In electromagnetics, optimization problems generally require high computational resources and involve a large number of unknowns. They are usually characterized by non-convex functionals and continuous spaces suitable for strategies based on Differential Evolution (DE). In such a framework, this paper is aimed at presenting an overview of Differential Evolution-based approaches used in electromagnetics, pointing out novelties and customizations with respect to other fields of application. Starting from a general description of the evolutionary mechanism of Differential Evolution, Differential Evolution-based techniques for electromagnetic optimization are presented. Some hints on the convergence properties and the sensitivity to control parameters are also given. Finally, a comprehensive coverage of different Differential Evolution formulations in solving optimization problems in the area of computational electromagnetics is presented, focusing on antenna synthesis and inverse scattering.

Differential Evolution as Applied to Electromagnetics

This review is aimed at presenting an overview of evolutionary algorithms (EAs) as applied to the solution of inverse scattering problems. The focus of this work is on the use of different population-based optimization algorithms for the reconstruction of unknown objects embedded in an inaccessible region when illuminated by a set of microwaves. Starting from a general description of the structure of EAs, the classical stochastic operators responsible for the evolution process are described. The extension to hybrid implementations when integrated with local search techniques and the exploitation of the 'domain knowledge', either a priori obtained or collected during the optimization process, are also presented. Some theoretical discussions concerned with the convergence issues and a sensitivity analysis on the parameters influencing the stochastic process are reported as well. Successively, a review on how various researchers have applied or customized different evolutionary approaches to inverse scattering problems is carried out ranging from the shape reconstruction of perfectly conducting objects to the detection of the dielectric properties of unknown scatterers up to applications to sub-surface or biomedical imaging. Finally, open problems and envisaged developments are discussed.

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Evolutionary optimization as applied to inverse scattering problems

This paper introduces several different design methodologies for multiband artificial magnetic conducting (AMC) surfaces. The paper begins by investigating the multiband properties exhibited by a conventional electromagnetic bandgap (EBG) AMC that consists of a frequency selective surface (FSS) on top of a thin dielectric substrate with a PEC back plane. The higher-order resonances associated with these surfaces have not been discussed in detail to date, as previous research has been concerned only with exploiting the primary resonant frequency. However, it will be shown that by understanding and making appropriate use of these higher order resonances, it is possible to design multiband AMC surfaces that work for nearly any desired combination of operating frequencies. The first multiband AMC design approach that will be considered is based on the introduction of FSS screens that have fractal or nearly fractal unit cell geometries. This is followed by a more general and robust genetic algorithm (GA) technique for the synthesis of optimal multiband AMC surfaces. In this case, a GA is used to evolve multiband AMC surface designs by simultaneously optimizing the geometry and size of the FSS unit cell as well as the thickness and dielectric constant of the substrate material. Finally, several examples of multiband AMC surfaces are presented, including some practical dual-band and tri-band designs genetically evolved for operation at GPS and cellular frequencies, as well as an example illustrating the success in creating a multiband AMC surface with angular stability.

The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces

This paper introduces a novel technique for efficiently combining genetic algorithms (GAs) with method of moments (MoM) for integrated antenna design and explores a two example applications of the GA/MoM approach. Integral to efficient GA/MoM integration is the use of direct Z-matrix manipulation (DMM). In DMM a "mother" structure is selected and its corresponding impedance or Z-matrix is filled only once prior to beginning the GA optimization process. The GA optimizer then optimizes the design by creating substructures of the mother structure as represented by the corresponding subsets of the original mother Z-matrix. Application of DMM with GA/MoM significantly reduces the total optimization time by eliminating multiple Z-matrix fill operations. DMM also facilitates the use of matrix partitioning and presolving to further reduce the optimization time in many practical cases. The design of a broad-band patch antenna with greater than 20% bandwidth and a dual-band patch antenna are presented as examples of the utility of GA/MoM with DMM. Measured results for the dual-band antenna are compared to numerical results. Excellent agreement between numerical and measured results is observed.

Genetic algorithms and method of moments (GA/MOM) for the design of integrated antennas

In this article, two particular methods for the synthesis of the complex radiation pattern of a linear and a planar array, based on genetic algorithms (GAs), are discussed. First, we present a combination of Schelkunoff's method and GAs for linear arrays with arbitrary radiation patterns; then, we consider the synthesis of planar arrays with rectangular cells. The results show the flexibility of GAs to solve complex problems related to antenna synthesis, subject to many restrictions which are difficult to treat by classical optimization techniques. There is good agreement between the desired and calculated radiation patterns.

Synthesis of antenna arrays using genetic algorithms

This paper presents a tutorial and overview of genetic algorithms for electromagnetic optimization. Genetic-algorithm (GA) optimizers are robust, stochastic search methods modeled on the concepts of natural selection and evolution. The relationship between traditional optimization techniques and the GA is discussed. Step-by-step implementation aspects of the GA are detailed, through an example with the objective of providing useful guidelines for the potential user. Extensive use is made of sidebars and graphical presentation to facilitate understanding. The tutorial is followed by a discussion of several electromagnetic applications in which the GA has proven useful. The applications discussed include the design of lightweight, broadband microwave absorbers, the reduction of array sidelobes in thinned arrays, the design of shaped-beam antenna arrays, the extraction of natural resonance modes of radar targets from backscattered response data, and the design of broadband patch antennas. Genetic-algorithm optimization is shown to be suitable for optimizing a broad class of problems of interest to the electromagnetic community. A comprehensive list of key references, organized by application category, is also provided.

J.M. Johnson

Papers

Genetic algorithms in engineering electromagnetics