Multi-objective frequency planning: concept, modeling, and solution

doi:10.23919/JSEE.2026.000058

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 337-356.doi: 10.23919/JSEE.2026.000058

• ELECTRONICS TECHNOLOGY • Previous Articles

Multi-objective frequency planning: concept, modeling, and solution

Hang GAO(), Song ZHA(), Jijun HUANG(), Haiyang XIA(), Jibin LIU()

College of Electronic Science and Technology, National University of Defense Technology, Changsha 410000, China

Received:2024-05-09 Accepted:2026-03-30 Online:2026-04-18 Published:2026-04-30
Contact: Song ZHA E-mail:836418930@qq.com;zhasong0551@163.com;huangjijun1989@nudt.edu.cn;easonhsia@sina.com;liujibin@gfkd.edu.com
About author:
GAO Hang was born in 2001. He received his B.E. degree from National University of Defense Technology (NUDT). He is currently working toward his master degree with the College of Electronic Science and Technology, National University of Defense Technology, Changsha, China. His research interests include spectrum management and electromagnetic resource optimization. E-mail: 836418930@qq.com

ZHA Song was born in 1987. He received his M.S. degree in signal and information processing from the Electronic Engineering Institute (EEI) and Ph. D. degree in electronic science and technology from the National University of Defense Technology (NUDT), in 2010 and 2014, respectively. He is currently a lecturer in NUDT. His research interests include electromagnetic environment sensing and electromagnetic compatibility. E-mail: zhasong0551@163.com

HUANG Jijun was born in 1970. He received his M.S degree in electromagnetic field and microwave technologies and the Ph.D. degree in electronic science and technology from the National University of Defense Technology (NUDT), in 1997, and 2005, respectively. He is currently an Associate Professor in NUDT. His current research interests include spectrum management and electromagnetic resource optimization. E-mail: huangjijun1989@nudt.edu.cn

XIA Haiyang was born in 1993. He received his B.E. degree from the College of Electronic Science and Technology, National University of Defense Technology, 2015. He is currently working toward his master’s degree with the College of Electronic Science and Technology, National University of Defense Technology, Changsha, China. His research interests include radio environment map construction, cognitive radio, and radio spectrum sensing and management. E-mail: easonhsia@sina.com

LIU Jibin was born in 1974. He received his M.S degree in electromagnetic field and microwave technologies and the Ph.D. degree in electronic science and technology from the National University of Defense Technology (NUDT), in 1998, and 2007, respectively. He is currently a full Professor with the school of electronic science and technology at NUDT. His current research interests include spectrum management, electromagnetic compatibility and RF front-end electromagnetic protection. E-mail: liujibin@gfkd.edu.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61901486; U19A2058).

Abstract

Abstract:

Frequency planning is of great significance which can effectively dispatch the battlefield resources of radio equipment. To enhance the efficiency of scheduling, this paper investigates the frequency planning problem (FPP) and puts forward a multi-objective approach. The proposed multi-objective model considers the coordination constraints of radio equipment alongside diverse resources, defining key points to delineate the cooperative interactions among radio equipment. The model integrates considerations of time, space, and energy, focusing on electromagnetic interference, frequency demand satisfaction and frequency occupancy as its primary optimization objectives. To improve the accuracy of the solution, this study proposes a multi-population multi-objective memetic algorithm (MPMA). This algorithm employs a segment-based coding strategy and a specialized genetic operator to facilitate the integration of global and local search techniques. Additionally, chaos initialization and a multi-population-based scheduling approach are incorporated to enhance global search performance. The experimental results demonstrate the superiority of the proposed model and MPMA in meeting the diverse scheduling needs of radio equipment across various scenarios.

Key words: frequency planning, resource scheduling, multi-objective optimization, memetic algorithm

Hang GAO, Song ZHA, Jijun HUANG, Haiyang XIA, Jibin LIU. Multi-objective frequency planning: concept, modeling, and solution[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 337-356.

