Linear antenna array synthesis using fitness-adaptive differential evolution algorithm

Design of non-uniform linear antenna arrays is one of the most important electromagnetic optimization problems of current interest. In this article, an adaptive Differential Evolution (DE) algorithm has been used to optimize the spacing between the elements of the linear array to produce a radiation pattern with minimum side lobe level and null placement control. DE is arguably one of the best real parameter optimizers of current interest takes very few control parameters and is easy to implement in any programming language. In this study two very simple adaptation schemes are used to regulate the control parameters F and Cr, upon which the performance of DE is critically dependent. The adaptation schemes are based on the objective function values of the target vectors and donor vectors. The adaptive DE-variant has been used to solve three difficult instances of the design problem and the optimization goal in each example is easily achieved. The results of the proposed algorithm have been shown to meet or beat the recently published results obtained using other state-of-the-art metaheuristics like the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Memetic Algorithms (MA), and Tabu Search (TS) in a statistically meaningful way.

[1]  Yavuz Cengiz,et al.  Linear Antenna Array Design with Use of Genetic, Memetic and Tabu Search Optimization Algorithms , 2008 .

[2]  M. Montaz Ali,et al.  Population set-based global optimization algorithms: some modifications and numerical studies , 2004, Comput. Oper. Res..

[3]  Giuseppe D'Elia,et al.  Antenna pattern synthesis: a new general approach , 1994, Proc. IEEE.

[4]  Rainer Storn,et al.  Minimizing the real functions of the ICEC'96 contest by differential evolution , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[5]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[6]  Andy J. Keane,et al.  Meta-Lamarckian learning in memetic algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[7]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[8]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[9]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[10]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[11]  S. Rengarajan,et al.  Genetic algorithms in the design and optimization of antenna array patterns , 1999 .

[12]  C. Christodoulou,et al.  Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization , 2005, IEEE Transactions on Antennas and Propagation.

[13]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[14]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[15]  Yu-Bo Tian,et al.  Improve the performance of a linear array by changing the spaces among array elements in terms of genetic algorithm , 2005, IEEE Transactions on Antennas and Propagation.

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..

[18]  L. C. Godara,et al.  Handbook of Antennas in Wireless Communications , 2001 .

[19]  Yahya Rahmat-Samii,et al.  Electromagnetic Optimization by Genetic Algorithms , 1999 .

[20]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[21]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[22]  J. Douglas Barrett,et al.  Taguchi's Quality Engineering Handbook , 2007, Technometrics.

[23]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[24]  Stephen P. Boyd,et al.  Antenna array pattern synthesis via convex optimization , 1997, IEEE Trans. Signal Process..

[26]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[27]  Fan Yang,et al.  Linear Antenna Array Synthesis Using Taguchi's Method: A Novel Optimization Technique in Electromagnetics , 2007, IEEE Transactions on Antennas and Propagation.

[28]  Lakhmi C. Jain,et al.  Linear antenna array optimisation by genetic means , 1999, 1999 Third International Conference on Knowledge-Based Intelligent Information Engineering Systems. Proceedings (Cat. No.99TH8410).