110 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011 Design of Non-Uniform Circular Antenna Arrays Using a Modified Invasive Weed Optimization Algorithm Gourab Ghosh Roy, Swagatam Das, Member, IEEE, Prithwish Chakraborty, and Ponnuthurai N. Suganthan, Senior Member, IEEE Abstract—An ecologically inspired optimization algorithm, called invasive weed optimization (IWO), is presented for the design of non-uniform, planar, and circular antenna arrays that can achieve minimum side lobe levels for a specific first null beamwidth while avoiding the mutual coupling effects simultane- ously. IWO recently emerged as a derivative-free real parameter optimizer that mimics the ecological behavior of colonizing weeds. For the present application, classical IWO has been modified by introducing a more explorative routine of changing the stan- dard deviation of the seed population (equivalent to mutation step-size in evolutionary algorithms) of the algorithm. Simulation results over three significant instances of the circular array design problem have been presented to illustrate the effectiveness of the modified IWO algorithm. The design results obtained with mod- ified IWO have been shown to comfortably beat those obtained with other state-of-the-art metaheuristics like genetic algorithm (GA), particle swarm optimization (PSO), original IWO and differential evolution (DE) in a statistically meaningful way. Index Terms—Circular antenna arrays, differential evolution (DE), genetic algorithms (GAs), invasive weed optimization (IWO), particle swarm optimization (PSO), real parameter optimization, sidelobe suppression. I. INTRODUCTION I N several occasions, a single element antenna is unable to meet the gain or highly directive radiation pattern require- ments especially suited for long distance communication. An- tenna arrays are formed to circumvent such problems by com- bining many individual antenna elements in certain electrical and geometrical configurations [1]–[3]. The primary design ob- jective of antenna array geometry is to determine the positions of array elements that jointly produce a radiation pattern to match the desired pattern as closely as possible [4]. Manuscript received January 18, 2010; revised June 01, 2010; accepted Au- gust 07, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. G. G. Roy, S. Das, and P. Chakraborty are with the Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, India. P. N. Suganthan is with the School of Electrical and Electronic Engi- neering, Nanyang Technological University, Singapore (e-mail: myself_ gourab@yahoo.co.in; swagatamdas19@yahoo.co.in; prithwish1611@gmail. com; epnsugan@ntu.edu.sg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090477 Since the classical derivative-based optimization techniques are prone to getting trapped in local optima and are strongly sensitive to initialization, metaheuristic approaches have been used to achieve optimized side lobe level (SLL) and null control from the designed linear arrays, e.g., see [5]–[10]. However, the design of arrays with geometrical shapes other than linear has not been studied to the same extent, although their importance has been steadily on the rise. Circular shaped antenna arrays find various applications in sonar, radar, mobile and commer- cial satellite communication systems [11]–[13]. The first meta- heuristic approach towards the design of circular arrays can be traced in the work of Panduro et al. [14] who applied the real-coded genetic algorithm (GA) for designing circular arrays with maximal side lobe level reduction coupled with the con- straint of a fixed beam width. Shihab et al. in [15] applied the particle swarm optimization (PSO) algorithm that draws inspi- ration from the intelligent collective behavior of a group of so- cial creatures, to the same problem and achieved better results as compared to those reported in [14]. Recently Panduro et al. [16] compared three powerful population-based optimization al- gorithms—PSO, GA, and differential evolution (DE) on the de- sign problem of scanned circular arrays. The algorithms were compared on a single instantiation of the design problem with number of antenna elements equal to 12 and for a uniform sepa- ration of by optimizing excitation current amplitudes and phase perturbations with a view to studying the behavior of array factor for the scanning range of 0 to 360 in angular steps of 30 . In this paper, we use an improved variant of one recently de- veloped metaheuristic algorithm, called the invasive weed op- timization (IWO) [17], for designing non-uniform circular ar- rays with optimized performance with respect to SLL, direc- tivity, and null control in a scanning range of . Since its inception, IWO has found several successful applications in engineering [17]–[22]. As evident from publications like [23], IWO is recently making a distinct place of its own in computa- tional electromagnetics. However, to the best of our knowledge, till date, powerful performance of IWO has not been exploited to optimize the amplitude excitation and spacing between the el- ements of a circular antenna array to produce a radiation pattern with optimal performance. We provide detailed simulation re- sults over three instantiations of the design problem here. Com- parisons with the results of other well-known real-parameter op- timizers like GA, PSO, original IWO, and DE [24] reflect the superiority of the proposed modified IWO in a statistically sig- nificant fashion. 0018-926X/$26.00 © 2010 IEEE