16-08-2012, 02:43 PM
An Introduction to Genetic Algorithms for Electromagnetics
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Abstract
This article is a tutorial on using genetic algorithms to
optimize antenna and scattering patterns. Genetic algorithms are
“global” numerical-optimization methods, patterned after the natural
processes of genetic recombination and evolution. The algorithms
encode each parameter into binary sequences, called a gene,
and a set of genes is a chromosome. These chromosomes undergo
natural selection, mating, and mutation, to arrive at the final optimal
solution. After providing a detailed explanation of how a genetic
algorithm works, and a listing of a MiZAB code, the article presents
three examples. These examples demonstrate how to optimize
antenna patterns and backscattering radar-cross-section patterns.
Finally, additional details about algorithm design are given.
Introduction
N ature abounds with examples of plants and animals adapting to their environments. An animal changes color to hide. A plant
develops extensively deep roots because of strong winds or little
moisture. Engineers can use nature’s philosophy of adaptation in
order to design better products. Computer algorithms that model
survival of the fittest are very attractive, because they are simple to
program, and not hidden in arcane mathematical jargon. Turning
these algorithms loose on a wide variety of optimization problems
leads to some stunning results. This paper shows how to apply
evolution and natural selection, in the form of genetic algorithms, to
optimize radiation patterns.
A genetic algorithm
This section begins with a quick overview of genetic algorithms,
and then provides a step-by-step implementation. Much
more detail on genetic algorithms is found in [lo]. In the following
sections, specific electromagnetics examples are presented. Hopefblly,
the reader can quickly use this information to implement a
working genetic algorithm. MATLAB code resembles a pseudo-
code, and should be understandable even to those not familiar with
this software package.
Conclusions
Genetic algorithms are very usehl for many electromagnetics-
optimization problems. These algorithms tend to be slow (as in
nature), but very powerful. They can optimize problems with many
parameters, and don’t require any gradient calculations. Another
advantage is that they inherently optimize discrete parameters
(unlike gradient-based algorithms that inherently optimize continuous
parameters). Many practical problems have a large, but finite,
number of possible parameter settings. Exhaustive and random
searches are too time consuming for these problems. Gradientbased
algorithms require the calculation of derivatives, and get
stuck in local minima. Two of the examples presented were compared
to results from a quasi-Newton algorithm.