Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (3): 928-936.DOI: 10.11772/j.issn.1001-9081.2024030370
• Advanced computing • Previous Articles Next Articles
Xingwang WANG1, Qingyang ZHANG1(), Shouyong JIANG2, Yongquan DONG1
Received:
2024-04-02
Revised:
2024-04-26
Accepted:
2024-04-28
Online:
2024-05-16
Published:
2025-03-10
Contact:
Qingyang ZHANG
About author:
WANG Xingwang, born in 1998, M. S. candidate. His research interests include evolutionary algorithm, intelligent algorithms.Supported by:
通讯作者:
张清杨
作者简介:
王兴旺(1998—),男,江苏徐州人,硕士研究生,主要研究方向:进化算法、智能算法基金资助:
CLC Number:
Xingwang WANG, Qingyang ZHANG, Shouyong JIANG, Yongquan DONG. Dynamic UAV path planning based on modified whale optimization algorithm[J]. Journal of Computer Applications, 2025, 45(3): 928-936.
王兴旺, 张清杨, 姜守勇, 董永权. 基于改进鲸鱼优化算法的动态无人机路径规划[J]. 《计算机应用》唯一官方网站, 2025, 45(3): 928-936.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2024030370
函数 | 指标 | WOA | PSO | AHA | TIWOA | IMWOA | HHO | MWOA |
---|---|---|---|---|---|---|---|---|
F1 | mean | 3.71E+04 | 1.51E+04 | 1.44E+04 | 4.11E+04 | 1.94E+04 | 9.66E+03 | 3.02E+02 |
std | 1.48E+04 | 8.08E+03 | 6.68E+03 | 2.50E+04 | 1.12E+04 | 6.46E+02 | 1.26E+00 | |
p | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F2 | mean | 5.61E+02 | 1.03E+03 | 4.61E+02 | 7.56E+02 | 6.02E+02 | 1.96E+03 | 4.24E+02 |
std | 1.34E+02 | 6.34E+02 | 4.55E+01 | 2.46E+02 | 2.03E+02 | 8.77E+02 | 3.22E+01 | |
p | 9.26E-09 | 3.02E-11 | 1.87E-05 | 3.02E-11 | 2.32E-06 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F3 | mean | 6.46E+02 | 6.93E+02 | 6.33E+02 | 6.48E+02 | 6.50E+02 | 6.56E+02 | 6.09E+02 |
std | 1.72E+01 | 1.43E+01 | 1.26E+01 | 1.76E+01 | 1.49E+01 | 7.67E+00 | 7.36E+00 | |
p | 1.61E-10 | 3.02E-11 | 1.17E-09 | 4.98E-11 | 3.69E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F4 | mean | 8.50E+02 | 9.09E+02 | 8.32E+02 | 8.57E+02 | 8.51E+02 | 8.58E+02 | 8.34E+02 |
std | 1.62E+01 | 1.74E+01 | 1.15E+01 | 1.09E+01 | 1.80E+01 | 7.33E+00 | 1.69E+01 | |
p | 4.46E-04 | 3.34E-11 | 8.53E-01 | 7.60E-07 | 4.71E-04 | 1.16E-07 | — | |
h | 1 | 1 | 0 | 1 | 1 | 1 | — | |
F5 | mean | 1.93E+03 | 3.85E+03 | 1.39E+03 | 1.61E+03 | 1.89E+03 | 1.55E+03 | 9.72E+02 |
std | 7.95E+02 | 9.58E+02 | 2.45E+02 | 3.79E+02 | 5.61E+02 | 2.01E+02 | 7.37E+01 | |
p | 6.70E-11 | 3.02E-11 | 4.62E-10 | 9.92E-11 | 6.07E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F6 | mean | 1.60E+07 | 2.52E+07 | 2.87E+05 | 1.21E+07 | 2.67E+07 | 2.98E+07 | 3.78E+03 |
std | 8.16E+07 | 8.88E+07 | 4.19E+05 | 2.65E+07 | 1.24E+08 | 2.13E+07 | 1.98E+03 | |
