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International Journal of Antennas and Propagation
Volume 2012, Article ID 202906, 7 pages
Research Article

Conformal Array Pattern Synthesis Using a Hybrid WARP/2LB-MOPSO Algorithm

1The Electrical Engineering Department, Tarbiat Modares University, Jalal Ale Ahmad Highway, Tehran 14115-111, Iran
2The Electrical and Computer Engineering Faculty, K. N. Toosi University of Technology, Tehran 1431714191, Iran

Received 18 July 2012; Revised 31 August 2012; Accepted 4 September 2012

Academic Editor: Stefano Selleri

Copyright © 2012 Roghieh Karimzadeh Baee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses conformal array synthesis as a constrained multiobjective optimization problem. Simultaneous reduction of side lobe level (SLL) and cross-polarization (XPL) level is aimed with a constraint on main beam direction. A hybrid of weighted alternating reverse projection (WARP) and two local best multiobjective particle swarm optimization (2LB-MOPSO) is proposed to optimize the pattern. First, the WARP method finds a moderate and feasible solution. Second, 2LB-MOPSO begins with an initial population including the solution of WARP and penalty functions for constraint handling. Involving WARP result in the initial population of 2LB-MOPSO leads to higher convergence rate, avoiding local extermum traps and less sensitivity to penalty functions. Compared to WARP method which stagnates rapidly, the proposed hybrid method gives better SLL and XPL after adequate iterations. In addition, as 2LB-MOPSO offers a set of optimum solutions (Pareto front) instead of a single solution, this method provides more degrees of freedom in selection of proper practical arrays. Finally, to examine the mutual coupling consideration in array design, the same procedure was applied ignoring the mutual coupling between elements. The results show that the SLL and XPL strongly depend on mutual coupling.