Figures/Tables 20

Table 1

Relevant notations for radio equipment in SFPP"

Notion	Definition
$e f b_i=\left(e f b_l, e f b_h\right) $	The working frequency band of radio equipment $e_i$, $e f b_i$ and $e f b_h$ respectively represents the lower and upper limits of the frequency
$eb_i$	The channel bandwidth of radio equipment $e_i$
$eg_i$	The antenna main lobe gain of radio equipment $e_i$
$er_i$	The interference threshold of the receiver of radio equipment $e_i$
$ep_i$	The frequency priority of radio equipment $e_i$
$ql_i$	The platform serial number of radio equipment $e_i$
$qn_i$	The frequency demand quantity of radio equipment $e_i$
$efp_i$	The pre-assigned frequency for radio equipment $e_i$
$epp_i^m$	The pre-assigned power for radio equipment $e_i$ at key point $p_i^m$
$esp_{i}^{m}$	The pre-assigned geographic coordinates for radio equipment $e_i$ at key point $p_{i}^{m}$
$ef_{i}$	The set of frequencies assigned to radio equipment $e_i$
$ep_{i}^{m}$	The power assigned to radio equipment $e_i$ at key point $p_i^m$
$es_{i}^{m}$	The geographic coordinates assigned to radio equipment $e_i$ at key point $p_{i}^{m}$
$f_{\max}$	The maximum number of equipment frequency requirements
$p_{\max}$	The maximum number of key points involved in power operation for each radio equipment
$c_{\max}$	The maximum number of key points involved in geographic location operation for each radio equipment
$E f c_i=\left\{e f c_i^1, e f c_i^2, \cdots, e f c_i^{\left\|E f c_i\right\|}\right\}$	The set of selectable frequencies for radio equipment $e_{i}$
$E p c_i=\left\{e p c_i^1, e p c_i^2, \cdots, e p c_i^{\left\|E p c_i\right\|}\right\}$	The set of selectable power for radio equipment $e_i $
$E s c_i=\left\{e s c_i^1, e s c_i^2, \cdots, e s c_i^{\left\|E s c_i\right\|}\right\}$	The set of selectable geographic coordinates for radio equipment $e_i$, where $e s c_i^k=\left(e s c_{i, x}^k, e s c_{i, y}^k\right) $ denotes the horizontal and vertical coordinates of the geographical location

Table 1

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Fig 7

Fig 8

Fig 9

Table 9

Fig 10

Fig 11

References 33

1	LU D J, WANG X, WU X T, et al Adaptive allocation strategy for cooperatively jamming netted radar system based on improved cuckoo search algorithm. Defense Technology, 2023, 24 (6): 285- 297. doi: 10.1016/j.dt.2022.04.013
2	KIOUCHE A E, BESSEDIK M, BENBOUZID F, et al An efficient hybrid multi-objective memetic algorithm for the frequency assignment problem. Engineering Applications of Artificial Intelligence, 2020, 87, 103265. doi: 10.1016/j.engappai.2019.103265
3	SARA C, LUCA D G, ROBERTO M R, et al Multi-neighborhood simulated annealing for the minimum interference frequency assignment problem. EURO Journal on Computational Optimization, 2022, 10, 100024. doi: 10.1016/j.ejco.2021.100024
4	WEISE T, WU Z Z, LI X L, et al Frequency fitness assignment: optimization without a bias for good solutions can be efficient. IEEE Trans. on Evolutionary Computation, 2021, 27, 980- 992.
5	FAN Q R, WANG X Y, LI J, et al Spectrum requirements matching degree-based frequency assignment algorithm. Radio Communication Technology, 2023, 49 (3): 583- 588.
6	HALE W K Frequency assignment: Theory and applications. Proceedings of the IEEE, 1980, 68 (12): 1497- 1514.
7	KOLEN A, VAN C. A constraint satisfaction approach to the radio link frequency assignment problem. Caparica: Relatório técnico da Universidade, 1994.
8	AARDAL K I, HIPOLITO A, VAN HOESEL C P M. A branch-and-cut algorithm for the frequency assignment problem. Maastricht: METEOR, Maastricht Research School of Economics of Technology and Organization, 1996.
9	ALRAJHI K, THOMPSON J, PADUNGWECH W. A heuristic approach for the dynamic frequency assignment problem. Proc. of the UK Workshop on Computational Intelligence, 2017: 91–103.
10	HAO J K, DORNE R, GALINIER P. Tabu search for frequency assignment in mobile radio networks. Heuristics, 1998, 4 (1): 47–62.
11	WANG F, DONG J, LU D M, et al Frequency assignment algorithm based on hybrid intelligent optimization method. Chinese Journal of Radio Science, 2013, 28 (5): 947- 952. doi: 10.1109/cvidl51233.2020.00-50
12	SIDDIQI U F , SAIT S M. An optimization heuristic based on non-dominated sorting and tabu search for the fixed spectrum frequency assignment problem. IEEE Access, 2018, 6: 72635−72648.
13	WANG G H Frequency assignment algorithm optimization based on simulated annealing algorithm. Radio Communications Technology, 2017, 43 (5): 57- 61.
14	XU Q, XIONG H, LI Z, et al An improved ANTS algorithm for frequency assignment problem. Radio Engineering, 2010, 40 (1): 58- 61.
15	LAU T L, TSANG E P K Guided genetic algorithm and its application to radio link frequency assignment problems. Constraints, 2001, 6 (4): 373- 398. doi: 10.1023/A:1011406425471
16	LI X C, HE Q H Multi-areas outstanding covering optimization method of HF network based on preference ranking elimination NSGAII algorithm. Journal of Electronics & Information Technology, 2017, 39 (8): 1779- 1787.
17	LIU M, ZHA S HUANG J J, et al. Frequency planning method for joint operations based on multi-objective optimization. Chinese Journal of Radio Science, 2022, 37 (3): 434- 442.
18	ZHUMA E, PURIS A Allocation of frequencies in GSM mobile networks using meta heuristics ACO. Revista Publicando, 2015, 2 (5): 47- 64.
19	NIU K, LI B, FU Q. Method of battlefield frequency allocation based on chaotic perturbation mechanism particle swarm optimization algorithm. Journal of System Simulation, 2021, 33(8): 1905−1913.(in Chinese)
20	OSMAN, ZEIN E, EMAM A M, et al Minimizing interference in frequency assignment problem based on guided particle swarm optimization algorithm. International Journal of Scientific & Technology Research, 2017, 27 (4): 980- 992.
21	HADJI E, BABES M Integrating tabu search in particle swarm optimization for the frequency assignment problem. China Communications, 2016, 13 (3): 137- 155. doi: 10.1109/cc.2016.7445509
22	SALCEDO S, BOUSOÑO C A hybrid neural-genetic algorithm for the frequency assignment problem in satellite communications. Applied Intelligence, 2005, 22 (3): 207- 217. doi: 10.1007/s10791-005-6619-y
23	WANG Y Y, ZHAO W J Multi-objective optimization of tasks scheduling problem for overlapping multiple tower cranes. Buildings, 2024, 14 (4): 867. doi: 10.3390/buildings14040867
24	YAN L, GUO W, XU D, et al. Dynamic frequency assignment method on the battlefield with complex interference constraints. Proc. of the International Conference on Information Science and Control Engineering, 2020: 1850−1855.
25	XU Z, LIU Y N, ZHANG Z B, et al Adaptive planning technology for strategy based battlefield frequency. Command Information System and Technology, 2023, 14 (1): 35- 41.
26	GRELLA F M Genetic algorithms in the multi-objective optimization. African Journal of Oral Health Sciences, 2011, 11, 81.
27	MOSCATO P. On evolution, search, genetic algorithms and martial arts-towards memetic algorithms. Caltech Concurrent Computation Program, Evolution, Search, Optimization, 1989: 1−68.
28	REN H, LIU, K, YAN G Z, et al A memetic algorithm for cooperative complex task offloading in heterogeneous vehicular networks. IEEE Trans. on Network Science and Engineering, 2023, 10 (1): 189- 204. doi: 10.1109/TNSE.2022.3206228
29	DU Y H, WANG T, XIN B, et al A data-driven parallel scheduling approach for multiple agile earth observation satellites. IEEE Trans. on Evolutionary Computation, 2020, 24 (4): 679- 693. doi: 10.1109/TEVC.2019.2934148
30	PARK J, PARK M W, KIM D W, et al Multi-population genetic algorithm for multilabel feature selection based on label complementary communication. Entropy, 2020, 22 (8): 876. doi: 10.3390/e22080876
31	XUE S, CHEN X, WANG Y T, et al Research on multi-objective resource constrained project scheduling problem based on improved multi population genetic algorithm. Journal of Industrial Engineering/Engineering Management, 2023, 37 (5): 167- 175.
32	LI Y, LI X Y, GAO L, et al An efficient critical path based method for permutation flow shop scheduling problem. Journal of Manufacturing Systems, 2022, 63, 344- 353. doi: 10.1016/j.jmsy.2022.04.005
33	LI S Y, WANG Y F, QIAO J F, et al A regional local search strategy for NSGA II algorithm. Acta Automatica Sinica, 2020, 46 (12): 2617- 2627.