p | 9.06E-08 | 4.50E-11 | 3.02E-11 | 1.96E-10 | 1.78E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F7 | mean | 2.10E+03 | 2.17E+03 | 2.07E+03 | 2.12E+03 | 2.11E+03 | 2.12E+03 | 2.04E+03 |
std | 4.14E+01 | 4.68E+01 | 2.38E+01 | 4.00E+01 | 4.76E+01 | 1.94E+01 | 1.41E+01 | |
p | 3.82E-09 | 3.02E-11 | 4.31E-08 | 3.69E-11 | 5.07E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F8 | mean | 2.24E+03 | 2.28E+03 | 2.25E+03 | 2.26E+03 | 2.26E+03 | 2.27E+03 | 2.22E+03 |
std | 2.46E+01 | 5.37E+01 | 3.87E+01 | 4.53E+01 | 4.61E+01 | 2.93E+01 | 3.89E+00 | |
p | 3.02E-11 | 3.02E-11 | 6.70E-11 | 3.02E-11 | 4.62E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F9 | mean | 2.69E+03 | 2.73E+03 | 2.62E+03 | 2.72E+03 | 2.68E+03 | 2.78E+03 | 2.53E+03 |
std | 6.70E+01 | 5.41E+01 | 4.59E+01 | 3.95E+01 | 4.68E+01 | 4.53E+01 | 2.68E+01 | |
p | 1.09E-10 | 4.50E-11 | 4.62E-10 | 4.08E-11 | 1.33E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F10 | mean | 2.70E+03 | 3.47E+03 | 2.59E+03 | 2.73E+03 | 2.62E+03 | 2.67E+03 | 2.56E+03 |
std | 3.37E+02 | 8.12E+02 | 1.02E+02 | 2.70E+02 | 1.55E+02 | 1.38E+02 | 7.18E+01 | |
p | 7.29E-03 | 4.57E-09 | 6.97E-03 | 6.01E-08 | 1.68E-03 | 6.91E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F11 | mean | 2.92E+03 | 3.28E+03 | 2.85E+03 | 3.12E+03 | 2.82E+03 | 3.61E+03 | 2.74E+03 |
std | 2.23E+02 | 4.83E+02 | 2.04E+02 | 2.98E+02 | 1.53E+02 | 3.57E+02 | 1.77E+02 | |
p | 2.77E-05 | 3.65E-08 | 7.96E-03 | 1.73E-07 | 2.16E-03 | 8.99E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F12 | mean | 1.33E+04 | 3.23E+03 | 2.89E+03 | 2.94E+03 | 7.92E+03 | 2.92E+03 | 2.88E+03 |
std | 8.25E+03 | 1.87E+02 | 3.13E+01 | 5.64E+01 | 6.85E+03 | 4.27E+01 | 1.49E+01 | |
p | 3.69E-11 | 3.02E-11 | 4.29E-01 | 1.43E-08 | 4.57E-09 | 3.08E-08 | — | |
h | 1 | 1 | 0 | 1 | 1 | 1 | — |
Tab. 1 Test results of different algorithms
函数 | 指标 | WOA | PSO | AHA | TIWOA | IMWOA | HHO | MWOA |
---|---|---|---|---|---|---|---|---|
F1 | mean | 3.71E+04 | 1.51E+04 | 1.44E+04 | 4.11E+04 | 1.94E+04 | 9.66E+03 | 3.02E+02 |
std | 1.48E+04 | 8.08E+03 | 6.68E+03 | 2.50E+04 | 1.12E+04 | 6.46E+02 | 1.26E+00 | |
p | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F2 | mean | 5.61E+02 | 1.03E+03 | 4.61E+02 | 7.56E+02 | 6.02E+02 | 1.96E+03 | 4.24E+02 |
std | 1.34E+02 | 6.34E+02 | 4.55E+01 | 2.46E+02 | 2.03E+02 | 8.77E+02 | 3.22E+01 | |
p | 9.26E-09 | 3.02E-11 | 1.87E-05 | 3.02E-11 | 2.32E-06 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F3 | mean | 6.46E+02 | 6.93E+02 | 6.33E+02 | 6.48E+02 | 6.50E+02 | 6.56E+02 | 6.09E+02 |
std | 1.72E+01 | 1.43E+01 | 1.26E+01 | 1.76E+01 | 1.49E+01 | 7.67E+00 | 7.36E+00 | |
