Thinned array optimization based on genetic model improved artificial bee colony algorithm

Jianbang Sun; Jianbing Li; Ding Wang; Yuqi Sun; [in Chinese]

doi:10.11884/HPLPB202133.210233

Journals >High Power Laser and Particle Beams >Volume 33 >Issue 12 >Page 123005 > Article

High Power Laser and Particle Beams
Vol. 33, Issue 12, 123005 (2021)

Thinned array optimization based on genetic model improved artificial bee colony algorithm

Jianbang Sun¹, Jianbing Li^1、*, Ding Wang¹, Yuqi Sun², and [in Chinese]¹

Author Affiliations

¹Strategic Support Force Information Engineering University, Zhengzhou 450001, China

²Wuhan Library, Chinese Academy of Sciences, Wuhan 430071, China

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DOI: 10.11884/HPLPB202133.210233 Cite this Article

Jianbang Sun, Jianbing Li, Ding Wang, Yuqi Sun, [in Chinese]. Thinned array optimization based on genetic model improved artificial bee colony algorithm[J]. High Power Laser and Particle Beams, 2021, 33(12): 123005 Copy Citation Text

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Fig. 1. Uniform linear array

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Fig. 2. Thinned array

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Fig. 3. Neighborhood search method of artificial bee colony algorithm

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Fig. 4. Global artificial bee colony algorithm neighborhood search method

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Fig. 5. Optimization results of GMIABC algorithm at different sparsity rates

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Fig. 6. Comparison of array sparsity optimization between GMIABC, GA and ABC algorithms when sparsity rate η=70%

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Fig. 7. Comparison of array sparsity optimization between GMIABC algorithm and in Ref. [27] algorithm

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function	expression	range	minimum value
Sphere	$ {f}_{1}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{x}_{i}^{2} $	$ {\left[-\mathrm{100,100}\right]}^{D} $	0
Elliptic	$ {f}_{2}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{{\left({10}^{6}\right)}^{\tfrac{i-1}{D-1}}}x_{i}^{2} $	$ {\left[-\mathrm{100,100}\right]}^{D} $	0
SumSquare	$ {f}_{3}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{ix}_{i}^{2} $	$ {\left[-\mathrm{10,10}\right]}^{D} $	0
Exponential	${f}_{4}\left(x\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left(0.5 {\displaystyle\sum }_{i=1}^{D}{x}_{i}\right)$	$ {\left[-\mathrm{10,10}\right]}^{D} $	0
Rosenbrock	$ {f}_{5}\left(x\right)={\displaystyle\sum }_{i}^{D-1}\left[{100\left({x}_{i+1}-{x}_{i}^{2}\right)}^{2}-{\left({x}_{i}-1\right)}^{2}\right] $	$ {\left[-\mathrm{5,10}\right]}^{D} $	0
Rastrigin	$ {f}_{6}\left(x\right)={\displaystyle\sum }_{i}^{D}\left[{x}_{i}^{2}-10\mathrm{cos}\left(2\pi {x}_{i}\right)+10\right] $	$ {\left[-\mathrm{5.12,5.12}\right]}^{D} $	0
Himmelblau	$ {f}_{7}\left(x\right)=1/\mathrm{D}{\displaystyle\sum }_{i}^{D}\left[{x}_{i}^{4}-16{x}_{i}^{2}+5{x}_{i}\right] $	$ {\left[-\mathrm{5,5}\right]}^{D} $	−78.33236

Table 1. Benchmark numerical functions

algorithm		$ {f}_{1}\left(x\right) $	$ {f}_{2}\left(x\right) $	$ {f}_{3}\left(x\right) $	$ {f}_{4}\left(x\right) $	$ {f}_{5}\left(x\right) $	$ {f}_{6}\left(x\right) $	$ {f}_{7}\left(x\right) $
ABC	mean	2.42e−15	4.52e−8	7.32e–15	7.18e−21	4.75e−01	1.34e−13	−78.332
ABC	std	3.20e−15	4.83e−8	8.18e−15	7.21e−21	5.81e−01	1.97e−13	0
GABC	mean	5.12e−16	4.19e−16	5.25e–15	7.18e−23	9.71e−02	0	−78.332
GABC	std	4.35e−17	4.25e−16	6.18e−15	7.07e−23	1.01e−01	0	3.13e−15
GA	mean	1.23e−13	4.47e−12	8.10e−11	0	4.1675e−05	0	−78.332
GA	std	1.63e−13	5.77e−12	7.82e−11	0	5.0100e−05	0	1.0974e−14
GMIABC	mean	3.73e−23	4.99e−21	3.57e−20	0	1.910158e−07	0	−78.33233
GMIABC	std	4.16e−23	1.21e−20	6.93e−20	0	2.110158e−07	0	0

Table 2. Comparison of GMIABC, ABC and GABC algorithms

algorithm	min/dB	mean/dB	std	min/dB	mean/dB	std	min/dB	mean/dB	std	min/dB	mean/dB	std
algorithm	η=50%（N_t= 50）			η=60%（N_t=60）			η=70%（N_t=70）			η=80%（N_t=80）
GA	−15.935	−15.677	0.189	−18.121	−17.521	0.353	−19.378	−19.110	0.187	−20.941	−20.752	0.178
ABC	−15.330	−15.061	0.237	−16.806	−16.563	0.207	−18.386	−17.722	0.423	−19.836	−18.430	0.967
ABCSIM	−17.211	−16.863	0.262	−17.426	−17.158	0.217	−18.202	−17.588	0.429	−18.172	−17.764	0.331
GMIABC min/dB	−18.541	−18.281	0.227	−19.368	−19.200	0.135	−21.365	−20.892	0.171	−21.338	−21.573	0.175

Table 3. Comparison of sparsity optimization between GMIABC and GA, ABC and ABCSIM algorithms

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