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A Mesh Adaptive Basin Hopping Method for the Design of Circular Antenna Arrays

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Abstract

The design of circular antenna arrays is a challenging optimization problem, which requires ad-hoc methods to fulfill the engineering requirements. In this work, we introduce the Mesh Adaptive Basin Hopping algorithm to tackle such problem effectively; the experimental results show that the new approach proposed outperforms the state-of-the-art methods, both in terms of quality of the solutions and computational efficiency.

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References

  1. Conn, A., Scheinberg, K., Vicente, L.: Introduction to Derivative-Free Optimization. Society for Industrial Mathematics, Philadelphia (2009)

    Book  MATH  Google Scholar 

  2. Horst, R., Pardalos, P., Thoai, N.: Introduction to Global Optimization. Springer, Dordrecht (2000)

    MATH  Google Scholar 

  3. Audet, C., Dennis, J., Le Digabel, S.: Globalization strategies for mesh adaptive direct search. Comput. Optim. Appl. 46(2), 193–215 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Leary, R.: Global optimization on funneling landscapes. J. Glob. Optim. 18(4), 367–383 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Panduro, M., Mendez, A., Dominguez, R., Romero, G.: Design of non-uniform circular antenna arrays for side lobe reduction using the method of genetic algorithms. AEÜ, Int. J. Electron. Commun. 60(10), 713–717 (2006)

    Article  Google Scholar 

  6. Gilmore, P., Kelley, C.: An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Optim. 5(2), 269–285 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jones, D., Perttunen, C., Stuckman, B.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Audet, C., Dennis, J. Jr.: Analysis of generalized pattern searches. SIAM J. Optim. 13(3), 889–903 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Audet, C.: Convergence results for generalized pattern search algorithms are tight. Optim. Eng. 5(2), 101–122 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Audet, C., Dennis, J. Jr.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Abramson, M., Audet, C., Dennis, J., Digabel, S.: OrthoMADS: a deterministic MADS instance with orthogonal directions. SIAM J. Optim. 20(2), 948–966 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pardalos, P., Schoen, F.: Recent advances and trends in global optimization: deterministic and stochastic methods. In: Proceedings of the Sixth International Conference on Foundations of Computer-Aided Process Design (2004)

    Google Scholar 

  13. Locatelli, M., Schoen, F.: Fast global optimization of difficult Lennard-Jones clusters. Comput. Optim. Appl. 21(1), 55–70 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Grosso, A., Locatelli, M., Schoen, F.: Solving molecular distance geometry problems by global optimization algorithms. Comput. Optim. Appl. 43(1), 23–37 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Addis, B., Cassioli, A., Locatelli, M., Schoen, F.: A global optimization method for the design of space trajectories. In: Computational Optimization and Applications, pp. 1–18 (2008)

    Google Scholar 

  16. Shylo, O., Middelkoop, T., Pardalos, P.: Restart strategies in optimization: parallel and serial cases. In: Parallel Computing (2010)

    Google Scholar 

  17. Dolph, C.: A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proc. IRE 34(6), 335–348 (1946)

    Article  Google Scholar 

  18. Visser, H., Wiley, J.: Array and Phased Array Antenna Basics. Wiley Online Library (2005)

  19. Rudge, A.: The Handbook of Antenna Design, vol. 2. Peter Peregrinus Ltd, London (1983)

    Book  Google Scholar 

  20. Stutzman, W., Thiele, G.: Antenna Theory and Design. Wiley, New York (1981). 608 p.

    Google Scholar 

  21. Basak, A., Pal, S., Das, S., Abraham, A.: Circular antenna array synthesis with a differential invasive weed optimization algorithm. In: 10th International Conference on Hybrid Intelligent Systems (HIS), pp. 153–158. IEEE, New York (2010)

    Chapter  Google Scholar 

  22. Aiex, R., Resende, M., Ribeiro, C.: TTT plots: a Perl program to create time-to-target plots. Optim. Lett. 1(4), 355–366 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Taguchi, G., Chowdhury, S., Wu, Y.: Taguchi’s Quality Engineering Handbook. Wiley-Interscience, New York (2005)

    MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and contributions.

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Authors and Affiliations

  1. Department of Biomedical Engineering, Johns Hopkins University, Baltimore, USA

    Giovanni Stracquadanio

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    Elisa Pappalardo & Panos M. Pardalos

  3. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Elisa Pappalardo

Authors
  1. Giovanni Stracquadanio
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  2. Elisa Pappalardo
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  3. Panos M. Pardalos
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Corresponding author

Correspondence to Giovanni Stracquadanio.

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Stracquadanio, G., Pappalardo, E. & Pardalos, P.M. A Mesh Adaptive Basin Hopping Method for the Design of Circular Antenna Arrays. J Optim Theory Appl 155, 1008–1024 (2012). https://doi.org/10.1007/s10957-012-0112-8

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  • DOI: https://doi.org/10.1007/s10957-012-0112-8

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