A Hybrid Optimization Algorithm for the Synthesis of Sparse Array Pattern Diagrams
Abstract
1. Introduction
2. Quantum Hybrid Particle Swarm Optimization Algorithm Combined with Quantum Behavior
2.1. Classical Particle Swarm Optimization Algorithm
2.2. Quantum-Behaved Optimization Algorithm
2.3. Quantum-Behaved Particle Swarm Optimization Algorithm
Algorithm 1 Quantum-behaved Particle Swarm Optimization Algorithm |
Input: Population size M, maximum generations , search space constraints: , , Initial parameters: , , , , Output: the optimal result Initialization Initialize population: , Initialize personal bests , for to do and , If ( satisfies the first item in Equation (9)) then The quantum gravitational center is calculated by Equation (8), and then by Equations (6), (7), (11) to (13) The update of its particle positions mainly relies on the first term of Equation (9) Else Update the inertia weight and learning factor through (3) to (5) The update of the positions of its particle swarm relies on the second term in Equation (9) If ( satisfies Equation (14)) then The stop particle triggers the mutation operation through Equation (14) The updated particle positions and boundaries are shown in Equations (15) and (16) else Retain the population positions end if Select the best individuals in the population and retain them for the next generation end for return Outputs |
3. Experiments and Analyses
3.1. Sparse Linear Array Simulation Test
3.2. Sparse Matrix Simulation Test
3.3. Sparse Multi-Ring Concentric Circular Array
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
QPSO | Quantum-behaved particle swarm optimization algorithm |
WOA | Whale optimization algorithm |
LFPSO | Levi’s flying particle swarm optimization |
PSLL | Peak sidelobe level |
GWO | Grey wolf optimization algorithm |
AOA | Arithmetic optimization algorithm |
CGA | Chaotic genetic algorithm |
DEA | Differential evolution algorithm |
ICO | Iterative convex optimization algorithm |
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Elements | Unit Spacing () | Elements | Unit Spacing () |
---|---|---|---|
1-2 | 1 | 9-10 | 0.5000 |
2-3 | 0.7597 | 10-11 | 0.5000 |
3-4 | 0.7599 | 11-12 | 0.5670 |
4-5 | 0.5136 | 12-13 | 0.5683 |
5-6 | 0.5000 | 13-14 | 0.7792 |
6-7 | 0.5000 | 14-15 | 0.7821 |
7-8 | 0.5065 | 15-16 | 0.9157 |
8-9 | 0.5000 | 16-17 | 0.7761 |
Work | Type | Array Elements | Array Type | Iterations | Spacing Requirement | PSLL (dB) |
---|---|---|---|---|---|---|
[29] | LFPSO | 17 | Symmetry | 500 | −19.61 | |
[30] | PSO | 100 | −19.87 | |||
This work | QPSO | Asymmetry | 300 | −20.46 |
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Liu, Y.; Huang, L.; Xie, X.; Ye, H. A Hybrid Optimization Algorithm for the Synthesis of Sparse Array Pattern Diagrams. Appl. Sci. 2025, 15, 6490. https://doi.org/10.3390/app15126490
Liu Y, Huang L, Xie X, Ye H. A Hybrid Optimization Algorithm for the Synthesis of Sparse Array Pattern Diagrams. Applied Sciences. 2025; 15(12):6490. https://doi.org/10.3390/app15126490
Chicago/Turabian StyleLiu, Youzhi, Linshu Huang, Xu Xie, and Huijuan Ye. 2025. "A Hybrid Optimization Algorithm for the Synthesis of Sparse Array Pattern Diagrams" Applied Sciences 15, no. 12: 6490. https://doi.org/10.3390/app15126490
APA StyleLiu, Y., Huang, L., Xie, X., & Ye, H. (2025). A Hybrid Optimization Algorithm for the Synthesis of Sparse Array Pattern Diagrams. Applied Sciences, 15(12), 6490. https://doi.org/10.3390/app15126490