International Journal of Antennas and Propagation

Volume 2017 (2017), Article ID 7158752, 11 pages

https://doi.org/10.1155/2017/7158752

## Pattern Synthesis of Linear Antenna Arrays Using Enhanced Flower Pollination Algorithm

Department of ECE, Thapar University, Patiala, India

Correspondence should be addressed to Rohit Salgotra; moc.liamg@00.avonossac

Received 18 October 2016; Revised 9 December 2016; Accepted 18 January 2017; Published 20 February 2017

Academic Editor: Shih Yuan Chen

Copyright © 2017 Urvinder Singh and Rohit Salgotra. 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.

#### Abstract

In this paper, a new variant of flower pollination algorithm (FPA), namely, enhanced flower pollination algorithm (EFPA), has been proposed for the pattern synthesis of nonuniform linear antenna arrays (LAA). The proposed algorithm uses the concept of Cauchy mutation in global pollination and enhanced local search to improve the exploration and exploitation tendencies of FPA. It also uses dynamic switching to control the rate of exploration and exploitation. The algorithm is tested on standard benchmark problems and has been compared statistically with state of the art to prove its worthiness. LAA design is a tricky and difficult electromagnetic problem. Hence to check the efficacy of the proposed algorithm it has been used for synthesis of four different LAA with different sizes. Experimental results show that EFPA algorithm provides enhanced performance in terms of side lobe suppression and null control compared to FPA and other popular algorithms.

#### 1. Introduction

Antenna arrays find their application in number of wireless applications such as radar, sonar, mobile, TV, and satellite. Antenna arrays are favored as these have high directivity, reduce power consumption, increase spectral efficiency and also have beam steering capability [1]. The design of antenna arrays with desired radiation pattern has found great interest in the literature. Antenna arrays design is intricate and nonlinear problem. Hence number of optimization techniques such as genetic algorithm (GA), differential algorithm (DE), particle swarm optimization (PSO), biogeography based optimization (BBO) and many others [2–21] have been used to synthesize these. It is required that antenna arrays radiate in desired directions so that these do no add to electromagnetic pollution. This can be achieved if the energy is maximum in the main lobe and minimum in side lobes. Moreover, to avoid interference from undesired directions and to circumvent jamming, null placement in radiation pattern has also gained importance. So, overall the main issues in designing the antenna arrays are reducing the side lobe level (SLL) and placing nulls in the desired directions of radiation pattern.

Linear antenna arrays (LAA) consist of number of antenna elements arranged in a straight line. LAA have become very popular because of their simple geometry and applications. LAA design has been investigated by numerous researchers using several optimization algorithms in the past. Recioui has used PSO for SLL reduction of LAA [2]. Khodier and Christodoulou have synthesized LAA for maximum SLL reduction and null placement. They have designed three arrays for different sizes and showed that PSO gives better results than uniform and quadrature programming method (QPM) [3]. Rattan et al. have applied GA [7] for the optimization of LAA. Their results were better than those obtained using PSO [3]. DE has been employed by Lin et al. to design unequally spaced LAA [8]. They have discussed about the impact of angular resolution on the final results. Dib et al. have compared the performance of self-adaptive DE (SADE) and Tagachi’s method for optimization of LAA [9]. Cengiz and Tokat have used GA, memetic algorithm (MA) and tabu search (TS) to optimize three different LAA [10]. Singh et al. [11] have applied BBO to synthesize uniform and nonuniform LAA and found that BBO is better than PSO and other methods for the design of arrays. BBO has also been used by Sharaqa and Dib to design LAA [12]. Ant colony optimization has been used by Rajo-lglesias and Quevedo-Teruel for the synthesis of LAA for SLL reduction and null placement [13]. A multiobjective approach using multiobjective DE (MOEA/D-DE) has been employed by Pal et al. to optimize LAA [14]. The authors have noted that MOEA/D-DE gives better trade-off curves between null placement and SLL. LAA synthesis using fitness adaptive differential evolution algorithm (fiADE) has been done by Chowdhury et al. [15]. Guney and Onay have utilized harmony search algorithm (HSA) for SLL minimization and null placement in different directions of radiation pattern of LAA [16]. A new algorithm based on the breeding strategy of cuckoos known as cuckoo optimization algorithm (COA) has been employed to optimize three different nonuniform LAA [17]. The authors have compared the results with the popular algorithms like DE, PSO, firefly algorithm (FA) and found that the results provided by COA in terms of SLL reduction and null placement are better than competitive algorithms. Moreover, convergence curves of different algorithms are compared and it is concluded that COA provides faster convergence than the other methods. Guney and Durmus have used back scattering algorithm (BSA) for the pattern nulling of LAA [18]. Khodier has used cuckoo search (CS) to optimize antenna arrays [19]. An enhanced version of PSO named as comprehensive learning PSO (CLPSO) has been used to design three different LAA [20]. Recently, a novel algorithm which mimics the behaviour of flowers known as flower pollination algorithm (FPA) has been used to synthesize LAA [21]. Though number of algorithms have been proposed for synthesis of LAA, these suffer from certain shortcomings like getting stuck in local minima, slow convergence speeds and require precise parameter tuning. So, in this work, the authors propose an enhanced version of FPA known as enhanced FPA (EFPA). The newly proposed algorithm uses the concept of Cauchy distribution to follow large steps in global pollination, enhanced local search and dynamic switch probability to control the rate of local and global pollination. It has better exploration and exploitation capability and is also less likely to stuck in local minima.

