Optimization of terahertz MIMO array radar based on dual strategy differential evolution algorithm

Fig. 4. (a) MIMO array comprehensive directional map (before optimization); (b) MIMO array comprehensive directional pattern (optimized by DSADE algorithm)

Download full size

View in Article

Fig. 5. Optimization algorithm convergence comparison chart

Download full size

View in Article

Fig. 6. Comparison chart of experimental results

Download full size

View in Article

Table 1. Uniformity comparison of initialization methods
View table
View in Article
Table 1. Uniformity comparison of initialization methods
n/dim 20 40 60 80 100
Kent 8.21 8.26 8.25 8.34 8.30
Random 7.53 7.84 8.03 8.09 8.16

Table 2. Standard test function

View table

View in Article

Table 2. Standard test function

Function	Function expression	Range	Optimum
$ {f}_{1} $	$ {\displaystyle\sum }_{i=1}^{n}{x}_{i}^{2} $	(−5.12,5.12)	0
$ {f}_{2} $	${\displaystyle\sum }_{i=1}^{n}\left\|{x}_{i}\right\|+{\displaystyle\prod }_{i=1}^{n}\left\|{x}_{i}\right\|$	(−10,10)	0
$ {f}_{3} $	$ {\displaystyle\sum }_{i=1}^{n}{\left({\displaystyle\sum }_{j=1}^{i}{x}_{j}\right)}^{2} $	(−100,100)	0
$ {f}_{4} $	$ {\displaystyle\sum }_{i=1}^{n}[{x}_{i}^{2}-10\mathrm{cos}\left(2\pi {x}_{i}\right)+10] $	(−5.12,5.12)	0
$ {f}_{5} $	${\displaystyle\sum }_{i=1}^{n-1}\left[{100\left({x}_{i}^{2}-{x}_{i+1}\right)}^{2}+{({x}_{i}-1)}^{2}\right]$	(−30,30)	0
$ {f}_{6} $	$ {\displaystyle\sum }_{i=1}^{n}\|{x}_{i}\mathrm{sin}\left({x}_{i}\right)+0.1{x}_{i}\| $	(−10,10)	0
$ {f}_{7} $	${\displaystyle\sum }_{i=1}^{n}\frac{ {x}_{i}^{2} }{4\;000}-{\displaystyle\prod }_{i=1}^{n}\mathrm{cos}\left(\dfrac{ {x}_{i} }{\sqrt{i} }\right)+1$	(−5.12,5.12)	0
$ {f}_{8} $	$ {\displaystyle\sum }_{i=1}^{n}{x}_{i}^{10} $	(−5.12,5.12)	0

Table 3. Experimental results of standard test function

View table

View in Article

Table 3. Experimental results of standard test function

Function	DE/rand/2		DE/best/2		DE/current-to-best/1		DSADE
Function	Mean	Std	Mean	Std	Mean	Std	Mean	Std
$ {f}_{1} $	2.59e-06	7.77e-06	1.58e-15	4.74e-15	3.95e-02	1.18e-03	9.96e-35	4.40e-35
$ {f}_{2} $	4.60e-03	1.38e-03	1.15e-05	3.46e-05	1.99e+01	5.27e+01	2.88e-20	1.35e-20
$ {f}_{3} $	4.73e+04	3.86e+04	1.80e+04	4.80e+04	7.26e+04	3.75e+04	2.00e-00	1.80e-00
$ {f}_{4} $	3.31e+02	18.3e+03	7.87e+02	8.41e+02	1.03e+02	2.00e+01	2.16e+00	1.96e+00
$ {f}_{5} $	2.34e+02	1.68e+02	2.40e+00	0.84e+01	3.72e+03	5.62e+03	1.89e+00	2.20e+00
$ {f}_{6} $	8.85e+01	3.38e+01	9.46e-02	1.89e-02	9.49e+01	2.38e+01	1.97e-18	1.37e-18
$ {f}_{7} $	6.38e-04	1.28e-04	0.00e+00	0.00e+00	3.69e-01	6.30e-01	0.00e+00	0.00e+00
$ {f}_{8} $	1.13e-13	2.26e-13	4.82e-43	9.64e-43	9.91e-02	1.94e-02	4.32e-75	7.24e-74

Table 4. Optimization algorithm parameter setting

View table

View in Article

Table 4. Optimization algorithm parameter setting

Algorithm	Related parameters
Algorithm	F		CR
DE/rand/1	0.5		0.9
DE/best/1	0.5		0.9
DE/current-to-best/1	0.5		0.9
ISMADE	Self-adaption		0.9
DSADE	Self-adaption		Self-adaption
ABC	Leading bee		Following bee
ABC	50%NP		50%NP
PSO	C1	C2		w
	2	2		0.8

Table 5. Comparison of simulation optimization results

View table

View in Article

Table 5. Comparison of simulation optimization results

Algorithm	Ave/dB	Std/ $ {\mathrm{d}\mathrm{B}}^{2} $	Best/dB
DE/rand/1	−16.57	1.24e-1	−16.88
DE/best/1	−16.03	3.21e-1	−16.68
DE/current-to-best/1	−16.49	1.70e-1	−16.87
ABC	−16.55	2.49e-1	−17.12
PSO	−16.15	1.33e-1	−16.41
ISMADE	−16.87	0.80e-1	−17.01
DSADE	−17.81	1.82e-1	−18.33

Table 6. Optimized MIMO array position(Unit: cm)

View table

View in Article

Table 6. Optimized MIMO array position(Unit: cm)

$ {x}_{1} $	$ {x}_{2} $	$ {x}_{3} $	$ {x}_{4} $	$ {x}_{5} $	$ {x}_{6} $	$ {x}_{7} $	$ {x}_{8} $
0	0.8706	1.5816	2.4426	3.6719	5.0402	6.4105	6.9
$ {y}_{1} $	$ {y}_{2} $	$ {y}_{3} $	$ {y}_{4} $	$ {y}_{5} $	$ {y}_{6} $	$ {y}_{7} $	$ {y}_{8} $
0.3	1.1895	2.7518	3.0651	4.7337	5.7784	6.0973	7.2

Tools

Get Citation

Copy Citation Text

Xudong Wei, Yajun Pang, Liying Lang. Optimization of terahertz MIMO array radar based on dual strategy differential evolution algorithm[J]. Infrared and Laser Engineering, 2023, 52(8): 20230244

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites