 | 2.88×106 | 1.47×106 | 1.11×105 | 6.18×106 | 1.46×106 |
Std | 3.74×105 | 1.63×106 | 2.69×106 | 1.56×106 | 6.94×104 | 6.17×106 | 1.81×106 | |
F18 | Avg | 5.06×103 | 1.01×106 | 2.75×106 | 6.32×105 | 5.43×103 | 1.01×107 | 7.19×105 |
Std | 5.11×103 | 2.64×106 | 2.60×106 | 6.98×105 | 1.55×103 | 9.36×106 | 6.25×105 | |
F19 | Avg | 2.66×103 | 2.62×103 | 3.02×103 | 2.42×103 | 2.38×103 | 2.79×103 | 2.71×103 |
Std | 1.63×102 | 1.83×102 | 1.72×102 | 1.59×102 | 6.24×101 | 2.03×102 | 1.96×102 | |
F20 | Avg | 2.26×103 | 2.49×103 | 2.56×103 | 2.39×103 | 2.42×103 | 2.59×103 | 2.56×103 |
Std | 1.03×102 | 4.86×101 | 2.71×101 | 3.48×101 | 1.37×101 | 5.96×101 | 6.13×101 | |
F21 | Avg | 2.30×103 | 5.73×103 | 3.46×103 | 4.84×103 | 2.30×103 | 7.05×103 | 5.29×103 |
Std | 1.25×100 | 1.96×103 | 3.25×102 | 1.88×103 | 3.89×100 | 2.00×103 | 2.27×103 | |
F22 | Avg | 2.81×103 | 2.87×103 | 3.03×103 | 2.75×103 | 2.76×103 | 3.08×103 | 3.12×103 |
Std | 4.99×101 | 4.43×101 | 6.14×101 | 4.48×101 | 1.48×101 | 1.33×102 | 1.22×102 | |
F23 | Avg | 3.00×103 | 3.06×103 | 3.12×103 | 2.94×103 | 2.91×103 | 3.22×103 | 3.36×103 |
Std | 4.61×101 | 6.16×101 | 4.34×101 | 7.18×101 | 2.08×101 | 9.45×101 | 1.15×102 | |
F24 | Avg | 2.89×103 | 2.95×103 | 3.26×103 | 2.96×103 | 2.92×103 | 3.05×103 | 2.95×103 |
Std | 1.00×101 | 5.02×101 | 9.04×101 | 3.71×101 | 1.77×101 | 4.53×101 | 2.24×101 | |
F25 | Avg | 3.15×103 | 5.92×103 | 7.70×103 | 4.57×103 | 3.28×103 | 8.13×103 | 7.43×103 |
Std | 1.31×103 | 9.57×102 | 5.69×102 | 3.60×102 | 7.53×102 | 1.19×103 | 1.04×103 | |
F26 | Avg | 3.21×103 | 3.28×103 | 3.38×103 | 3.25×103 | 3.22×103 | 3.43×103 | 3.43×103 |
Std | 3.17×101 | 3.14×101 | 5.14×101 | 1.88×101 | 8.02×100 | 1.17×102 | 1.21×102 | |
F27 | Avg | 3.21×103 | 3.38×103 | 4.00×103 | 3.36×103 | 3.28×103 | 3.46×103 | 3.32×103 |
Std | 1.24×101 | 7.48×101 | 2.37×102 | 5.54×101 | 1.38×101 | 7.21×101 | 3.76×101 | |
F28 | Avg | 3.92×103 | 4.05×103 | 5.80×103 | 3.74×103 | 3.91×103 | 5.14×103 | 4.59×103 |
Std | 3.01×102 | 2.52×102 | 4.27×102 | 1.45×102 | 1.42×102 | 6.00×102 | 3.96×102 | |
F29 | Avg | 8.78×104 | 1.55×106 | 2.42×107 | 8.58×106 | 1.99×104 | 3.07×107 | 3.03×106 |
Std | 1.84×105 | 2.56×106 | 1.05×107 | 5.80×106 | 2.15×104 | 2.59×107 | 1.80×106 |
Table 3 Evaluation results of CEC2017 objective functions
函数 | 指标 | GOTDBO | DBO | SABO | GWO | NGO | WOA | HHO |
---|---|---|---|---|---|---|---|---|
F1 | Avg | 3.84×103 | 5.47×107 | 7.30×109 | 1.73×109 | 2.29×105 | 4.82×108 | 2.29×107 |
Std | 5.23×103 | 6.96×107 | 2.71×109 | 1.56×109 | 2.56×105 | 2.30×108 | 6.23×106 | |
F2 | Avg | 2.35×104 | 9.80×104 | 5.66×104 | 4.30×104 | 5.37×104 | 2.52×105 | 2.87×104 |
Std | 6.52×103 | 3.23×104 | 6.55×103 | 1.05×104 | 5.77×103 | 7.38×104 | 6.15×103 | |
F3 | Avg | 4.95×102 | 5.85×102 | 1.19×103 | 5.70×102 | 5.06×102 | 6.75×102 | 5.50×102 |
Std | 2.00×101 | 9.59×101 | 3.99×102 | 3.77×101 | 1.72×101 | 8.77×101 | 3.38×101 | |
F4 | Avg | 6.35×102 | 6.93×102 | 7.52×102 | 5.92×102 | 6.61×102 | 7.97×102 | 7.48×102 |
Std | 3.04×101 | 4.47×101 | 3.00×101 | 2.08×101 | 2.48×101 | 5.67×101 | 3.93×101 | |
