Advertisement

Journal of Optimization Theory and Applications

, Volume 155, Issue 3, pp 1008–1024 | Cite as

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

  • Giovanni StracquadanioEmail author
  • Elisa Pappalardo
  • Panos M. Pardalos
Article
  • 281 Downloads

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.

Keywords

Derivative-free optimization Pattern search Heuristic methods Antennas design 

Notes

Acknowledgements

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

References

  1. 1.
    Conn, A., Scheinberg, K., Vicente, L.: Introduction to Derivative-Free Optimization. Society for Industrial Mathematics, Philadelphia (2009) zbMATHCrossRefGoogle Scholar
  2. 2.
    Horst, R., Pardalos, P., Thoai, N.: Introduction to Global Optimization. Springer, Dordrecht (2000) zbMATHGoogle Scholar
  3. 3.
    Audet, C., Dennis, J., Le Digabel, S.: Globalization strategies for mesh adaptive direct search. Comput. Optim. Appl. 46(2), 193–215 (2010) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Leary, R.: Global optimization on funneling landscapes. J. Glob. Optim. 18(4), 367–383 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  5. 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) CrossRefGoogle Scholar
  6. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Jones, D., Perttunen, C., Stuckman, B.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Audet, C., Dennis, J. Jr.: Analysis of generalized pattern searches. SIAM J. Optim. 13(3), 889–903 (2003) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Audet, C.: Convergence results for generalized pattern search algorithms are tight. Optim. Eng. 5(2), 101–122 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Audet, C., Dennis, J. Jr.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  12. 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. 13.
    Locatelli, M., Schoen, F.: Fast global optimization of difficult Lennard-Jones clusters. Comput. Optim. Appl. 21(1), 55–70 (2002) MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Grosso, A., Locatelli, M., Schoen, F.: Solving molecular distance geometry problems by global optimization algorithms. Comput. Optim. Appl. 43(1), 23–37 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 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. 16.
    Shylo, O., Middelkoop, T., Pardalos, P.: Restart strategies in optimization: parallel and serial cases. In: Parallel Computing (2010) Google Scholar
  17. 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) CrossRefGoogle Scholar
  18. 18.
    Visser, H., Wiley, J.: Array and Phased Array Antenna Basics. Wiley Online Library (2005) Google Scholar
  19. 19.
    Rudge, A.: The Handbook of Antenna Design, vol. 2. Peter Peregrinus Ltd, London (1983) CrossRefGoogle Scholar
  20. 20.
    Stutzman, W., Thiele, G.: Antenna Theory and Design. Wiley, New York (1981). 608 p. Google Scholar
  21. 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) CrossRefGoogle Scholar
  22. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Taguchi, G., Chowdhury, S., Wu, Y.: Taguchi’s Quality Engineering Handbook. Wiley-Interscience, New York (2005) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Giovanni Stracquadanio
    • 1
    Email author
  • Elisa Pappalardo
    • 2
    • 3
  • Panos M. Pardalos
    • 2
  1. 1.Department of Biomedical EngineeringJohns Hopkins UniversityBaltimoreUSA
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly

Personalised recommendations