A NEW HYBRID GENETIC ALGORITHM FOR MAXIMIZING AREA COVERAGE IN WIRELESS SENSOR NETWORKS

Boumedine, Nabil; Bouroubi, Sadek

doi:10.1590/0101-7438.2026.046.00299058

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ARTICLES • Pesqui. Oper. 46 • 2026 • https://doi.org/10.1590/0101-7438.2026.046.00299058 linkcopy

A NEW HYBRID GENETIC ALGORITHM FOR MAXIMIZING AREA COVERAGE IN WIRELESS SENSOR NETWORKS

Authorship SCIMAGO INSTITUTIONS RANKINGS

Wireless sensor networks are becoming increasingly important in many fields, such as management and security. They enable the collection and transmission of large volumes of data from a specific area to a data center for processing and analysis. One of the most challenging problems in sensor deployment is determining the optimal placement of each sensor to maximize the coverage area. It has been demonstrated that this problem is NP-hard. Due to its huge complexity, various metaheuristics have been proposed to solve the coverage problem in wireless sensor networks. In this paper, we propose an efficient hybrid genetic algorithm to maximize the coverage area in wireless sensor networks. The proposed approach combines a genetic algorithm with an enhanced simulated annealing algorithm. The efficiency of the proposed algorithm has been tested in 15 benchmark instances taken from the literature and compared with state-of-the-art algorithms.

Keywords:
wireless sensor networks; maximum coverage problem; simulated annealing; genetic algorithm; monte carlo method; overlapping fitenss

Symbol	Definition
n	The number of sensors
k	The number of sensor types
n _j	The number of sensors of the same type j, j=1, ..., k, with $\sum_{j = 1}^{k} n_{j} = n$
r _j	The sensing radius of sensors of the same type j, j=1, ..., k
A _W×H	H, W: the height and width of the 2D domain A, respectively

Gene	P1	P2	u	O1	O2
1	(1,2)	(2,1)	0.7	(1,2)	(2,1)
2	(3,4)	(4,3)	0.3	(4,3)	(3,4)
3	(5,6)	(6,5)	0.6	(5,6)	(6,5)
4	(7,8)	(8,7)	0.4	(8,7)	(7,8)
5	(9,10)	(10,9)	0.8	(9,10)	(10,9)
6	(11,12)	(12,11)	0.2	(12,11)	(11,12)

Instances	r ₁	n ₁	r ₂	n ₂	r ₃	n ₃	n	α
S1	14.00	5	11.20	5	8.96	7	17	0.68
S2	12.00	6	9.60	8	7.68	10	24	0.69
S3	10.00	8	8.00	12	6.40	16	36	0.70
S4	8.00	12	6.40	18	5.12	27	57	0.70
S5	6.00	22	4.80	32	3.84	47	101	0.70
S6	14.00	5	11.20	6	8.96	10	21	0.80
S7	12.00	6	9.60	9	7.68	14	29	0.79
S8	10.00	9	8.00	13	6.40	19	41	0.79
S9	8.00	14	6.40	20	5.12	29	63	0.78
S10	6.00	25	4.80	36	3.84	55	116	0.80
S11	14.00	6	11.20	7	8.96	10	23	0.90
S12	12.00	7	9.60	11	7.68	14	32	0.89
S13	10.00	11	8.00	14	6.40	21	46	0.90
S14	8.00	16	6.40	23	5.12	34	73	0.90
S15	6.00	28	4.80	41	3.84	61	130	0.90

Parameter	Value
Population size	m=15
Number of points generated in Monte Carlo method	l=1,00,000
Perturbation operator threshold in ISA	q=100
Step length of Lévy flights	β=1.5
Number of selected solutions in tournament selection	g=6
Uniform crossover ratio	p=0.3
Initial temperature in ISA	T=1000
Cooling rate in ISA	α=0.98
The application rate of ISA	τ=0.25
Maximum number of generations	200

