Skip to main content
Log in

Large thinned array design based on multi-objective cross entropy algorithm

  • Published:
Journal of Shanghai Jiaotong University (Science) Aims and scope Submit manuscript

Abstract

To consider multi-objective optimization problem with the number of feed array elements and sidelobe level of large antenna array, multi-objective cross entropy (CE) algorithm is proposed by combining fuzzy c-mean clustering algorithm with traditional cross entropy algorithm, and specific program flow of the algorithm is given. Using the algorithm, large thinned array (200 elements) given sidelobe level (−10, −19 and −30 dB) problem is solved successfully. Compared with the traditional statistical algorithms, the optimization results of the algorithm validate that the number of feed array elements reduces by 51%, 11% and 6% respectively. In addition, compared with the particle swarm optimization (PSO) algorithm, the number of feed array elements from the algorithm is more similar, but the algorithm is more efficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cohen I, Golany B, Shtub A. Managing stochastic, finite capacity, multi-project systems through the cross-entropy methodology [J]. Annals of Operations Research, 2005, 134(1): 183–199.

    Article  MathSciNet  MATH  Google Scholar 

  2. Deb K. Multi-objective optimization using evolutionary algorithms [M]. Chichester, UK: Wiley, 2001: 84–90.

    MATH  Google Scholar 

  3. Deb K, Agrawal S, Pratap A, et al. A fast and elitist multi-objective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002, 2(6): 182–196.

    Article  Google Scholar 

  4. Corne D W, Jerram N R, Knowles J D, et al. PESA-II: Region-based selection in evolutionary multiobjective optimization [C]//Proceedings of the Genetic and Evolutionary Computation Conference. San Francisco, California: Morgan Kaufmann Publishers, 2001: 283–290.

    Google Scholar 

  5. Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the strength Pareto evolutionary algorithm [R]. Zurich, Switzerland: Swiss Federal Institute of Technology, 2001.

    Google Scholar 

  6. Skolnik M, Sherman J, Ogg F. Statistically designed density-tapered arrays [J]. IEEE Transactions on Antennas and Propagation, 1964, 12(4): 408–417.

    Article  Google Scholar 

  7. Lo Y. A mathematical theory of antenna arrays with randomly spaced elements [J]. IEEE Transactions on Antennas and Propagation, 1964, 12(3): 257–268.

    Article  Google Scholar 

  8. Steinberg B D. Microwave imaging with large antenna arrays [M]. New York: Wiley, 1983: 37–39.

    Google Scholar 

  9. Yan K K, Lu Y. Sidelobe reduction in array-pattern synthesis using genetic algorithm [J]. IEEE Transactions on Antennas and Propagation, 1997, 45(7): 1117–1122.

    Article  Google Scholar 

  10. Wang L L, Fang D G. Genetic algorithm for the synthesis of thinned array [J]. Acta Electronica Sinica, 2003, 31(12): 2135–2138 (in Chinese).

    MathSciNet  Google Scholar 

  11. Trucco A. Thinning and weighting of large planar arrays by simulated annealing [J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1999, 46(2): 347–355.

    Article  Google Scholar 

  12. Jin N, Rahmat-Samii Y. Advances in particle swarm optimization for antenna designs: Real-number, binary, single-objective and multi-objective implementations [J]. IEEE Transactions on Antennas and Propagation, 2007, 55(3): 556–567.

    Article  Google Scholar 

  13. Pulido G T, Coello C A C. Using clustering techniques to improve the performance of a particle swarm optimizer [C]//Proceedings of the 2004 Genetic and Evolutionary Computation Conference. Seattle, USA: Springer, 2004: 225–237.

    Chapter  Google Scholar 

  14. Mostaghim S, Teich J. The role of e-dominance in multi-objective particle swarm optimization method [C]//Proceedings of the 2003 Congress on Evolutionary Computation. Canberra, Australia: IEEE 2003: 1764–1771.

    Google Scholar 

  15. Balling R. The maximin fitness function: Multiobjective city and regional planning [C]//Proceedings of the 2nd International Conference on Evolutionary Multi-criterion Optimization. Faro, Portugal: Springer, 2003: 1–15.

    Chapter  Google Scholar 

  16. Quevedo-Teruel O, Rajo-Iglesias E. Ant colony optimization in thinned array synthesis with minimum sidelobe level [J]. IEEE Antennas and Wireless Propagation Letter, 2006, 5(1): 349–352.

    Article  Google Scholar 

  17. Razavi A, Forooraghi K. Thinned arrays using pattern search algorithms [J]. Progress in Electromagnetics Research, 2008, 78: 61–71.

    Article  Google Scholar 

  18. Rubinstein R Y. Optimization of computer simulation models with rare events [J]. European Journal of Operational Research, 1997, 99(1): 89–112.

    Article  Google Scholar 

  19. Mailloux R J. Phased array antenna handbook [M]. 2nd ed. Norwood, MA: Artech House, 2005: 92–106.

    Google Scholar 

  20. Bezdek J C. Pattern recognition with fuzzy objective function algorithms [M]. New York: Springer, 1981: 56–57.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li Bian  (边 莉).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 51474100), the Youth Science Fund of Heilongjiang Province in China (No. QC2010023), and the Youth Outstanding Ability Program in Heilongjiang University of Science and Technology

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bian, L., Bian, Cy. & Wang, Sm. Large thinned array design based on multi-objective cross entropy algorithm. J. Shanghai Jiaotong Univ. (Sci.) 20, 437–442 (2015). https://doi.org/10.1007/s12204-015-1645-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12204-015-1645-4

Keywords

CLC number

Navigation