2014-11-03
Kriging-Pareto Front Approach for the Multi-Objective Exploration of Metamaterial Topologies
By
Progress In Electromagnetics Research M, Vol. 39, 141-150, 2014
Abstract
Metamaterials provide the opportunity for designers to create customisable artificial materials by independently tailoring the electric and magnetic response of sub-wavelength geometric structures to electromagnetic energy. Due to the increased complexity of these geometric structures, exacerbated by the increased interest in generating inhomogeneous and anisotropic metamaterials, direct optimisation of these designs using conventional approaches often becomes impractical and limited. In order to alleviate this issue, we propose an alternative optimisation approach which exploits the Kriging methodology in conjunction with an adaptive sampling plan to simultaneously optimise multiple conflicting objectives. Results show the effectiveness of the outlined algorithm in calculating a uniform spread of optimal trade-off designs, balancing the real and imaginary components of the refractive index over a wide range of values.
Citation
Patrick J. Bradley, "Kriging-Pareto Front Approach for the Multi-Objective Exploration of Metamaterial Topologies," Progress In Electromagnetics Research M, Vol. 39, 141-150, 2014.
doi:10.2528/PIERM14091203
References

1. Cui, T. J., D. Smith, and R. Liu, Metamaterials: Theory, Design, and Applications, 1st Edition, Springer Publishing Company, Incorporated, 2009.

2. Fang, F., Y. Cheng, and H. Liao, "Numerical study on a three-dimensional broadband isotropic left-handed metamaterial based on closed rings," Physica Scripta, Vol. 89, No. 2, 025501, 2014.
doi:10.1088/0031-8949/89/02/025501        Google Scholar

3. Bradley, P. J., "A multi-fidelity based adaptive sampling optimisation approach for the rapid design of double-negative metamaterials," Progress In Electromagnetics Research B, Vol. 55, 87-114, 2013.
doi:10.2528/PIERB13071003        Google Scholar

4. Wagner, T., M. Emmerich, A. Deutz, and W. Ponweiser, "On expected-improvement criteria for model-based multi-objective optimization," Parallel Problem Solving from Nature, Vol. 6238, 718-727, Springer, Berlin, Heidelberg, 2010.        Google Scholar

5. Wilson, B., D. Cappelleri, T. W. Simpson, and M. Frecker, "Efficient pareto frontier exploration using surrogate approximations," Optimization and Engineering, Vol. 2, No. 1, 31-50, 2001.
doi:10.1023/A:1011818803494        Google Scholar

6. Jones, D. R., "A taxonomy of global optimization methods based on response surfaces," Journal of Global Optimization, Vol. 21, No. 4, 345-383, 2001.
doi:10.1023/A:1012771025575        Google Scholar

7. Forrester, A., A. Sobester, and A. Keane, Engineering Design via Surrogate Modelling: A Practical Guide, Wiley, 2008.
doi:10.1002/9780470770801

8. Mohan, M., K. Deb, and S. Mishra, "Evaluating the Edomination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions," Evolutionary Computation, Vol. 13, No. 4, 501-525, 2005.
doi:10.1162/106365605774666895        Google Scholar

9. Martinez-Iranzo, M., J. M. Herrero, J. Sanchis, X. Blasco, and S. Garcia-Nieto, "Applied Pareto multi-objective optimization by stochastic solvers," Engineering Applications of Artificial Intelligence, Vol. 22, No. 3, 455-465, 2009.
doi:10.1016/j.engappai.2008.10.018        Google Scholar

10. Deschrijver, D., K. Crombecq, H. M. Nguyen, and T. Dhaene, "Adaptive sampling algorithm for macromodeling of parameterized S-parameter responses," IEEE Transactions on Microwave Theory and Techniques, Vol. 59, No. 1, 39-45, Jan. 2011.
doi:10.1109/TMTT.2010.2090407        Google Scholar

11. Toal, D. J. J., A. I. J. Forrester, N. W. Bressloff, A. J. Keane, and C. Holden, "An adjoint for likelihood maximization," Proceedings of the R, Vol. 465, No. 2111, 3267-3287, Nov. 2009.
doi:10.1098/rspa.2009.0096        Google Scholar

12. Jones, D. R., M. Schonlau, and W. J. Welch, "Efficient global optimization of expensive black-box functions," Journal of Global Optimization, Vol. 13, No. 4, 455-492, Dec. 1998.
doi:10.1023/A:1008306431147        Google Scholar

13. Keane, A., "Statistical improvement criteria for use in multiobjective design optimization," AIAA Journal, Vol. 44, No. 4, 879-891, 2006.
doi:10.2514/1.16875        Google Scholar

14. Morris, M. D. and T. J. Mitchell, "Exploratory designs for computational experiments," Journal of Statistical Planning and Inference, Vol. 43, No. 3, 381-402, 1995.
doi:10.1016/0378-3758(94)00035-T        Google Scholar

15. Smith, D. R., D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E, Vol. 71, 036617, Mar. 2005.
doi:10.1103/PhysRevE.71.036617        Google Scholar

16. Barroso, J. J. and U. C. Hasar, "Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method," Journal of Infrared, Millimeter, and Terahertz Waves, Vol. 33, No. 2, 237-244, 2012.
doi:10.1007/s10762-011-9869-3        Google Scholar

17. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by timedomain techniques," IEEE Transactions on Instrumentation and Measurement, Vol. 19, No. 4, 377-382, 1970.
doi:10.1109/TIM.1970.4313932        Google Scholar

18. Yu, S., Z. Wu, H. Wang, and Z. Chen, "A hybrid particle swarm optimization algorithm based on space transformation search and a modified velocity model," High Performance Computing and Applications, Vol. 5938, 522-527, 2010.
doi:10.1007/978-3-642-11842-5_73        Google Scholar

19. Mansoornejad, B., N. Mostoufi, and F. Jalali-Farahani, "A hybrid GA-SQP optimization technique for determination of kinetic parameters of hydrogenation reactions," Computers & Chemical Engineering, Vol. 32, No. 7, 1447-1455, 2008.
doi:10.1016/j.compchemeng.2007.06.018        Google Scholar

20. Zaoui, W. S., K. Chen, W. Vogel, and M. Berroth, "Low loss broadband polarization independent fishnet negative index metamaterial at 40GHz," Photonics and Nanostructures — Fundamentals and Applications, Vol. 10, No. 3, 245-250, 2012.
doi:10.1016/j.photonics.2011.02.003        Google Scholar