The rest of the paper is organized as follows: Section 2 gives details about the basic FPA algorithm, Section 3 proposes a new EFPA algorithm, Section 4 gives result and discussion, and Section 5 provides an extensive conclusion.

#### 2. Flower Pollination Algorithm

Flowers are the most fascinating plant species and have been dominating earth from the cretaceous period, partly from about 125 million years. Almost 80% of plant species are flowering and it has been made possible by the process of pollination [22]. Pollination in flowers, refer to transfer of pollen grains from one flower to another via pollinators such as wind, diffusion, bees, birds, bats and other animals [23]. If the pollination process is through insects, it is called biotic pollination and if it takes place via wind or diffusion, it is called abiotic pollination. Overall, 200,000 varieties of flower pollinators exist in nature. Pollinators such as honey bee has been found to show some specific phenomenon known as flower constancy. This phenomenon helps them to visit only specific flower species and by pass others, hence maximizing the transfer of pollens from a particular plant species. This helps pollinators in finding better food sources and minimize the exploration or learning cost [24]. Pollination can further be classified based upon the pollens of same or different flowers. If a pollinator transfers pollens from one flower to another, it is called cross-pollination while if it does for the same species, it is self-pollination.

Based upon the phenomenon of pollination, flower constancy and behaviour of pollinators, flower pollination algorithm (FPA) was proposed by Yang [25]. He proposed four sets of rules for governing this algorithm as follows:(1)For long distances, the pollination used is biotic cross-pollination; the process is called global pollination and is performed via Levy flights.(2)Abiotic self-pollination process forms the basis of local pollination.(3)The reproduction probability of different flowers involved in pollination is considered as flower constancy.(4)A switch probability is defined for controlling local and global pollination.For simplicity, a single flower producing only one pollen gamete is considered. This means a single solution for problem under test is equivalent to a pollen gamete or a flower. From the rules above, two key features of global and local pollination have been used to formulate FPA.

The first step in FPA is global pollination, where pollinators such as insects carry pollen to long distances. This process helps in pollination of the best fit flower or solution so far and is represented as . Rule with a combination of flower constancy is represented aswhere is the th solution of the problem in the th iteration, is the step size, and Levy flight is generally used to mimic this phenomenon [25]. Levy flight is drawn from a Levy distribution aswhere is the standard gamma function with a step size of .

In the second step, Rule is used along with flower constancy to represent local pollination aswhere and are pollen gametes of same plants but different flowers and is uniformly distributed in . This phase mimics glower constancy at a local scale or in a limited search space.

So, we can say that global and local pollination carry out pollination activities at large and small scale, respectively. In practice, we use a switching probability based on Rule to define the extent of local and global pollination. In the next section, a new enhanced version of flower pollination algorithm is proposed.

#### 3. Enhanced Flower Pollination Algorithm

In the recent past, a large number of researchers have focused on enhancing the basic capabilities of FPA. The algorithm due to its linear nature, make it suitable for deeper analysis. But it has been proved qualitatively and quantitatively in [26] that the FPA algorithm has a very limited scope for optimization problems at hand. Also, the performance of FPA has not been analyzed to a deeper level and the algorithm is still to prove its worthiness for becoming a state-of-the-art algorithm. Keeping in view the above analysis, a new version of FPA namely EFPA has been proposed. The newly proposed EFPA aims at providing three different modifications to the basic FPA. These include Cauchy based global pollination, enhanced local pollination based upon experience of current best flower pollinator as well as local flowers in proximity, and, thirdly, using dynamic switching probabilities.

*(I) Cauchy Based Global Pollination.* In the global pollination phase, instead of using a standard Levy distribution, a Cauchy based operator is used. This operator is basically a Cauchy random variable with distribution given byThe Cauchy density function is given by The general equation of global pollination becomes where is a scale parameter and its value is generally set to 1. The use of Cauchy operator allows for larger mutation by searching the search space at a faster pace and further accounts for avoiding premature convergence.

*(II) Enhanced Local Pollination. *The second modification is added in the local pollination phase. Here based upon the experience of local and current best pollinators, the position of new pollinators is updated. Further, if the fitness of new position is greater than the old one, each pollinator updates its position with respect to the previous one. The general equation is given bywhere* a *and* b* are uniformly distributed random numbers in the range of . Also, the solutions and , corresponds to th and th flower pollinator in the group with . This phase enhances the local search capabilities of FPA algorithm.

*(III) Dynamic Switch Probability.* In FPA, local and global pollinations are controlled by switching probability . For a standard state-of-the-art algorithm, it is imperative to follow more global search at the start and as the algorithm progresses more intensive local search is followed. Using this basic concept, the value of switching probability is selected dynamically. The switch probability is updated by following a general formula asThe above general equation decreases the value of* p* linearly with iterations and hence adds to intensive global search at the beginning and local search towards the end. Here maxiter corresponds to the maximum number of iterations and* t* is the current iteration. The pseudocode for the EFPA is given in Pseudocode 1.