Parameter	Value
Parameter	Category 1	Category 1
Equipment serial number	1−15	16−30
Function	Radar	Radio station
Frequency band/MHz	[4000,7200]	[30,88]
Optional frequency interval /MHz	50	2.5
Channel bandwidth/MHz	100	2.5
Antenna main lobe gain/dBi	5	5
Receiver interference threshold/dBm	−115	−120
Optional transmit power/kW	10,20,30,40	0.01,0.02,0.03
Number of frequency requirements	2	1

Case	Radio equipment
Case 1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	●	●	●	●	●	○	○	○	○	○	○	○	○	○	○
	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
	○	○	○	○	○	○	○	○	○	○	○	○	○	○	○
Case 2	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	●	●	●	●	●	●	●	●	●	●	●	●	●	●	●
	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
	○	○	○	○	○	○	○	○	○	○	○	○	○	○	○
Case 3	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	●	●	●	●	●	●	●	●	●	●	●	●	●	●	●
	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
	●	●	●	●	●	●	●	●	●	●	●	●	●	●	●

Equipment	Key point	Start time	Operation	Priority
1	Point 1	0	1	5
1	Point 2	2	3	2
2	Point 1	0	1	4
2	Point 2	1	4	2
3	Point 1	1	1	3
3	Point 2	2	5	2
4	Point 1	1	1	1
4	Point 2	2	2	1
5	Point 1	1	1	2
5	Point 2	2	3,5	2

Equipment	Key point	Start time	Operation	Priority	Equipment	Key point	Start time	Operation	Priority
1	Point 1	0	1	5	9	Point 1	0	1	2
1	Point2	1	3	2	9	Point 2	1	3	4
2	Point 1	0	1	4	10	Point 1	1	1	2
2	Point 2	1	2	2	10	Point 2	2	4	3
3	Point 1	0	1	3	11	Point 1	1	1	2
3	Point 2	1	2	2	11	Point 2	2	5	1
4	Point 1	1	1	1	12	Point 1	0	1	3
4	Point 2	2	3	3	12	Point 2	1	5	5
5	Point 1	1	1	5	13	Point 1	0	1	2
5	Point 2	2	2	2	13	Point 2	1	5	1
6	Point 1	2	1	1	14	Point 1	0	1	4
6	Point 2	3	3,5	4	14	Point 2	1	3	5
7	Point 1	2	1	5	15	Point 1	0	1	2
7	Point 2	3	4,5	2	15	Point 2	1	2	2
8	Point 1	0	1	2
8	Point 2	1	2	5

Equipment	Key point	Start time	Operation	Priority	Equipment	Key point	Start time	Operation	Priority
1	Point 1	0	1	5	16	Point 1	0	1	2
2	Point 1	0	1	2	17	Point 1	0	1	2
3	Point 1	0	1	4	18	Point 1	0	1	3
4	Point 1	0	1	2	19	Point 1	1	1	3
5	Point 1	0	1	3	20	Point 1	1	1	2
6	Point 1	1	1	2	21	Point 1	1	1	2
7	Point 1	1	1	1	22	Point 1	1	1	2
8	Point 1	1	1	3	23	Point 1	2	1	3
9	Point 1	1	1	5	24	Point 1	2	1	3
10	Point 1	2	1	2	25	Point 1	2	1	3
11	Point 1	2	1	1	26	Point 1	2	1	3
12	Point 1	2	1	4	27	Point 1	1	1	4
13	Point 1	2	1	5	28	Point 1	1	1	5
14	Point 1	0	1	2	29	Point 1	1	1	5
15	Point 1	0	1	2	30	Point 1	1	1	1

Multi-objective frequency planning: concept, modeling, and solution

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 20

References 33

Related Articles 15

Recommended Articles

Metrics

Comments

Parameter	Value
Operating system	Win11
CPU	AMD Ryzen 7 6800HS @ 3.20 GHz
RAM/G	16
Programming platform	Matlab2021b

Parameter	Value
N	50
M	3
T	100
Pc₁	[0.4,0.6]
Pc₂	[0.4,0.6]
Pr	[0.05,0.15]
step	[3,6]