F5 | Avg | 6.01×102 | 6.27×102 | 6.41×102 | 6.06×102 | 6.07×102 | 6.74×102 | 6.63×102 |
Std | 1.18×101 | 1.12×101 | 1.28×101 | 2.26×100 | 5.45×100 | 1.07×100 | 8.38×100 | |
F6 | Avg | 8.90×102 | 9.11×102 | 1.01×103 | 8.59×102 | 9.29×102 | 1.25×103 | 1.26×103 |
Std | 4.44×101 | 6.10×101 | 2.80×101 | 3.88×101 | 3.36×101 | 8.18×101 | 5.86×101 | |
F7 | Avg | 8.15×102 | 9.89×102 | 1.04×103 | 8.82×102 | 9.39×102 | 1.01×103 | 9.59×102 |
Std | 2.81×101 | 5.27×101 | 2.71×101 | 2.81×101 | 1.96×101 | 5.03×101 | 2.15×101 | |
F8 | Avg | 2.12×103 | 6.25×103 | 3.90×103 | 1.49×103 | 2.89×103 | 9.03×103 | 7.10×103 |
Std | 1.02×103 | 1.73×103 | 1.56×103 | 3.93×102 | 4.27×102 | 3.83×103 | 7.19×102 | |
F9 | Avg | 5.03×103 | 5.13×103 | 8.69×103 | 4.29×103 | 5.14×103 | 6.51×103 | 5.78×103 |
Std | 7.10×102 | 6.78×102 | 3.35×102 | 8.75×102 | 3.50×102 | 7.64×102 | 6.81×102 | |
F10 | Avg | 1.18×103 | 1.53×103 | 4.06×103 | 1.48×103 | 1.22×103 | 4.61×103 | 1.26×103 |
Std | 5.57×101 | 2.10×102 | 1.15×103 | 4.23×102 | 2.55×101 | 2.40×103 | 4.92×101 | |
F11 | Avg | 5.31×105 | 4.61×107 | 4.73×108 | 3.88×107 | 7.65×105 | 1.70×108 | 2.13×107 |
Std | 5.28×105 | 6.84×107 | 4.17×108 | 5.01×107 | 4.65×105 | 1.14×108 | 1.16×107 | |
F12 | Avg | 9.27×103 | 4.95×106 | 2.13×107 | 9.32×106 | 1.47×104 | 4.15×105 | 5.84×105 |
Std | 7.25×103 | 1.38×107 | 2.62×107 | 3.54×107 | 9.02×103 | 3.76×105 | 4.09×105 | |
F13 | Avg | 4.61×103 | 1.20×105 | 5.63×105 | 2.84×105 | 8.58×103 | 2.18×106 | 4.46×105 |
Std | 7.33×104 | 1.30×105 | 2.84×105 | 4.48×105 | 4.54×103 | 2.25×106 | 4.07×105 | |
F14 | Avg | 3.46×103 | 6.57×104 | 1.34×106 | 3.50×105 | 5.19×103 | 2.12×105 | 7.49×104 |
Std | 1.57×103 | 4.86×104 | 1.95×106 | 7.48×105 | 2.76×103 | 2.03×105 | 5.60×104 | |
F15 | Avg | 2.65×103 | 2.97×103 | 4.07×103 | 2.50×103 | 2.56×103 | 4.04×103 | 3.34×103 |
Std | 2.83×102 | 3.47×102 | 2.55×102 | 2.79×102 | 1.59×102 | 7.16×102 | 3.12×102 | |
F16 | Avg | 1.58×103 | 2.40×103 | 2.97×103 | 2.02×103 | 1.98×103 | 2.65×103 | 2.67×103 |
Std | 1.36×102 | 3.07×102 | 1.76×102 | 1.65×102 | 6.51×101 | 2.74×102 | 2.26×102 | |
F17 | Avg | 1.25×105 | 1.00×106 | 2.88×106 | 1.47×106 | 1.11×105 | 6.18×106 | 1.46×106 |
Std | 3.74×105 | 1.63×106 | 2.69×106 | 1.56×106 | 6.94×104 | 6.17×106 | 1.81×106 | |
F18 | Avg | 5.06×103 | 1.01×106 | 2.75×106 | 6.32×105 | 5.43×103 | 1.01×107 | 7.19×105 |
Std | 5.11×103 | 2.64×106 | 2.60×106 | 6.98×105 | 1.55×103 | 9.36×106 | 6.25×105 | |
F19 | Avg | 2.66×103 | 2.62×103 | 3.02×103 | 2.42×103 | 2.38×103 | 2.79×103 | 2.71×103 |
Std | 1.63×102 | 1.83×102 | 1.72×102 | 1.59×102 | 6.24×101 | 2.03×102 | 1.96×102 | |
F20 | Avg | 2.26×103 | 2.49×103 | 2.56×103 | 2.39×103 | 2.42×103 | 2.59×103 | 2.56×103 |
Std | 1.03×102 | 4.86×101 | 2.71×101 | 3.48×101 | 1.37×101 | 5.96×101 | 6.13×101 | |
F21 | Avg | 2.30×103 | 5.73×103 | 3.46×103 | 4.84×103 | 2.30×103 | 7.05×103 | 5.29×103 |
Std | 1.25×100 | 1.96×103 | 3.25×102 | 1.88×103 | 3.89×100 | 2.00×103 | 2.27×103 | |
F22 | Avg | 2.81×103 | 2.87×103 | 3.03×103 | 2.75×103 | 2.76×103 | 3.08×103 | 3.12×103 |
Std | 4.99×101 | 4.43×101 | 6.14×101 | 4.48×101 | 1.48×101 | 1.33×102 | 1.22×102 | |
