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

摘要/Abstract

摘要：

为进一步提升分布式光伏电站巡检效率，降低巡检成本，将无人机机场选址、巡检任务分配及无人机飞行路径规划等抽象为选址-路径组合优化问题，构建双目标混合整数线性规划模型同时最小化机场建设成本和巡检任务时长。为求解该问题，首先利用ε-约束算法进行求解，随后提出改进的基于非支配解排序的遗传算法（non-dominated sorting genetic algorithm，NSGA-II），通过加入可行性判断机制、考虑灵活度的分配规则以及运用混合粒子群算法等提升算法性能。实验部分，首先基于相关数据开展案例分析。随后生成80个随机算例进行数值实验，将改进NSGA-II与ε-约束算法及基础NSGA-II的求解结果进行对比分析，并开展关键参数灵敏度实验，充分验证本文提出的改进NSGA-Ⅱ算法的良好性能。

关键词: 分布式光伏电站, 智能巡检, 无人机调度, 多目标优化, 选址-路径组合优化

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

中图分类号:

V 355

李延通, 李子璠, 周姗姗, 张闯. 无人机光伏电站巡检双目标选址-路径问题研究[J]. 系统工程与电子技术, 2025, 47(8): 2612-2621.

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.

图/表 14

表1

表2

图1

图2

图3

表3

表4

图4

图5

图6

表5

表6

图7

图8

参考文献 30

1	国家能源局. 2023年光伏发电建设情况[EB/OL]. [2024-06-01]. https://www.nea.gov.cn/2024-06/01/c_1310765696.html.
	National Energy Administration. Construction Status of Photovoltaic Power Generation in 2023[EB/OL]. [2024-06-01]. https://www.nea.gov.cn/2024-06/01/c_1310765696.html.
2	王建峰, 贾高伟, 郭正, 等. 多无人机协同任务规划方法研究综述[J]. 系统工程与电子技术, 2024, 46 (10): 3437- 3451.
	WANG J F, JIA G W, GUO Z. Research status and development of multi-UAV system mission planning[J]. Systems Engineering and Electronics, 2024, 46 (10): 3437- 3451.
3	LI Z R, ZHANG Y W, WU H, et al. Design and application of a UAV autonomous inspection system for high-voltage power transmission lines[J]. Remote Sensing, 2023, 15 (3): 865.
4	WANG Z Y, GAO Q, XU J B, et al. A review of UAV power line inspection[C]// Proc. of the International Conference on Guidance, Navigation and Control, 2020.
5	CHEN X B, WANG C X, LIU C, et al. Autonomous crack detection for mountainous roads using UAV inspection system[J]. Sensors, 2024, 24 (14): 4751.
6	ZHANG R, HAO G B, ZHANG K, et al. Unmanned aerial vehicle navigation in underground structure inspection: a review[J]. Geological Journal, 2023, 58 (6): 2454- 2472.
7	刘春, 艾克然木·艾克拜尔, 蔡天池. 面向建筑健康监测的无人机自主巡检与裂缝识别[J]. 同济大学学报（自然科学版）, 2022, 50 (7): 921- 932.
	LIU C, AKBAR A, CAI T C. UAV Autonomous inspection and crack detection towards building health monitoring[J]. Journal of Tongji University （Natural Science）, 2022, 50 (7): 921- 932.
8	NICCOLAI A, GRIMACCIA F, LEVA S, et al. Photovoltaic plant inspection by means of UAV: current practices and future perspectives[C]// Proc. of the IEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe, 2021.
9	XIAO K L, ZHOU Y, XU R X, et al. An inspection mode based on unmanned aerial vehicle for photovoltaic system[C]// Proc. of the IEEE 5th Advanced Information Management, Communicates, Electronic and Automation Control Conference, 2022.
10	BENEDETTI M M D, BASCETTA L, FALSONE A, et al. Automated photovoltaic power plant inspection via unmanned vehicles[J]. IEEE Trans. on Control Systems Technology, 2024, 32 (2): 399- 412.
11	DING Y F, CAO R, LIANG S M, et al. Density-based optimal UAV path planning for photovoltaic farm inspection in complex topography[C]// Proc. of the Chinese Control and Decision Conference, 2020.
12	MICHAIL A, LIVERA A, TZIOLIS G, et al. A comprehensive review of unmanned aerial vehicle-based approaches to support photovoltaic plant diagnosis[J]. Heliyon, 2024, 10(1): e 23983.
13	HIJIAWI U, LAKSHMINARAYANA S, XU T H, et al. A review of automated solar photovoltaic defect detection systems: approaches, challenges, and future orientations[J]. Solar Energy, 2023, 266, 112186.
14	SALHI S, RAND G K. The effect of ignoring routes when locating depots[J]. European Journal of Operational Research, 1989, 39 (2): 150- 156.
