Self-Adaptive Differential Evolution Algorithms for Wireless Communications and the Antenna and Microwave Design Problems

Several evolutionary algorithms (EAs) have emerged in the past decade that mimic biological entities behavior and evolution. Darwin’s theory of evolution is the major inspiration source for EAs. The foundation of Darwin’s theory of evolution is natural selection. The study of evolutionary algorithms began in the 1960s. Several researchers independently developed three mainstream evolutionary algorithms, namely, genetic algorithms (Goldberg, 1989), evolutionary programming (Fogel, 1995), and evolution strategies (Beyer & Schwefel, 2002). EAs are widely used for the solution of single and multi-objective optimization problems. Swarm Intelligence (SI) algorithms are also a special type of EAs. SI can be defined as the collective behavior of decentralized and self-organized swarms. SI algorithms among others include Particle Swarm Optimization (PSO) (Kennedy & Eberhart, 1995), Ant Colony Optimization (Dorigo & Stutzle, 2004), and Artificial Bee Colony (ABC) (Karaboga & Basturk, 2007). An evolutionary algorithm that has recently gained popularity is Differential Evolution (DE) (R. Storn & Price, 1995; R. Storn & Price, 1997). DE is a populationbased stochastic global optimization algorithm. DE has been used in several real world engineering problems like fuzzy logic controller design problem (Cheong & Lai, 2007), molecular sequence alignment problem (Kukkonen, Jangam, & Chakraborti, 2007), and automatic image pixel clustering (Das & Konar, 2009). The fact that the DE algorithm can handle efficiently arbitrary optimization problems has made it popular for solving problems in electromagnetics. Therefore, DE has been applied successfully to a variety of constrained or unconstrained design problems in electromagnetics (Goudos, Siakavara, Samaras, Vafiadis, & Sahalos, 2011a; Goudos, Siakavara, Vafiadis, & Sahalos, 2010; Goudos, Zaharis, & Yioultsis, 2010 ; Kurup, Himdi, & Rydberg, 2003). The purpose of this article is to briefly describe the DE algorithm and its variants and present their application to antenna and microwave design problems. This article presents results from design cases using selfadaptive DE. These include E-shaped patch antenna, linear array, and tri-band microwave filter design for wireless communications. The article is supported with an adequate number of references. This article is subdivided into five sections. The “Background” Section presents the issues, problems and trends with DE for wireless communications. Then we briefly present the different DE algorithms. In the next Section, we describe the design cases and present the numerical results. An outline of future research directions is provided in the following Section while in the “Conclusion” Section we conclude the article and discuss the advantages of using a self-adaptive DE-based approach in the design and optimization of microwave systems and antennas. Finally, an “Additional Reading Section” gives a list of readings to provide the interested reader with useful sources in the field.