F23 | Avg | 3.00×103 | 3.06×103 | 3.12×103 | 2.94×103 | 2.91×103 | 3.22×103 | 3.36×103 |
Std | 4.61×101 | 6.16×101 | 4.34×101 | 7.18×101 | 2.08×101 | 9.45×101 | 1.15×102 | |
F24 | Avg | 2.89×103 | 2.95×103 | 3.26×103 | 2.96×103 | 2.92×103 | 3.05×103 | 2.95×103 |
Std | 1.00×101 | 5.02×101 | 9.04×101 | 3.71×101 | 1.77×101 | 4.53×101 | 2.24×101 | |
F25 | Avg | 3.15×103 | 5.92×103 | 7.70×103 | 4.57×103 | 3.28×103 | 8.13×103 | 7.43×103 |
Std | 1.31×103 | 9.57×102 | 5.69×102 | 3.60×102 | 7.53×102 | 1.19×103 | 1.04×103 | |
F26 | Avg | 3.21×103 | 3.28×103 | 3.38×103 | 3.25×103 | 3.22×103 | 3.43×103 | 3.43×103 |
Std | 3.17×101 | 3.14×101 | 5.14×101 | 1.88×101 | 8.02×100 | 1.17×102 | 1.21×102 | |
F27 | Avg | 3.21×103 | 3.38×103 | 4.00×103 | 3.36×103 | 3.28×103 | 3.46×103 | 3.32×103 |
Std | 1.24×101 | 7.48×101 | 2.37×102 | 5.54×101 | 1.38×101 | 7.21×101 | 3.76×101 | |
F28 | Avg | 3.92×103 | 4.05×103 | 5.80×103 | 3.74×103 | 3.91×103 | 5.14×103 | 4.59×103 |
Std | 3.01×102 | 2.52×102 | 4.27×102 | 1.45×102 | 1.42×102 | 6.00×102 | 3.96×102 | |
F29 | Avg | 8.78×104 | 1.55×106 | 2.42×107 | 8.58×106 | 1.99×104 | 3.07×107 | 3.03×106 |
Std | 1.84×105 | 2.56×106 | 1.05×107 | 5.80×106 | 2.15×104 | 2.59×107 | 1.80×106 |
函数 | GOTDBO vs.DBO | GOTDBO vs.SABO | GOTDBO vs.GWO | GOTDBO vs.NGO | GOTDBO vs.WOA | GOTDBO vs.HHO |
---|---|---|---|---|---|---|
F1 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 |
F2 | 3.02×10-11 | 3.02×10-11 | 2.23×10-9 | 3.02×10-11 | 3.02×10-11 | 2.50×10-2 |
F3 | 1.41×10-9 | 3.02×10-11 | 6.70×10-7 | 5.19×10-2 | 3.02×10-11 | 7.12×10-9 |
F4 | 1.61×10-6 | 3.02×10-11 | 5.19×10-7 | 1.24×10-3 | 3.02×10-11 | 1.09×10-10 |
F5 | 1.84×10-2 | 7.73×10-2 | 6.7×10-11 | 1.41×10-9 | 3.02×10-11 | 8.15×10-11 |
F6 | 2.01×10-1 | 3.16×10-10 | 3.18×10-3 | 1.11×10-4 | 3.02×10-11 | 3.02×10-11 |
F7 | 4.31×10-8 | 3.02×10-11 | 2.49×10-6 | 8.66×10-5 | 6.72×10-10 | 1.60×10-7 |
F8 | 1.33×10-10 | 3.81×10-7 | 6.38×10-3 | 2.43×10-5 | 5.49×10-11 | 3.34×10-11 |
F9 | 6.31×10-1 | 3.02×10-11 | 1.49×10-4 | 4.20×10-1 | 1.85×10-8 | 3.01×10-4 |
F10 | 4.98×10-11 | 3.02×10-11 | 2.60×10-3 | 5.20×10-1 | 3.02×10-11 | 3.92×10-2 |
F11 | 2.61×10-10 | 3.02×10-11 | 4.08×10-11 | 7.62×10-3 | 3.02×10-11 | 3.02×10-11 |
F12 | 9.92×10-11 | 3.02×10-11 | 3.02×10-11 | 1.12×10-2 | 3.02×10-11 | 3.02×10-11 |
F13 | 7.62×10-2 | 9.92×10-11 | 1.17×10-3 | 7.6×10-7 | 2.61×10-10 | 7.09×10-8 |
F14 | 8.99×10-11 | 3.02×10-11 | 3.02×10-11 | 5.57×10-3 | 3.02×10-11 | 3.02×10-11 |
F15 | 3.56×10-4 | 3.02×10-11 | 4.21×10-3 | 1.91×10-1 | 8.15×10-11 | 2.23×10-9 |
F16 | 2.16×10-3 | 3.02×10-11 | 4.98×10-4 | 3.65×10-8 | 1.31×10-8 | 2.15×10-10 |
F17 | 7.96×10-1 | 3.52×10-7 | 1.95×10-2 | 2.57×10-7 | 4.11×10-7 | 5.32×10-3 |
F18 | 5.19×10-7 | 3.02×10-11 | 3.02×10-11 | 9.12×10-1 | 3.02×10-11 | 3.02×10-11 |
F19 | 2.28×10-1 | 1.70×10-8 | 3.57×10-6 | 3.35×10-8 | 4.86×10-3 | 4.83×10-1 |
F20 | 3.82×10-10 | 3.02×10-11 | 2.39×10-4 | 1.03×10-6 | 3.34×10-11 | 8.15×10-11 |
F21 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 9.53×10-7 | 3.02×10-11 | 3.02×10-11 |
F22 | 1.25×10-5 | 3.34×10-11 | 1.34×10-5 | 1.78×10-4 | 5.57×10-10 | 3.69×10-11 |
F23 | 1.68×10-4 | 5.49×10-11 | 4.22×10-4 | 7.38×10-10 | 8.99×10-11 | 3.02×10-11 |
F24 | 7.38×10-10 | 3.02×10-11 | 3.34×10-11 | 2.23×10-9 | 3.02×10-11 | 5.49×10-11 |
F25 | 1.16×10-7 | 4.50×10-11 | 1.17×10-3 | 1.91×10-1 | 7.39×10-11 | 1.46×10-10 |
F26 | 1.11×10-3 | 1.78×10-10 | 8.30×10-1 | 3.35×10-8 | 1.46×10-10 | 1.78×10-10 |
F27 | 3.02×10-11 | 3.02×10-11 | 3.34×10-11 | 3.69×10-11 | 3.02×10-11 | 3.02×10-11 |
F28 | 3.78×10-2 | 3.34×10-11 | 1.50×10-2 | 5.99×10-1 | 1.46×10-10 | 2.39×10-8 |
F29 | 6.53×10-8 | 3.02×10-11 | 3.02×10-11 | 4.12×10-1 | 3.02×10-11 | 3.34×10-11 |
Table 4 The statistical results of Wilcoxon rank-sum test for seven algorithms
函数 | GOTDBO vs.DBO | GOTDBO vs.SABO | GOTDBO vs.GWO | GOTDBO vs.NGO | GOTDBO vs.WOA | GOTDBO vs.HHO |
---|---|---|---|---|---|---|
F1 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 |
F2 | 3.02×10-11 | 3.02×10-11 | 2.23×10-9 | 3.02×10-11 | 3.02×10-11 | 2.50×10-2 |
F3 | 1.41×10-9 | 3.02×10-11 | 6.70×10-7 | 5.19×10-2 | 3.02×10-11 | 7.12×10-9 |
F4 | 1.61×10-6 | 3.02×10-11 | 5.19×10-7 | 1.24×10-3 | 3.02×10-11 | 1.09×10-10 |
F5 | 1.84×10-2 | 7.73×10-2 | 6.7×10-11 | 1.41×10-9 | 3.02×10-11 | 8.15×10-11 |
F6 | 2.01×10-1 | 3.16×10-10 | 3.18×10-3 | 1.11×10-4 | 3.02×10-11 | 3.02×10-11 |
F7 | 4.31×10-8 | 3.02×10-11 | 2.49×10-6 | 8.66×10-5 | 6.72×10-10 | 1.60×10-7 |
F8 | 1.33×10-10 | 3.81×10-7 | 6.38×10-3 | 2.43×10-5 | 5.49×10-11 | 3.34×10-11 |
F9 | 6.31×10-1 | 3.02×10-11 | 1.49×10-4 | 4.20×10-1 | 1.85×10-8 | 3.01×10-4 |
F10 | 4.98×10-11 | 3.02×10-11 | 2.60×10-3 | 5.20×10-1 | 3.02×10-11 | 3.92×10-2 |
F11 | 2.61×10-10 | 3.02×10-11 | 4.08×10-11 | 7.62×10-3 | 3.02×10-11 | 3.02×10-11 |
F12 | 9.92×10-11 | 3.02×10-11 | 3.02×10-11 | 1.12×10-2 | 3.02×10-11 | 3.02×10-11 |
F13 | 7.62×10-2 | 9.92×10-11 | 1.17×10-3 | 7.6×10-7 | 2.61×10-10 | 7.09×10-8 |
F14 | 8.99×10-11 | 3.02×10-11 | 3.02×10-11 | 5.57×10-3 | 3.02×10-11 | 3.02×10-11 |
F15 | 3.56×10-4 | 3.02×10-11 | 4.21×10-3 | 1.91×10-1 | 8.15×10-11 | 2.23×10-9 |
F16 | 2.16×10-3 | 3.02×10-11 | 4.98×10-4 | 3.65×10-8 | 1.31×10-8 | 2.15×10-10 |
F17 | 7.96×10-1 | 3.52×10-7 | 1.95×10-2 | 2.57×10-7 | 4.11×10-7 | 5.32×10-3 |
F18 | 5.19×10-7 | 3.02×10-11 | 3.02×10-11 | 9.12×10-1 | 3.02×10-11 | 3.02×10-11 |
F19 | 2.28×10-1 | 1.70×10-8 | 3.57×10-6 | 3.35×10-8 | 4.86×10-3 | 4.83×10-1 |
F20 | 3.82×10-10 | 3.02×10-11 | 2.39×10-4 | 1.03×10-6 | 3.34×10-11 | 8.15×10-11 |
F21 | 3.02×10-11 | 3.02×10-11 | 3.02×10-11 | 9.53×10-7 | 3.02×10-11 | 3.02×10-11 |
F22 | 1.25×10-5 | 3.34×10-11 | 1.34×10-5 | 1.78×10-4 | 5.57×10-10 | 3.69×10-11 |
F23 | 1.68×10-4 | 5.49×10-11 | 4.22×10-4 | 7.38×10-10 | 8.99×10-11 | 3.02×10-11 |
F24 | 7.38×10-10 | 3.02×10-11 | 3.34×10-11 | 2.23×10-9 | 3.02×10-11 | 5.49×10-11 |
F25 | 1.16×10-7 | 4.50×10-11 | 1.17×10-3 | 1.91×10-1 | 7.39×10-11 | 1.46×10-10 |
F26 | 1.11×10-3 | 1.78×10-10 | 8.30×10-1 | 3.35×10-8 | 1.46×10-10 | 1.78×10-10 |
F27 | 3.02×10-11 | 3.02×10-11 | 3.34×10-11 | 3.69×10-11 | 3.02×10-11 | 3.02×10-11 |
F28 | 3.78×10-2 | 3.34×10-11 | 1.50×10-2 | 5.99×10-1 | 1.46×10-10 | 2.39×10-8 |
