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In the past decade, several swarm intelligence (SI) algorithms that mimic the social behavior of swarms of birds, insects and other animals emerged. Among others, Particle Swarm Optimization (PSO) is a popular SI algorithm, which is based on the intelligence and movement of swarms of birds and resembles their behavior (Kennedy & Eberhart, 1995).
PSO and other evolutionary computation techniques such as Genetic Algorithms (GAs) exhibit several similarities. The main difference between PSO and GAs is the fact that PSO does not have any evolution operators like crossover and mutation. Moreover, PSO compared to GAs requires the adjustment of lesser parameters. Furthermore, PSO is an easy to implement algorithm in just a few lines of code in any programming language. PSO can also be regarded as computationally more efficient than a GA with the same population size.
Several PSO applications exist in the literature in different engineering disciplines: function optimization, artificial neural network training, fuzzy system control and other areas where GAs are also applied. PSO algorithms are very popular for solving problems in electromagnetics, (Baskar, Alphones, Suganthan, & Liang, 2005; Deligkaris et al., 2009; Goudos, Moysiadou, Samaras, Siakavara, & Sahalos, 2010; Goudos, Rekanos, & Sahalos, 2008; Goudos & Sahalos, 2006; Goudos, Zaharis, Kampitaki, Rekanos, & Hilas, 2009; Khodier & Christodoulou, 2005; Robinson & Rahmat-Samii, 2004; Zaharis, 2008; Zaharis, Kampitaki, Lazaridis, Papastergiou, & Gallion, 2007).
There are several different PSO algorithms in the literature. Among the common algorithms are the classical Inertia Weight PSO (IWPSO) and the Constriction Factor PSO (CFPSO) (Clerc, 1999). A PSO variant that speeds up convergence and improves PSO performance especially on complex multimodal problems is proposed in (Liang, Qin, Suganthan, & Baskar, 2006). This is called the Comprehensive Learning Particle Swarm Optimizer (CLPSO) and utilizes a new learning strategy. The main advantage of CLPSO algorithm is that can converge faster than the original PSO. CLSPO has been applied successfully to Yagi-Uda antenna design by Baskar et al. (2005) and to linear array synthesis by Goudos et al. (2010).
The above algorithms are inherently used only for real-valued problems but can easily expand to discrete-valued problems. This can be made using a mapping of the real values of the particles positions to binary values by means of a transfer function. This simple modification of the real-valued PSO called binary PSO (binPSO) has been presented by Kennedy & Eberhart (1997). The transfer function of the original binPSO is an S-shape function. The application and the performance evaluation of different S-shaped and V-shaped transfer functions to binPSO is studied in a recent paper (Mirjalili & Lewis, 2013). Moreover, in (Marandi, Afshinmanesh, Shahabadi, & Bahrami, 2006) another discrete valued PSO called the Boolean PSO is introduced and applied to dual-band planar antenna design. The Boolean PSO is based on the idea of using exclusively Boolean update expressions in the binary space. An extension to Boolean PSO, that improves the algorithm performance, is the Boolean PSO with velocity mutation (BPSO-vm) which has been applied successfully to patch antenna design (Deligkaris et al., 2009).
PSO has also been modified for multi-objective problems, among others multi-objective extensions of PSO include the Multi-Objective Particle Swarm Optimization (MOPSO) (Coello Coello, Pulido, & Lechuga, 2004) and the Multi-Objective Particle Swarm Optimization with fitness sharing (MOPSO-fs) (Salazar-Lechuga & Rowe, 2005). The above algorithms have also been used in antenna and microwave design problems (Goudos & Sahalos, 2006; Goudos et al., 2009).