Ins.	GA	IGA	PSO	DPSO	CFPA	ICS	MA	HGA-ISA
S1	6779.40	6814.66	6815.14	6815.27	6813.34	6815.01	6814.65	6816.24
S2	6833.01	6882.98	6883.25	6884.79	6884.72	6883.26	6883.56	6884.88
S3	6906.43	6984.39	6986.82	6985.52	6986.14	6984.89	6984.89	6886.26
S4	6852.32	6952.54	6952.78	6953.53	6952.38	6952.82	6952.56	6955.69
S5	6799.29	6981.65	6985.59	6984.34	6981.11	6981.43	6981.63	6981.66
S6	7758.31	7923.84	7930.91	7915.18	7925.37	7902.49	7954.47	7928.37
S7	7706.98	7892.72	7885.19	7882.57	7886.59	7888.70	7907.88	7889.28
S8	7662.09	7869.23	7884.60	7872.44	7875.14	7876.51	7879.79	7884.42
S9	7532.39	7773.61	7778.36	7776.98	7776.96	7776.32	7773.80	7778.12
S10	7587.27	7975.01	7980.83	7978.79	7979.04	7981.85	7971.10	7978.57
S11	8474.15	8661.06	8589.88	8616.99	8637.19	8595.54	8763.62	8661.20
S12	8430.32	8648.65	8654.41	8645.71	8623.44	8629.43	8739.38	8654.47
S13	8444.49	8681.20	8706.77	8688.13	8675.48	8704.35	8765.42	8705.89
S14	8388.12	8730.00	8745.10	8725.22	8707.50	8742.22	8781.06	8742.69
S15	8258.97	8755.44	8760.38	8741.31	8722.98	8774.14	8784.68	8755.22

Ins.	GA (Ly et al. (2015))			CSA (Binh et al.(2018))			HGA-ISA
Ins.	Avg.	Std	Time	Avg.	Std	Time	Avg.	Std	Time
S1	6810.41	5.13	193.55	6812.31	2.33	213.55	6814.64	0.892	207.62
S2	6861.53	7.19	241.12	6879.07	1.43	291.77	6884.40	0.27	295.41
S3	6978.32	5.17	301.33	6984.89	3.81	359.66	6984.61	1.01	394.05
S4	6949.03	8.93	407.27	6943.09	1.79	401.47	6954.59	1.48	453.93
S5	6791.31	11.53	574.13	6980.07	1.58	694.21	6979.85	1.72	741.12
S6	7914.09	16.76	221.77	7884.98	11.13	214.55	7939.89	8.08	284.33
S7	7883.79	9.04	271.11	7876.38	5.01	241.19	7896.95	4.28	307.67
S8	7871.24	3.55	300.92	7878.63	1.52	361.86	7884.53	1.12	403.29
S9	7760.06	5.13	403.04	7777.01	1.41	405.60	7777.94	1.32	478.51
S10	7976.41	4.09	715.23	7971.07	1.53	819.85	7978.64	1.15	992.23
S11	8656.27	23.88	112.41	8597.72	18.61	151.07	8662.05	17.34	194.54
S12	8650.02	21.58	218.97	8651.22	14.19	284.21	8655.39	13.52	331.11
S13	8678.56	27.66	267.22	8704.35	22.46	270.97	8721.65	19.14	344.76
S14	8732.49	15.77	498.08	8745.03	13.04	467.11	8747.27	12.55	554.17
S15	8739.47	11.49	782.17	8774.17	9.91	703.05	8754.83	10.81	873.44

Ins.	Size	GA without RO	GA+RO	HGA-ISA without RO	HGA-ISA+RO
S1	17	5200,11	5664,87	6513,16	6816.24
S2	24	5721,08	6204,41	6622,47	6884.88
S3	36	5209,26	6117,55	6598,19	6886.26
S4	57	6427,13	6642,24	6709,79	6955.69
S5	101	5991.57	6222,91	6714,11	6981.66
S6	21	6383.29	6873,89	7672,84	7928.37
S7	29	6004.08	6959,22	7702,12	7889.28
S8	41	7107,02	7397,19	7689,28	7884.42
S9	63	6451,83	6955,03	7581,63	7778.12
S10	116	6520.76	7100,11	1725,02	7978.57
S11	23	7502,17	8043,46	8479,92	8661.20
S12	32	7232,45	7527,05	8563,53	8654.47
S13	46	6687,41	7229,17	8602,07	8705.89
S14	73	7154,13	7875,79	8503,36	8742.69
S15	130	7093,33	7993,37	8413,48	8755.22

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[TFN1] NB: Values in bold indicate the best obtained results for the correspondent instance.