15	LOPES R B, FERREIRA C, SANTOS B S, et al. A taxonomical analysis, current methods and objectives on location-routing problems[J]. International Transactions in Operational Research, 2013, 20 (6): 795- 822.
16	PRODHON C, PRINS C. A survey of recent research on location-routing problems[J]. European Journal of Operational Research, 2014, 238 (1): 1- 17.
17	MARA S T W, KUO R J, ASIH A M S. Location-routing problem: a classification of recent research[J]. International Transactions in Operational Research, 2021, 28 (6): 2941- 2983.
18	RIBERIO R G, JUNIOR J R C, COTA L P, et al. Unmanned aerial vehicle location routing problem with charging stations for belt conveyor inspection system in the mining industry[J]. IEEE Trans. on Intelligent Transportation Systems, 2019, 21 (10): 4186- 4195.
19	AYDIN N, YILMAZ O, DEVECI M, et al. Heuristics based optimization for multi-depot drone location and routing problem to detect post-earthquake damages[J]. IEEE Trans. on Intelligent Transportation Systems, 2022, 25 (1): 850- 858.
20	SANTIN R, ASSIA L, VIVAS A, et al. Matheuristics for multi-UAV routing and recharge station location for complete area coverage[J]. Sensors, 2021, 21 (5): 1705.
21	DASDEMIR E, BATTA R, KOKSALAN M, et al. UAV routing for reconnaissance mission: a multi-objective orienteering problem with time-dependent prizes and multiple connections[J]. Computers & Operations Research, 2022, 145, 105882.
22	SINGH M K, CHOUDHARY A, GULIA S, et al. Multi-objective NSGA-II optimization framework for UAV path planning in a UAV-assisted WSN[J]. The Journal of Supercomputing, 2023, 79 (1): 832- 866.
23	KARATAS M, YAKICI E, DASCI A. Solving a bi-objective unmanned aircraft system location-allocation problem[J]. Annals of Operations Research, 2022, 319 (2): 1631- 1654.
24	LI Y T, CHU F, FENG C P, et al. Integrated production inventory routing planning for intelligent food logistics systems[J]. IEEE Trans. on Intelligent Transportation Systems, 2018, 20 (3): 867- 878.
25	MA H P, ZHANG Y J, SUN S Y, et al. A comprehensive survey on NSGA-II for multi-objective optimization and applications[J]. Artificial Intelligence Review, 2023, 56 (12): 15217- 15270.
26	WANG Y J, WANG G G, TIAN F M, et al. Solving energy-efficient fuzzy hybrid flow-shop scheduling problem at a variable machine speed using an extended NSGA-II[J]. Engineering Applications of Artificial Intelligence, 2023, 121, 105977.
27	KUO R J, EDBERT E, ZULVIA F E, et al. Applying NSGA-II to vehicle routing problem with drones considering makespan and carbon emission[J]. Expert Systems with Applications, 2023, 221, 119777.
28	RAHBARI M, KHAMSEH A A, SADTI-KENETI Y, et al. A risk-based green location-inventory-routing problem for hazardous materials: NSGA II, MOSA, and multi-objective black widow optimization[J]. Environment, Development and Sustainability, 2022, 24 (2): 2804- 2840.
29	TANG L H, LI Y T, BAI D Y, et al. Bi-objective optimization for a multi-period COVID-19 vaccination planning problem[J]. Omega, 2022, 110, 102617. doi: 10.1016/j.omega.2022.102617
30	高尚, 韩斌, 吴小俊, 等. 求解旅行商问题的混合粒子群优化算法[J]. 控制与决策, 2004, (11): 1286- 1289. doi: 10.3321/j.issn:1001-0920.2004.11.020
	GAO S, HAN B, WU X J. Solving traveling salesman problem by hybrid particle swarm optimization algorithm[J]. Control and Decision, 2004, (11): 1286- 1289. doi: 10.3321/j.issn:1001-0920.2004.11.020

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	—	—	—	—