Case	Method	Min ET			Min ND			Min OP
Case	Method	ET	ND	OP	ET	ND	OP	ET	ND	OP
Case 1	MPMA	0.010	0.00274	900	3.603	0.002299	700	21.606	0.004255	200
	MA	0.014	0.003736	900	1.209	0.002447	800	13.223	0.003874	300
	MOPSO	0.019	0.003125	1000	1.829	0.00274	600	15.657	0.004082	350
	NSGA-II	0.621	0.003279	900	7.818	0.00274	400	10.203	0.002985	300
Case 2	MPMA	0.607	0.000277	712.5	1.460	0.000256	662.5	17.500	0.000533	312.5
	MA	0.750	0.000291	715	0.750	0.000291	715	24.241	0.000966	220
	MOPSO	1.738	0.000347	817.5	2.213	0.000256	715	16.965	0.00056	312.5
	NSGA-II	1.437	0.000477	720	2.286	0.000331	712.5	31.646	0.001407	215
Case 3	MPMA	33.399	0.000667	927.5	39.872	0.000344	1022.5	61.978	0.000667	725
	MA	37.490	0.002778	1127.5	52.606	0.000758	920	59.010	0.001282	725
	MOPSO	44.562	0.001667	1027.5	53.074	0.000617	1077.5	130.528	0.002222	675
	NSGA-II	40.193	0.00098	1075	68.076	0.00049	825	79.560	0.000758	725

[1]	Yunong WANG, Wenhao BI, Qiucen FAN, Shuangfei XU, An ZHANG. Multi-objective optimization of top-level arrangement for flight test [J]. Journal of Systems Engineering and Electronics, 2025, 36(3): 714-724.
[2]	Yaqian YOU, Jianbin SUN, Yuejin TAN, Jiang JIANG. Multi-objective optimization framework in the modeling of belief rule-based systems with interpretability-accuracy trade-off [J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 423-435.
[3]	Sixing LIU, Changbao PEI, Xiaodong YE, Hao WANG, Fan WU, Shifei TAO. Efficient sampling strategy driven surrogate-based multi-objective optimization for broadband microwave metamaterial absorbers [J]. Journal of Systems Engineering and Electronics, 2024, 35(6): 1388-1396.
[4]	Licong ZHANG, Chunlin GONG, Hua SU, Da Ronch ANDREA. Design methodology of a mini-missile considering flight performance and guidance precision [J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 195-210.
[5]	Xi LONG, Weiwei CAI, Leping YANG, Tianyu WANG. Mission scheduling of multi-sensor collaborative observation for space surveillance network [J]. Journal of Systems Engineering and Electronics, 2023, 34(4): 906-923.
[6]	Lin ZHU, Junjiang LI, Zijie LIU, Dengyin ZHANG. A multi-resource scheduling scheme of Kubernetes for IIoT [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 683-692.
[7]	Jiaxin HU, Leping YANG, Huan HUANG, Yanwei ZHU. Optimal reconfiguration of constellation using adaptive innovation driven multiobjective evolutionary algorithm [J]. Journal of Systems Engineering and Electronics, 2021, 32(6): 1527-1538.
[8]	Zining WANG, Min LIN, Xiaogang TANG, Kefeng GUO, Shuo HUANG, Ming CHENG. Multi-objective robust secure beamforming for cognitive satellite and UAV networks [J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 789-798.
[9]	Shiyun LI, Sheng ZHONG, Zhi PEI, Wenchao YI, Yong CHEN, Cheng WANG, Wenzhu ZHANG. Multi-objective reconfigurable production line scheduling for smart home appliances [J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 297-317.
[10]	Jianjiang WANG, Xuejun HU, Chuan HE. Reactive scheduling of multiple EOSs under cloud uncertainties: model and algorithms [J]. Journal of Systems Engineering and Electronics, 2021, 32(1): 163-177.
[11]	Bo LI, Linyu TIAN, Daqing CHEN, Shiyang LIANG. An adaptive dwell time scheduling model for phased array radar based on three-way decision [J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 500-509.
[12]	Zhen XU, Enze ZHANG, Qingwei CHEN. Rotary unmanned aerial vehicles path planning in rough terrain based on multi-objective particle swarm optimization [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 130-141.
[13]	Yan'gang LIANG, Zheng QIN. A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making [J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 535-544.
[14]	Jiale GAO, Qinghua XING, Chengli FAN, Zhibing LIANG. Double adaptive selection strategy for MOEA/D [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 132-143.
[15]	Jiting Li, Sheng Zhang, Xiaolu Liu, and Renjie He. Multi-objective evolutionary optimization for geostationary orbit satellite mission planning [J]. Systems Engineering and Electronics, 2017, 28(5): 934-945.