p | 1.61E-10 | 3.02E-11 | 1.17E-09 | 4.98E-11 | 3.69E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F4 | mean | 8.50E+02 | 9.09E+02 | 8.32E+02 | 8.57E+02 | 8.51E+02 | 8.58E+02 | 8.34E+02 |
std | 1.62E+01 | 1.74E+01 | 1.15E+01 | 1.09E+01 | 1.80E+01 | 7.33E+00 | 1.69E+01 | |
p | 4.46E-04 | 3.34E-11 | 8.53E-01 | 7.60E-07 | 4.71E-04 | 1.16E-07 | — | |
h | 1 | 1 | 0 | 1 | 1 | 1 | — | |
F5 | mean | 1.93E+03 | 3.85E+03 | 1.39E+03 | 1.61E+03 | 1.89E+03 | 1.55E+03 | 9.72E+02 |
std | 7.95E+02 | 9.58E+02 | 2.45E+02 | 3.79E+02 | 5.61E+02 | 2.01E+02 | 7.37E+01 | |
p | 6.70E-11 | 3.02E-11 | 4.62E-10 | 9.92E-11 | 6.07E-11 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F6 | mean | 1.60E+07 | 2.52E+07 | 2.87E+05 | 1.21E+07 | 2.67E+07 | 2.98E+07 | 3.78E+03 |
std | 8.16E+07 | 8.88E+07 | 4.19E+05 | 2.65E+07 | 1.24E+08 | 2.13E+07 | 1.98E+03 | |
p | 9.06E-08 | 4.50E-11 | 3.02E-11 | 1.96E-10 | 1.78E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F7 | mean | 2.10E+03 | 2.17E+03 | 2.07E+03 | 2.12E+03 | 2.11E+03 | 2.12E+03 | 2.04E+03 |
std | 4.14E+01 | 4.68E+01 | 2.38E+01 | 4.00E+01 | 4.76E+01 | 1.94E+01 | 1.41E+01 | |
p | 3.82E-09 | 3.02E-11 | 4.31E-08 | 3.69E-11 | 5.07E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F8 | mean | 2.24E+03 | 2.28E+03 | 2.25E+03 | 2.26E+03 | 2.26E+03 | 2.27E+03 | 2.22E+03 |
std | 2.46E+01 | 5.37E+01 | 3.87E+01 | 4.53E+01 | 4.61E+01 | 2.93E+01 | 3.89E+00 | |
p | 3.02E-11 | 3.02E-11 | 6.70E-11 | 3.02E-11 | 4.62E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F9 | mean | 2.69E+03 | 2.73E+03 | 2.62E+03 | 2.72E+03 | 2.68E+03 | 2.78E+03 | 2.53E+03 |
std | 6.70E+01 | 5.41E+01 | 4.59E+01 | 3.95E+01 | 4.68E+01 | 4.53E+01 | 2.68E+01 | |
p | 1.09E-10 | 4.50E-11 | 4.62E-10 | 4.08E-11 | 1.33E-10 | 3.02E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F10 | mean | 2.70E+03 | 3.47E+03 | 2.59E+03 | 2.73E+03 | 2.62E+03 | 2.67E+03 | 2.56E+03 |
std | 3.37E+02 | 8.12E+02 | 1.02E+02 | 2.70E+02 | 1.55E+02 | 1.38E+02 | 7.18E+01 | |
p | 7.29E-03 | 4.57E-09 | 6.97E-03 | 6.01E-08 | 1.68E-03 | 6.91E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F11 | mean | 2.92E+03 | 3.28E+03 | 2.85E+03 | 3.12E+03 | 2.82E+03 | 3.61E+03 | 2.74E+03 |
std | 2.23E+02 | 4.83E+02 | 2.04E+02 | 2.98E+02 | 1.53E+02 | 3.57E+02 | 1.77E+02 | |
p | 2.77E-05 | 3.65E-08 | 7.96E-03 | 1.73E-07 | 2.16E-03 | 8.99E-11 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
F12 | mean | 1.33E+04 | 3.23E+03 | 2.89E+03 | 2.94E+03 | 7.92E+03 | 2.92E+03 | 2.88E+03 |
std | 8.25E+03 | 1.87E+02 | 3.13E+01 | 5.64E+01 | 6.85E+03 | 4.27E+01 | 1.49E+01 | |