F29 | 6.53×10-8 | 3.02×10-11 | 3.02×10-11 | 4.12×10-1 | 3.02×10-11 | 3.34×10-11 |
函数 | 种群数量 | |||
---|---|---|---|---|
20 | 40 | 60 | 80 | |
F1 | 14357250870.1265 | 116.0104 | 100.7044 | 100.0188 |
F2 | 65731.2988 | 27611.8116 | 18926.7152 | 15363.2131 |
F3 | 732.0261 | 472.9462 | 469.2622 | 465.2131 |
F4 | 721.0206 | 576.6115 | 595.0123 | 585.5663 |
F5 | 639.5180 | 621.2830 | 610.6377 | 605.4304 |
F6 | 1145.3922 | 823.5415 | 831.0976 | 813.5674 |
F7 | 985.6784 | 881.5864 | 886.5611 | 868.6520 |
F8 | 4461.1263 | 1413.6466 | 1646.2919 | 1277.0191 |
F9 | 5115.3986 | 4549.5359 | 3998.7796 | 3827.529 |
F10 | 4377.1858 | 1154.1395 | 1146.3560 | 1143.6654 |
F11 | 343079033.7023 | 109358.0727 | 84566.1251 | 77408.8254 |
F12 | 11295693.4089 | 4303.1477 | 2686.8763 | 1537.8348 |
F13 | 129699.1408 | 3486.9245 | 5768.3868 | 2357.362 |
F14 | 73552.9374 | 1740.6270 | 1811.4656 | 1648.6888 |
F15 | 3235.2565 | 2243.9587 | 2000.4655 | 1948.6322 |
F16 | 2225.8664 | 1829.6791 | 1782.0605 | 1764.9297 |
F17 | 462204.8433 | 149600.1802 | 103637.4103 | 73093.2517 |
F18 | 376026.8268 | 2131.4679 | 2134.4968 | 2067.0915 |
F19 | 2373.2010 | 2269.4362 | 2384.7475 | 2289.5849 |
F20 | 2287.9287 | 2202.7809 | 2201.8412 | 2201.5803 |
F21 | 3704.8980 | 2300.0105 | 2300.0001 | 2300.0000 |
F22 | 2873.5480 | 2749.4721 | 2746.2056 | 2730.8182 |
F23 | 3105.9160 | 2915.9362 | 2923.5757 | 2883.5074 |
F24 | 3177.4275 | 2883.5940 | 2883.5074 | 2883.5033 |
F25 | 5792.8516 | 2800.2459 | 2800.0014 | 2800.0001 |
F26 | 3281.3135 | 3225.1038 | 3227.5987 | 3220.5637 |
F27 | 3667.0093 | 3201.8490 | 3207.4085 | 3197.1586 |
F28 | 4245.8979 | 3547.3142 | 3556.7941 | 3474.9072 |
F29 | 21691161.8028 | 6876.3282 | 5592.0057 | 5405.1612 |
Table 5 Sensitivity analysis of GOTDBO algorithm for the number of population members N
函数 | 种群数量 | |||
---|---|---|---|---|
20 | 40 | 60 | 80 | |
F1 | 14357250870.1265 | 116.0104 | 100.7044 | 100.0188 |
F2 | 65731.2988 | 27611.8116 | 18926.7152 | 15363.2131 |
F3 | 732.0261 | 472.9462 | 469.2622 | 465.2131 |
F4 | 721.0206 | 576.6115 | 595.0123 | 585.5663 |
F5 | 639.5180 | 621.2830 | 610.6377 | 605.4304 |
F6 | 1145.3922 | 823.5415 | 831.0976 | 813.5674 |
F7 | 985.6784 | 881.5864 | 886.5611 | 868.6520 |
F8 | 4461.1263 | 1413.6466 | 1646.2919 | 1277.0191 |
F9 | 5115.3986 | 4549.5359 | 3998.7796 | 3827.529 |
F10 | 4377.1858 | 1154.1395 | 1146.3560 | 1143.6654 |
F11 | 343079033.7023 | 109358.0727 | 84566.1251 | 77408.8254 |
F12 | 11295693.4089 | 4303.1477 | 2686.8763 | 1537.8348 |
F13 | 129699.1408 | 3486.9245 | 5768.3868 | 2357.362 |
F14 | 73552.9374 | 1740.6270 | 1811.4656 | 1648.6888 |
F15 | 3235.2565 | 2243.9587 | 2000.4655 | 1948.6322 |
F16 | 2225.8664 | 1829.6791 | 1782.0605 | 1764.9297 |
F17 | 462204.8433 | 149600.1802 | 103637.4103 | 73093.2517 |
F18 | 376026.8268 | 2131.4679 | 2134.4968 | 2067.0915 |
F19 | 2373.2010 | 2269.4362 | 2384.7475 | 2289.5849 |
F20 | 2287.9287 | 2202.7809 | 2201.8412 | 2201.5803 |
F21 | 3704.8980 | 2300.0105 | 2300.0001 | 2300.0000 |
F22 | 2873.5480 | 2749.4721 | 2746.2056 | 2730.8182 |
F23 | 3105.9160 | 2915.9362 | 2923.5757 | 2883.5074 |
