Synthesis of New Reconfigurable Limited Size FSS Structures Using an Improved Hybrid Particle Swarm Optimization

Lacouth, Patric; D’Assunção, Adaildo Gomes; Gomes, Alfrêdo

doi:10.1590/2179-10742019v18i21550

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Journal of Microwaves, Optoelectronics and Electromagnetic Applications

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Article • J. Microw. Optoelectron. Electromagn. Appl. 18 (2) • June 2019 • https://doi.org/10.1590/2179-10742019v18i21550 copy

Synthesis of New Reconfigurable Limited Size FSS Structures Using an Improved Hybrid Particle Swarm Optimization

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This paper describes a new design methodology for reconfigurable printed circuits with limited size, using an improved hybrid particle swarm optimization (HPSO) algorithm, reducing the search space by the definition of negative zones (NZ), regions where the swarm of particles should not travel. The proposed design methodology (HPSO-NZ) is used in the development of reconfigurable frequency selective surfaces (RFSSs), restricted to a limited overall size, resulting in entirely new frequency selective surface (FSS) geometries. Two FSS prototypes are designed, fabricated, and measured for comparison purpose. A good agreement is observed between simulation and measurements results, confirming the efficiency and accuracy of the HPSO-NZ algorithm. Also, the performance of the HPSO-NZ algorithm is compared to the ones of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, showing good consistency results.

Index Terms
Particle swarm optimization; PSO; negative zones; HPSO-NZ; GA; reconfigurable FSS

	REAL PART	BINARY PART
$\bar{x} = [\bar{r} \bar{b}]$	$\bar{r} = {R_{1}, R_{2}}$	$\bar{b} = {B_{1}, B_{2}, \dots B_{N}}$
p_best, g_best	Both parts share the same p_best and the same g_best
v-update	$V_{t} = w V_{t - 1} + c_{1} η_{1} (P_{t - 1} - X_{t - 1}) + c_{2} η_{2} (G_{t - 1} - X_{t - 1})$
Inertia weight	time varying, 0.9-0.4	constant 1.0
V_max	$0.1 \times (R_{m a x} - R_{m i n})$	6.0
x-update	$\bar{r} = {\bar{r}}_{t - 1} + {\bar{v}}_{r, t}$	$\begin{matrix} S (v_{m n, t}) = \frac{1}{1 + e^{- v_{m n, t}}} \\ x_{m n, t} = {\begin{array}{l} 1, r_{m n, t} < S (v_{m n, t}) \\ 0, r_{m n, t} \geq S (v_{m n, t}) \end{array} \end{matrix}$
Boundary	Yes	No
NZ - Radius	$0.05 \times (B o u n d a r y_{m a x} - B o u n d a r y_{m i n})$

Algorithm	g_best < 0.5
HPSO-NZ (this work)	169
HPSO (this work)	136
HPSO [¹⁴14 N. Jin and Y. Rahmat-Samii, “Hybrid Real-Binary Particle Swarm Optimization (HPSO) in Engineering Electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 12, pp. 3786-3794, December 2010.]	137
Binary PSO [¹⁴14 N. Jin and Y. Rahmat-Samii, “Hybrid Real-Binary Particle Swarm Optimization (HPSO) in Engineering Electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 12, pp. 3786-3794, December 2010.]	80
Binary GA [¹⁴14 N. Jin and Y. Rahmat-Samii, “Hybrid Real-Binary Particle Swarm Optimization (HPSO) in Engineering Electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 12, pp. 3786-3794, December 2010.]	12
Round-Off Real PSO [¹⁴14 N. Jin and Y. Rahmat-Samii, “Hybrid Real-Binary Particle Swarm Optimization (HPSO) in Engineering Electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 12, pp. 3786-3794, December 2010.]	6

Optimized FSS Parameters	Values
Maximum rectangular cell width (mm), W_X	100
Maximum rectangular cell length (mm), W_Y	100
Minimum rectangular cell width (mm), W_X	10
Minimum rectangular cell length (mm), W_Y	10
Frequency design goal (GHz), F	7.0
Substrate layer relative permittivity (FR4), ε_r	4.4
Substrate layer loss tangent, tanδ	0.02
Substrate layer height (mm), h₁	1.57
Number of internal patches (“PIXELS”)	400
Number of patches used in HPSO-NZ	100
Dimensional problem space	2100
Swarm size	20
Maximum iteration number	600

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