Differential Evolution (DE) is a popular evolutionary algorithm that has been applied to several antenna design problems. However, DE is best suited for continuous search spaces. Therefore, in order to apply it to combinatorial optimization problems for antenna design a binary version of the DE algorithm has to be used. In this chapter, the author presents a design technique based on Novel Binary DE (NBDE). The main benefit of NBDE is reserving the DE updating strategy to binary space. This chapter presents results from design cases that include array thinning, phased array design with discrete phase shifters, and conformal array design with discrete excitations based on NBDE.
TopIntroduction
A huge number of antenna design problems is discrete-valued. Such antenna problems include array thinning and phased array design with discrete phase shifters (Bucci, Perna, & Pinchera, 2012 ; Randy L. Haupt, 1994; R. L. Haupt, 1997, 2007; Keizer, 2008, 2011; Oliveri, Donelli, & Massa, 2009; Oliveri, Manica, & Massa, 2010; Oliveri & Massa, 2011). The solution space for such problems is binary and often high-dimensional. Binary coded Genetic Algorithms (GAs) (Randy L. Haupt, 1994; R. L. Haupt, 1997, 2005) have been used for solving the above-mentioned problems. Genetic Algorithms (GAs) is the most widely used evolutionary algorithm in the literature (Vasant, 2011, 2012, 2014).
Particle Swarm Optimization (PSO) (Kennedy & Eberhart, 1995) and Differential evolution (DE) (Storn & Price, 1995; Storn & Price, 1997) are among the popular evolutionary algorithms which can handle efficiently arbitrary optimization problems. The application of PSO and DE to antenna design problems has received widespread interest in the literature (Benedetti, Azaro, & Massa, 2008; Jin & Rahmat-Samii, 2007; Khodier & Christodoulou, 2005; Robinson & Rahmat-Samii, 2004). In a recent paper, an overview of different features to be considered in antenna optimization is given (Rahmat-Samii, Kovitz, & Rajagopalan, 2012). The application of DE to antenna design includes array synthesis (Caorsi, Massa, Pastorino, & Randazzo, 2005; Y. Chen, Yang, & Nie, 2008; Ding & Wang, 2013; Gang, Shiwen, & Zaiping, 2009; S. K. Goudos, Gotsis, Siakavara, Vafiadis, & Sahalos, 2013; S. K. Goudos, Siakavara, Samaras, Vafiadis, & Sahalos, 2011; Guo & Li, 2009; Kurup, Himdi, & Rydberg, 2003; Panduro & Del Rio Bocio, 2008; Quanjiang, Shiwen, Li, & Zaiping, 2012; S. Yang, Gan, & Qing, 2004), multi beam antenna design (D. Yang, Yong-Chang, Li, & Biao, 2014), and microstrip antennas (Deb, Roy, & Gupta, 2014). In other cases, the DE is combined with Artificial Bee Colony (ABC) (J. Yang, Li, Shi, Xin, & Yu, 2013) or with machine learning techniques (Bo et al., 2014). A Hybrid DE algorithm which uses both real and integer variables has been reported in (Caorsi, et al., 2005; Massa, Pastorino, & Randazzo, 2006), that uses the original DE rule for mutant vector generation and introduces a new crossover operator. More details about the DE application in electromagentics can be found in (Qing, 2009; Rocca, Oliveri, & Massa, 2011).