F24 | 3177.4275 | 2883.5940 | 2883.5074 | 2883.5033 |
F25 | 5792.8516 | 2800.2459 | 2800.0014 | 2800.0001 |
F26 | 3281.3135 | 3225.1038 | 3227.5987 | 3220.5637 |
F27 | 3667.0093 | 3201.8490 | 3207.4085 | 3197.1586 |
F28 | 4245.8979 | 3547.3142 | 3556.7941 | 3474.9072 |
F29 | 21691161.8028 | 6876.3282 | 5592.0057 | 5405.1612 |
函数 | 最大迭代次数 | |||
---|---|---|---|---|
100 | 200 | 300 | 400 | |
F1 | 6831638.3447 | 3251.8275 | 206.9639 | 101.3222 |
F2 | 43569.3900 | 25383.1472 | 25025.6982 | 15639.6810 |
F3 | 505.1954 | 473.8925 | 448.5478 | 407.3512 |
F4 | 568.1175 | 565.9402 | 561.6883 | 556.7126 |
F5 | 614.7980 | 613.0693 | 612.137 | 601.6673 |
F6 | 831.8287 | 804.4745 | 794.7180 | 791.2057 |
F7 | 874.4845 | 869.6553 | 864.6723 | 845.8460 |
F8 | 1696.7997 | 1133.7189 | 1112.0113 | 1109.1512 |
F9 | 3898.4745 | 3860.5282 | 3624.9605 | 3474.8728 |
F10 | 1299.1835 | 1202.6093 | 1155.6158 | 1149.7177 |
F11 | 169631.1818 | 147179.3458 | 113914.4288 | 73389.2358 |
F12 | 5732.9769 | 4221.5604 | 2047.2659 | 1463.7406 |
F13 | 10923.7531 | 9513.3577 | 3642.7905 | 3492.4111 |
F14 | 2001.3367 | 1832.1725 | 1682.1324 | 1652.7808 |
F15 | 2285.6363 | 2177.5805 | 2173.7263 | 1753.5940 |
F16 | 1795.1903 | 1782.5427 | 1725.0936 | 1672.1121 |
F17 | 203649.0877 | 103841.9727 | 94030.1582 | 80713.4592 |
F18 | 3390.8159 | 2076.1651 | 2002.1769 | 1926.4038 |
F19 | 2392.0476 | 2342.2296 | 2314.9721 | 2307.1965 |
F20 | 2213.5223 | 2206.0126 | 2203.5757 | 2201.5648 |
F21 | 2316.8770 | 2300.3332 | 2300.0094 | 2300.0002 |
F22 | 2751.7004 | 2726.9892 | 2709.9929 | 2698.9780 |
F23 | 2938.0872 | 2914.6407 | 2892.3779 | 2854.6137 |
F24 | 2887.7467 | 2885.5081 | 2883.4799 | 2875.5611 |
F25 | 2908.9355 | 2802.5851 | 2800.0917 | 2786.1178 |
F26 | 3228.4299 | 3219.1615 | 3218.7353 | 3206.8530 |
F27 | 3247.9189 | 3204.2670 | 3203.3867 | 3182.4388 |
F28 | 11001.0994 | 3417.5418 | 3351.6151 | 3336.3271 |
F29 | 11001.0994 | 6552.7274 | 5629.1220 | 5453.7255 |
Table 6 Sensitivity analysis of GOTDBO algorithm for the number of iterations T
函数 | 最大迭代次数 | |||
---|---|---|---|---|
100 | 200 | 300 | 400 | |
F1 | 6831638.3447 | 3251.8275 | 206.9639 | 101.3222 |
F2 | 43569.3900 | 25383.1472 | 25025.6982 | 15639.6810 |
F3 | 505.1954 | 473.8925 | 448.5478 | 407.3512 |
F4 | 568.1175 | 565.9402 | 561.6883 | 556.7126 |
F5 | 614.7980 | 613.0693 | 612.137 | 601.6673 |
F6 | 831.8287 | 804.4745 | 794.7180 | 791.2057 |
F7 | 874.4845 | 869.6553 | 864.6723 | 845.8460 |
F8 | 1696.7997 | 1133.7189 | 1112.0113 | 1109.1512 |
F9 | 3898.4745 | 3860.5282 | 3624.9605 | 3474.8728 |
F10 | 1299.1835 | 1202.6093 | 1155.6158 | 1149.7177 |
F11 | 169631.1818 | 147179.3458 | 113914.4288 | 73389.2358 |
F12 | 5732.9769 | 4221.5604 | 2047.2659 | 1463.7406 |
F13 | 10923.7531 | 9513.3577 | 3642.7905 | 3492.4111 |
F14 | 2001.3367 | 1832.1725 | 1682.1324 | 1652.7808 |
F15 | 2285.6363 | 2177.5805 | 2173.7263 | 1753.5940 |
F16 | 1795.1903 | 1782.5427 | 1725.0936 | 1672.1121 |
F17 | 203649.0877 | 103841.9727 | 94030.1582 | 80713.4592 |
F18 | 3390.8159 | 2076.1651 | 2002.1769 | 1926.4038 |
F19 | 2392.0476 | 2342.2296 | 2314.9721 | 2307.1965 |
F20 | 2213.5223 | 2206.0126 | 2203.5757 | 2201.5648 |
F21 | 2316.8770 | 2300.3332 | 2300.0094 | 2300.0002 |
F22 | 2751.7004 | 2726.9892 | 2709.9929 | 2698.9780 |
F23 | 2938.0872 | 2914.6407 | 2892.3779 | 2854.6137 |
F24 | 2887.7467 | 2885.5081 | 2883.4799 | 2875.5611 |
F25 | 2908.9355 | 2802.5851 | 2800.0917 | 2786.1178 |
F26 | 3228.4299 | 3219.1615 | 3218.7353 | 3206.8530 |
F27 | 3247.9189 | 3204.2670 | 3203.3867 | 3182.4388 |
F28 | 11001.0994 | 3417.5418 | 3351.6151 | 3336.3271 |
F29 | 11001.0994 | 6552.7274 | 5629.1220 | 5453.7255 |
禁飞区域 | 中心坐标/km | 半径/km |
---|---|---|
NF1 | (300,400,200) | 50 |
NF2 | (700,150,200) | 40 |
NF3 | (450,350,200) | 60 |
NF4 | (500,600,200) | 50 |
NF5 | (800,500,200) | 40 |
NF6 | (650,750,150) | 40 |
NF7 | (550,550,250) | 60 |
NF8 | (250,600,250) | 50 |
NF9 | (150,150,200) | 40 |
NF10 | (750,300,200) | 30 |
NF11 | (650,250,150) | 50 |
NF12 | (700,600,200) | 60 |
NF13 | (500,250,200) | 50 |
Table 7 Trajectory planning mission information
禁飞区域 | 中心坐标/km | 半径/km |
---|---|---|
NF1 | (300,400,200) | 50 |
NF2 | (700,150,200) | 40 |
NF3 | (450,350,200) | 60 |
NF4 | (500,600,200) | 50 |
NF5 | (800,500,200) | 40 |
NF6 | (650,750,150) | 40 |
NF7 | (550,550,250) | 60 |
NF8 | (250,600,250) | 50 |
NF9 | (150,150,200) | 40 |
NF10 | (750,300,200) | 30 |
NF11 | (650,250,150) | 50 |
NF12 | (700,600,200) | 60 |
NF13 | (500,250,200) | 50 |
初始设置及 实验编号 | ω1 | ω2 | ω3 | ω4 | ω5 |
---|---|---|---|---|---|
初始设置 | 10 | 100 | 10 | 50 | 1000 |
1 | 5 | 100 | 10 | 50 | 1000 |
2 | 20 | 100 | 10 | 50 | 1000 |
3 | 10 | 50 | 10 | 50 | 1000 |
4 | 10 | 200 | 10 | 50 | 1000 |
5 | 10 | 100 | 5 | 50 | 1000 |
6 | 10 | 100 | 20 | 50 | 1000 |
7 | 10 | 100 | 10 | 20 | 1000 |
8 | 10 | 100 | 10 | 80 | 1000 |
9 | 10 | 100 | 10 | 50 | 500 |
10 | 10 | 100 | 10 | 50 | 2000 |
Table 8 Experimental parameter setting
初始设置及 实验编号 | ω1 | ω2 | ω3 | ω4 | ω5 |
---|---|---|---|---|---|
初始设置 | 10 | 100 | 10 | 50 | 1000 |
1 | 5 | 100 | 10 | 50 | 1000 |
2 | 20 | 100 | 10 | 50 | 1000 |
3 | 10 | 50 | 10 | 50 | 1000 |
4 | 10 | 200 | 10 | 50 | 1000 |
5 | 10 | 100 | 5 | 50 | 1000 |
6 | 10 | 100 | 20 | 50 | 1000 |
7 | 10 | 100 | 10 | 20 | 1000 |
8 | 10 | 100 | 10 | 80 | 1000 |
9 | 10 | 100 | 10 | 50 | 500 |
10 | 10 | 100 | 10 | 50 | 2000 |
初始设置及 实验编号 | 最大航程/ km | 威胁区域接 近次数/次 | 高度偏离 程度/km | 路径平 滑度 |
---|---|---|---|---|
初始设置 | 1225.16 | 2 | 408.36 | 1 |
1 | 1250.35 | 3 | 408.86 | 1 |
2 | 1230.82 | 2 | 407.96 | 1 |
3 | 1230.74 | 3 | 406.56 | 1 |
4 | 1226.53 | 1 | 408.26 | 1 |
5 | 1227.44 | 2 | 420.56 | 1 |
6 | 1234.26 | 2 | 415.96 | 1 |
7 | 1228.93 | 2 | 406.46 | 0 |
8 | 1424.68 | 2 | 409.36 | 1 |
9 | 1678.45 | 3 | 404.66 | 1 |
10 | 1233.59 | 1 | 411.16 | 1 |
Table 9 Performance results of trajectory planning with different weight combinations
初始设置及 实验编号 | 最大航程/ km | 威胁区域接 近次数/次 | 高度偏离 程度/km | 路径平 滑度 |
---|---|---|---|---|
初始设置 | 1225.16 | 2 | 408.36 | 1 |
1 | 1250.35 | 3 | 408.86 | 1 |
2 | 1230.82 | 2 | 407.96 | 1 |
3 | 1230.74 | 3 | 406.56 | 1 |
4 | 1226.53 | 1 | 408.26 | 1 |
5 | 1227.44 | 2 | 420.56 | 1 |
6 | 1234.26 | 2 | 415.96 | 1 |
