Constrained Pareto Optimization of Wide Band and Steerable Concentric Ring Arrays

A multi-objective evolutionary algorithm that explicitly introduces the management of a single or multiple constraints on the solutions of an electromagnetic problem is presented in this paper. The proposed strategy is based upon a modified genetic algorithm which evaluates the strength of a solution by considering both the match to the desired performance (objectives) as well as the satisfaction of specific requirements imposed to the design (constraints). The key issue is represented by the adaptive constraints management and its influence on the selective pressure of the genetic algorithm. The procedure is applied to the optimization of concentric ring arrays. Several design examples of steerable and wideband arrays are provided to prove the flexibility and reliability of the approach. A particular emphasis is given to the changes in array performance when the same objectives are requested but different kinds of constraints are forced.

[1]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[2]  D.H. Werner,et al.  The Pareto Optimization of Ultrawideband Polyfractal Arrays , 2008, IEEE Transactions on Antennas and Propagation.

[3]  O. P. Gandhi,et al.  Phase-only synthesis of minimum peak sidelobe patterns for linear and planar arrays , 1988 .

[4]  Jie Cui,et al.  Pareto optimal design of multilayer microwave absorbers for wide-angle incidence using genetic algorithms , 2009 .

[5]  C. Balanis,et al.  Geometry and Weight Optimization for Minimizing Sidelobes in Wideband Planar Arrays , 2009, IEEE Transactions on Antennas and Propagation.

[6]  Chiman Kwan,et al.  3-D array pattern synthesis with frequency Invariant property for concentric ring array , 2006, IEEE Transactions on Signal Processing.

[7]  T. Milligan,et al.  Space-tapered circular (ring) array , 2004, IEEE Antennas and Propagation Magazine.

[8]  Gary B. Lamont,et al.  Considerations in engineering parallel multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[9]  Hao Ling,et al.  Design of electrically small wire antennas using a pareto genetic algorithm , 2005, IEEE Transactions on Antennas and Propagation.

[10]  D. Werner,et al.  Design of Broadband Planar Arrays Based on the Optimization of Aperiodic Tilings , 2008, IEEE Transactions on Antennas and Propagation.

[11]  Gary G. Yen,et al.  A Self Adaptive Penalty Function Based Algorithm for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[12]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[13]  B. P. Kumar,et al.  Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry , 2005, IEEE Transactions on Antennas and Propagation.

[14]  Yahya Rahmat-Samii,et al.  Directivity of planar array feeds for satellite reflector applications , 1983 .

[15]  R. Das,et al.  Concentric ring array , 1966 .

[16]  David E. Goldberg,et al.  Genetic algorithm design of Pareto optimal broadband microwave absorbers , 1996 .

[17]  T. T. Binh.  MOBES : A multiobjective evolution strategy for constrained optimization problems , 1997 .

[18]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[19]  Randy L. Haupt,et al.  Optimum quantised low sidelobe phase tapers for arrays , 1995 .

[20]  C. Stearns,et al.  An investigation of concentric ring antennas with low sidelobes , 1965 .

[21]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[22]  Y. Rahmat-Samii,et al.  Advances in Particle Swarm Optimization for Antenna Designs: Real-Number, Binary, Single-Objective and Multiobjective Implementations , 2007, IEEE Transactions on Antennas and Propagation.

[23]  Carlos A. Coello Coello,et al.  A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques , 1999, Knowledge and Information Systems.

[24]  Khaled Rasheed,et al.  Constrained Multi-objective Optimization Using Steady State Genetic Algorithms , 2003, GECCO.

[25]  Hao Ling,et al.  On a Class of Planar Absorbers With Periodic Square Resistive Patches , 2008, IEEE Transactions on Antennas and Propagation.

[26]  R. Marler,et al.  The weighted sum method for multi-objective optimization: new insights , 2010 .

[27]  L. Biller,et al.  Optimization of radiation patterns for an array of concentric ring sources , 1973 .

[28]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[29]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[30]  M. I. Skolnik,et al.  Planar arrays with unequally spaced elements , 1964 .

[31]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[32]  Hao Wang,et al.  Introduction to Genetic Algorithms in Electromagnetics , 1995 .

[33]  Gary G. Yen,et al.  Constraint Handling in Multiobjective Evolutionary Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[34]  R. Haupt,et al.  Optimized Element Spacing for Low Sidelobe Concentric Ring Arrays , 2008, IEEE Transactions on Antennas and Propagation.

[35]  J. Volakis,et al.  Multiobjective Optimal Antenna Design Based on Volumetric Material Optimization , 2007, IEEE Transactions on Antennas and Propagation.