p | 3.69E-11 | 3.02E-11 | 4.29E-01 | 1.43E-08 | 4.57E-09 | 3.08E-08 | — | |
h | 1 | 1 | 0 | 1 | 1 | 1 | — |
序号 | Map1 | 序号 | Map2 | ||
---|---|---|---|---|---|
威胁中心 | 威胁半径 | 威胁中心 | 威胁半径 | ||
1 | (65,52) | 6 | 1 | (75,52) | 7 |
2 | (15,30) | 5 | 2 | (25,20) | 5 |
3 | (32,68) | 6 | 3 | (12,80) | 6 |
4 | (49,26) | 5 | 4 | (49,56) | 5 |
5 | (55,80) | 4 | 5 | (55,88) | 6 |
Tab. 2 Threat zone information
序号 | Map1 | 序号 | Map2 | ||
---|---|---|---|---|---|
威胁中心 | 威胁半径 | 威胁中心 | 威胁半径 | ||
1 | (65,52) | 6 | 1 | (75,52) | 7 |
2 | (15,30) | 5 | 2 | (25,20) | 5 |
3 | (32,68) | 6 | 3 | (12,80) | 6 |
4 | (49,26) | 5 | 4 | (49,56) | 5 |
5 | (55,80) | 4 | 5 | (55,88) | 6 |
地图 | 指标 | WOA | PSO | AHA | TIWOA | IMWOA | HHO | MWOA |
---|---|---|---|---|---|---|---|---|
Map1 | mean | 1.24E+02 | 2.02E+02 | 1.17E+02 | 1.29E+02 | 1.20E+02 | 1.76E+02 | 1.13E+02 |
std | 3.38E+00 | 1.76E+01 | 2.29E+00 | 1.44E+01 | 6.42E+00 | 4.89E+01 | 2.12E+00 | |
p | 1.83E-04 | 1.83E-04 | 5.83E-04 | 1.83E-04 | 4.40E-04 | 1.83E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
Map2 | mean | 1.17E+02 | 5.15E+02 | 1.18E+02 | 1.18E+02 | 1.19E+02 | 1.86E+02 | 1.13E+02 |
std | 3.87E+00 | 2.58E+02 | 2.74E+00 | 5.46E+00 | 1.91E+00 | 6.10E+01 | 1.88E+00 | |
p | 2.57E-02 | 1.83E-04 | 4.40E-04 | 1.83E-04 | 2.46E-04 | 1.83E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — |
Tab. 3 Experimental results of path planning
地图 | 指标 | WOA | PSO | AHA | TIWOA | IMWOA | HHO | MWOA |
---|---|---|---|---|---|---|---|---|
Map1 | mean | 1.24E+02 | 2.02E+02 | 1.17E+02 | 1.29E+02 | 1.20E+02 | 1.76E+02 | 1.13E+02 |
std | 3.38E+00 | 1.76E+01 | 2.29E+00 | 1.44E+01 | 6.42E+00 | 4.89E+01 | 2.12E+00 | |
p | 1.83E-04 | 1.83E-04 | 5.83E-04 | 1.83E-04 | 4.40E-04 | 1.83E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — | |
Map2 | mean | 1.17E+02 | 5.15E+02 | 1.18E+02 | 1.18E+02 | 1.19E+02 | 1.86E+02 | 1.13E+02 |
std | 3.87E+00 | 2.58E+02 | 2.74E+00 | 5.46E+00 | 1.91E+00 | 6.10E+01 | 1.88E+00 | |
p | 2.57E-02 | 1.83E-04 | 4.40E-04 | 1.83E-04 | 2.46E-04 | 1.83E-04 | — | |
h | 1 | 1 | 1 | 1 | 1 | 1 | — |
参数 | BKA | GOOSE | NRBO | CPO | HO | MWOA |
---|---|---|---|---|---|---|
Exploitation | 50.69 | 5.42 | 18.93 | 80.18 | 90.04 | 7.36 |
Exploration | 49.31 | 94.58 | 81.07 | 19.82 | 9.96 | 92.64 |
Tab. 4 Exploration and exploitation results of different algorithms
参数 | BKA | GOOSE | NRBO | CPO | HO | MWOA |
---|---|---|---|---|---|---|
Exploitation | 50.69 | 5.42 | 18.93 | 80.18 | 90.04 | 7.36 |
Exploration | 49.31 | 94.58 | 81.07 | 19.82 | 9.96 | 92.64 |
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