7 | 1228.93 | 2 | 406.46 | 0 |
8 | 1424.68 | 2 | 409.36 | 1 |
9 | 1678.45 | 3 | 404.66 | 1 |
10 | 1233.59 | 1 | 411.16 | 1 |
算法 | 参数设定 |
---|---|
ACO[ | 信息素启发因子α∈[1,2],启发函数因子β∈[2,5],信息素挥发系数ρ∈(0.1,0.5) |
ABC[ | 雇佣蜂和观察蜂数量同为30,引领蜂数量为30,蜜源放弃阈值limit∈[20,100] |
Table 10 Algorithm parameter settings
算法 | 参数设定 |
---|---|
ACO[ | 信息素启发因子α∈[1,2],启发函数因子β∈[2,5],信息素挥发系数ρ∈(0.1,0.5) |
ABC[ | 雇佣蜂和观察蜂数量同为30,引领蜂数量为30,蜜源放弃阈值limit∈[20,100] |
算法 | 场景A | 场景B | 场景C |
---|---|---|---|
ACO | 5.334298 | 6.973373 | 11.235155 |
DBO | 5.038684 | 6.649935 | 10.443480 |
GWO | 5.103155 | 6.392838 | 10.433408 |
ABC | 5.102468 | 6.706328 | 10.700655 |
WOA | 5.466211 | 6.332292 | 10.572490 |
HHO | 11.832312 | 17.23000 | 27.527141 |
GOTDBO | 5.028615 | 6.745984 | 10.456419 |
Table 11 The running time of trajectory planning algorithm s
算法 | 场景A | 场景B | 场景C |
---|---|---|---|
ACO | 5.334298 | 6.973373 | 11.235155 |
DBO | 5.038684 | 6.649935 | 10.443480 |
GWO | 5.103155 | 6.392838 | 10.433408 |
ABC | 5.102468 | 6.706328 | 10.700655 |
WOA | 5.466211 | 6.332292 | 10.572490 |
HHO | 11.832312 | 17.23000 | 27.527141 |
GOTDBO | 5.028615 | 6.745984 | 10.456419 |
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1503.25 | 2 | 425.18 | 1 |
DBO | 1665.42 | 2 | 493.08 | 1 |
GWO | 1583.77 | 2 | 408.36 | 1 |
ABC | 1259.09 | 2 | 411.73 | 1 |
WOA | 1424.68 | 2 | 466.11 | 1 |
HHO | 1678.45 | 2 | 493.08 | 1 |
GWTDBO | 1233.59 | 2 | 393.08 | 1 |
Table 12 Evaluated results of trajectory planning for Scenario A
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1503.25 | 2 | 425.18 | 1 |
DBO | 1665.42 | 2 | 493.08 | 1 |
GWO | 1583.77 | 2 | 408.36 | 1 |
ABC | 1259.09 | 2 | 411.73 | 1 |
WOA | 1424.68 | 2 | 466.11 | 1 |
HHO | 1678.45 | 2 | 493.08 | 1 |
GWTDBO | 1233.59 | 2 | 393.08 | 1 |
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1552.28 | 4 | 435.37 | 1 |
DBO | 1733.59 | 4 | 493.08 | 1 |
GWO | 1567.33 | 5 | 413.71 | 1 |
ABC | 1610.77 | 4 | 484.64 | 1 |
WOA | 1733.59 | 4 | 493.08 | 1 |
HHO | 1600.35 | 5 | 416.26 | 1 |
GWTDBO | 1569.17 | 3 | 409.38 | 1 |
Table 13 Evaluated results of trajectory planning for Scenario B
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1552.28 | 4 | 435.37 | 1 |
DBO | 1733.59 | 4 | 493.08 | 1 |
GWO | 1567.33 | 5 | 413.71 | 1 |
ABC | 1610.77 | 4 | 484.64 | 1 |
WOA | 1733.59 | 4 | 493.08 | 1 |
HHO | 1600.35 | 5 | 416.26 | 1 |
GWTDBO | 1569.17 | 3 | 409.38 | 1 |
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1472.79 | 10 | 446.87 | 1 |
DBO | 1261.96 | 10 | 468.77 | 1 |
GWO | 1457.42 | 10 | 383.50 | 1 |
ABC | 1521.77 | 10 | 388.09 | 1 |
WOA | 1324.67 | 11 | 432.93 | 1 |
HHO | 1423.34 | 10 | 392.74 | 1 |
GWTDBO | 1192.43 | 9 | 388.69 | 1 |
Table 14 Evaluated results of trajectory planning for Scenario C
算法 | 最大航程/km | 威胁区域 接近次数 | 高度偏离 程度/km | 路径平滑度 |
---|---|---|---|---|
ACO | 1472.79 | 10 | 446.87 | 1 |
DBO | 1261.96 | 10 | 468.77 | 1 |
GWO | 1457.42 | 10 | 383.50 | 1 |
ABC | 1521.77 | 10 | 388.09 | 1 |
WOA | 1324.67 | 11 | 432.93 | 1 |
HHO | 1423.34 | 10 | 392.74 | 1 |
GWTDBO | 1192.43 | 9 | 388.69 | 1 |
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