无人机光伏电站巡检双目标选址-路径问题研究

doi:10.12305/j.issn.1001-506X.2025.08.18

Abstract

Abstract:

To improve the efficiency while reduce the cost of distributed photovoltaic power station inspection, this paper integrates the unmanned aerial vehicle （UAV） airport location selection, inspection task allocation, and UAV flight path planning into a class of location-path combination optimization problems. To simultaneously minimize the airport construction costs and inspection makespan, a bi-objective mixed integer linear programming model is constructed. To solve this problem, the ε-constraint algorithm is first used, followed by an improved non-dominated sorting genetic algorithm （NSGA-II）. The improved NSGA-II incorporates a feasibility judgment mechanism and designs task point allocation based on the flexibility-oriented, to improve algorithm performance. In the experimental section, a case analysis is conducted based on relevant data. Then, 80 randomly-generated instances are generated for numerical experiments, to compare the performances between the improved NSGA-II with the ε-constrained algorithm and the basic NSGA-II. Sensitivity analysis of key parameters is also conducted to fully verify the good performance of the improved NSGA-II proposed in this paper.

Key words: distributed photovoltaic power station, intelligent inspection, unmanned aerial vehicle scheduling, bi-objective optimization, location-routing combinatorial optimization

CLC Number:

V 355

Yantong LI, Zifan LI, Shanshan ZHOU, Chuang ZHANG. Bi-objective location-routing problem of UAV for photovoltaic power station inspection research[J]. Systems Engineering and Electronics, 2025, 47(8): 2612-2621.

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References 30

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符号	含义
$N$	待巡检光伏区域集合$N = \{ 1,2,...,n\} $
$K$	无人机机场候选位置集合$K = \{ 1,2,...,m\} $
$V$	节点集合，$V = N \cup 0$其中0表示无人机起始点（机场）
$R$	起飞次数集合，$R = \{ 1,2,...,n\} $
${s_i}$	无人机巡检任务点i所需时间
${\tau _{ij}}$	无人机从节点i飞行至节点j所需时间
$a$	无人机一次充电时间
$U$	无人机最大续航时间
$B$	单个无人机场建设成本
M	足够大的正整数

符号	含义
${z_k}$	0-1变量，1表示候选机场k开启，否则为0
${v_{jk}}$	0-1变量，1表示候选机场k中的无人机巡检任务点j，否则为0
${y_{jkr}}$	0-1变量，1表示候选机场k中的无人机第r次起飞巡检任务点j，否则为0
$x_{ij}^{kr}$	0-1变量，1表示候选机场k中的无人机第r次起飞由节点i飞行至节点j，否则为0
${t_{kr}}$	候选机场k中的无人机第r次起飞，完成巡检任务后返回至机场的时刻
${t_i}$	无人机到达巡检任务点i的时刻
$C_{{\mathrm{max}}} $	巡检任务完成时间

位置	经度/(°)	纬度/(°)	巡检时间/min
1	113.69065	36.58544	11.06
2	113.55794	36.742542	15.95
3	113.73787	36.735363	18.86
4	113.69065	36.68733	13.83
5	113.71034	36.618713	18.82
6	113.64712	36.696712	16.23
7	113.51195	36.682579	17.85
8	113.47817	36.719521	17.92
9	113.7359	36.770985	14.39
10	113.78767	36.67873	15.6
11	113.70919	36.676083	19.58
12	113.67721	36.661713	11.8
13	113.63738	36.653194	11.84
14	113.52851	36.63398	17.47
15	113.73056	36.643299	13.09
16	113.68954	36.637291	17.43
17	113.63693	36.587761	18.89
18	113.79086	36.605854	13.68
19	113.75798	36.750904	17.48
20	113.76867	36.561501	16.57
21	113.7571	36.532169	19.29
22	113.73436	36.502319	18.55
23	113.69089	36.51535	12.42
24	113.57665	36.58544	16.04

机场候选点	经度/(°)	纬度/(°)
1	113.675377	36.744762
2	113.534492	36.694904
3	113.604111	36.637623
4	113.752342	36.607475
5	113.716110	36.701012
6	113.676308	36.578804

（n, m）	改进NSGA-II				ε-约束法
（n, m）	Nd	Hv	e	Time/s	Nd	Hv	e	Time/s
（10,1）	1	0.13	1.55	1	1	1.00	1.00	1800
（10,2）	2	0.43	1.28	1	2	1.00	1.00	1683
（10,3）	2	0.68	1.08	1	3	1.00	1.00	1927
（10,4）	2	1.00	1.00	6	—	—	—	—
（10,5）	4	1.00	1.31	3	—	—	—	—
（10,6）	4	1.00	1.00	5	—	—	—	—
（10,7）	4	0.96	1.00	6	—	—	—	—
（10,8）	4	0.92	1.01	5	—	—	—	—

Bi-objective location-routing problem of UAV for photovoltaic power station inspection research

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n	改进NSGA-II				基础NSGA-II
n	Nd	Hv	e	Time/s	Nd	Hv	e	Time/s
10	2.88	0.76	1.15	3.50	2.50	0.64	1.13	0.63
20	2.88	0.94	1.01	2.13	2.50	0.62	1.02	1.00
30	3.00	0.93	1.01	5.75	2.63	0.86	1.01	1.25
40	2.38	0.94	1.01	2.88	2.75	0.81	1.03	1.75
50	2.88	0.95	1.00	3.13	2.50	0.85	1.03	1.88
60	3.25	0.99	1.01	3.00	2.75	0.84	1.06	1.75
70	3.25	0.98	1.01	3.38	2.50	0.73	1.03	2.50
80	3.38	0.98	1.02	3.63	3.00	0.91	1.03	2.63
90	3.50	0.95	1.02	4.13	2.75	0.85	1.02	2.88
100	3.38	0.99	1.01	4.25	2.88	0.93	1.03	3.50
均值	3.08	0.94	1.02	3.58	2.68	0.80	1.04	1.98