Antenna and microwave design problems are, in general, multi-objective. Multi-objective Evolutionary Algorithms (MOEAs) are suitable optimization techniques for solving such problems. Particle Swarm Optimization (PSO) and Differential Evolution (DE) have received increased interest from the electromagnetics community. The fact that both algorithms can efficiently handle arbitrary optimization problems has made them popular for solving antenna and microwave design problems. This chapter presents three different state-of-the-art MOEAs based on PSO and DE, namely: the Multi-objective Particle Swarm Optimization (MOPSO), the Multi-objective Particle Swarm Optimization with fitness sharing (MOPSO-fs), and the Generalized Differential Evolution (GDE3). Their applications to different design cases from antenna and microwave problems are reported. These include microwave absorber, microwave filters and Yagi-uda antenna design. The algorithms are compared and evaluated against other evolutionary multi-objective algorithms like Nondominated Sorting Genetic Algorithm-II (NSGA-II). The results show the advantages of using each algorithm.
TopIntroduction
Antenna and microwave design problems often require the optimization of several conflicting objectives. For example, objectives like gain maximization, sidelobe level (SLL) reduction and input impedance matching are common in antenna design problems. In addition, the microwave filter and absorber design problems are in general multi-objective. Multi-objective Evolutionary Algorithms (MOEAs) are suitable optimization techniques for solving such problems. The application of multi-objective evolutionary algorithms to such design problems provides the researcher with a set of solutions. Then the most suitable design case for any given specifications can be selected.
Several evolutionary algorithms (EAs) have emerged in the past decade that mimic biological entities behavior and evolution. In this book chapter, we consider the Genetic Algorithms (GAs), the Particle Swarm Optimization (PSO) and the Differential evolution (DE). The GAs have been applied to a variety of microwave component and antenna design problems. In (Venkatarayalu, Ray, & Gan, 2005) a multi-objective EA is used for the generation of the Pareto front for the constraint dielectric filter design problem. In (Kuwahara, 2005) Pareto GA, a multi-objective GA, is used for the generation of the Pareto front for the Yagi-Uda design problem. Nondominated Sorting Genetic Algorithm-II (NSGA-II) (K. Deb, Pratap, Agarwal, & Meyarivan, 2002) is a popular and efficient multi-objective genetic algorithm, which has been used in several engineering design problems.
PSO (Kennedy & Eberhart, 1995) is an evolutionary algorithm based on the bird fly. PSO is an easy to implement algorithm with computational efficiency. PSO has been used successfully in constrained or unconstrained electromagnetic design problems. Multi-objective PSO algorithms include the Multi-objective Particle Swarm Optimization (MOPSO) (Coello Coello, Pulido, & Lechuga, 2004) and Multi-objective Particle Swarm Optimization with fitness sharing (MOPSO-fs) (Salazar-Lechuga & Rowe, 2005). MOPSO is utilized in (S. K. Goudos & Sahalos, 2006) for microwave absorber design while MOPSO-fs is applied to the filter design problem in (S. K. Goudos, Zaharis, Salazar-Lechuga, Lazaridis, & Gallion, 2007) and to antenna base station design in (S. K. Goudos, Zaharis, Kampitaki, Rekanos, & Hilas, 2009).
An evolutionary algorithm that has gained popularity recently is Differential evolution (DE), proposed by Price and Storn (Storn & Price, 1995; Storn & Price, 1997). Several DE variants or strategies exist. One of the DE advantages is the fact that very few parameters have to be adjusted in order to produce results. Several DE extensions for multi-objective optimization have been proposed so far. Generalized Differential Evolution (GDE3) (Kukkonen & Lampinen, 2005) is a multi-objective DE algorithm that has outperformed other multi-objective evolutionary algorithm for a given set of numerical problems (Kukkonen & Lampinen, 2007; Tan, 2008). An overview of both PSO and DE algorithms and the hybridizations of these algorithms with other soft computing tools can be found in (Das, Abraham, & Konar, 2008).
The main objective of this chapter is to introduce these state-of-art algorithms and present their application to antenna and microwave design problems. This chapter presents results from design cases using Multi-objective Particle Swarm Optimization and Multi-objective Differential Evolution. These include microwave absorber design, microwave filters and Yagi-uda antenna design. The chapter is supported with an adequate number of references.
This chapter is subdivided into four sections. Section 2 presents the definition of the general multi-objective optimization problem under constraints and the details of the algorithms. Section 3 describes the design cases and presents the numerical results. Finally, section 4 contains the discussion about the advantages of using a multi-objective approach and the conclusions.