IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY 2013 2745
The Wind Driven Optimization Technique and its
Application in Electromagnetics
Zikri Bayraktar, Member, IEEE, Muge Komurcu, Jeremy A. Bossard, Member, IEEE,and
Douglas H. Werner, Fellow, IEEE
Abstract—A new type of nature-inspired global optimization
methodology based on atmospheric motion is introduced. The
proposed Wind Driven O ptimization (WDO) technique is a popu-
lation based iterative heuristic global optimization algorithm for
multi-dimensional and multi-modal problems with the potential
to implement constraints on the search domain. At its core, a
population of infinitesimally small air parcels navigates over an
-dimensional search space following Newton’s second law of
motion, which is also used to describe the motion of air parcels
within the earth’s atmosphere. Compared to similar particle based
algorithms, WDO employs additional terms in the velocity update
equation (e.g., gravitation and Coriolis forces), providing robust-
ness and extra degrees of freedom to fine tune. Along with the
theory and terminology of WDO, a n umerical study for tuning the
WDO parameters is presented. WDO is further applied to three
electromagnetics optimization problems, including the synthesis
of a linear antenna array, a double-sided artificial magnetic con-
ductor for WiFi applications, and an E-shaped microstrip patch
antenna. These examples suggest that WDO can, in some cases,
out-perform other well-known techniques such as Particle Swarm
Optimization (PSO), Genetic Algorithm (GA) or Differential
Evolution (DE) and that WDO is well-suited for problems with
both discrete and continuous-valued parameters.
Index Terms—Artificial magnetic conductor, differential evolu-
tion, genetic algorithms, linear antenna arrays, microstrip patch
antenna, particle swarm optimization, wind driven optimization.
I. INTRODUCTION
N
ATURE i
s a wonderful source of inspiration for devel-
oping optimization techniques that can tackle difficult
problems in science and eng ineering . Sinc e the early 1970s,
vario
us nature-inspired optimization alg orithm s have emerged
starting with the Geneti c A lgorithm (GA) [1], som e of whic h
have proven to be very efficient global optimization methods.
Along
with the GA, Particle Swarm Optim ization (PSO) [2],
Ant Colony Optimization (ACO) [3], Differential Evolution
(DE) [4], [5], Clonal Selection Algorithm (CLONALG) [6], Co-
varia
nce Matrix Adaptation Evolutionary Strategy (CMA-ES)
[7] and many others have been proposed and successfully
implemented. However, because each algorithm possesses
stre
ngths and weaknesses, there is no single method within the
family of natur e -inspired numerical optimization algorithms
Manuscript received February 01, 2012; revised November 13, 2012; ac-
cepted December 26, 2012. Date of publication January 09, 2013; date of current
version May 01, 2013.
The authors are with the w ith the Com putational Electromag netics and
Antennas Research Lab (CEARL), Departm ent o f E lectrical Engineering, The
Pennsylvania State Univer sity (Pen n Stat e), Un iversity Park, PA, 16802 USA
(e-mail: dhw@psu.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Dig
ital Object Identifier 10.1109/TAP.2013.2238654
that stands out as the best for solving all types of problems, a
fact which was mathematically proven by Wolpert et al. in [8].
Synthesis and op timization problems in electromagnetics
have long utilized these nature-inspired techniques t o varying
degrees of success. Application areas within the field of elec-
tromagnetics are very broad , ran gin g from antenna design to
metamaterial synthesis. For example, a considerable body of
work has been devoted to the design optimization of individual
antenna elem ents [1], [9]–[15] from simple wire antennas to
complex printed antenna elements for a variety of applications
including GPS, WiFi, mobile pho nes, vehicular, shipboard,
aircraft and satellite systems. Antenna arrays [16]–[25] have
also been the target of nature-inspired optimization techniques
for element thinnin g, sid e lobe reduction, radiation pattern
synthesis, coupling reduction, as well as ultra-wideband perfor-
mance. In addition to array synthesis techniques, application o f
these algorithms to inverse scattering problems [26], non-linear
media [27], and metamaterials is noteworthy. Examples of
metamaterial and related structures that have been successfully
optimized include absorbers [28], [29], frequency selective
surfaces [30], [31], electromagnetic bandgap surfaces [32],
[33], and many more applications covering a wid e range of
frequencies [34]–[37]. Building on the successful record of
the existing natur e-i nspi red o pti mi zation algorithms, this paper
introduces and utilizes an entirely new optimization m ethod
which w e call Wind Driven Optim izat ion (WDO).
In essence, WDO is a population based iterative heuristic
global optimization t echnique for multi-dimensional and multi-
modal problems w ith the potential to i mp lement constraints on
the search dom a in si mi lar t o PSO, although this pot enti al is
not explicitly demonstrated in this manuscript. The inspiration
for WDO comes from atmospheric mo tion in which the traj ec-
tory of an in finitesimally small air parcel can be described via
Newton’s second law of motion. The rem ain der of this paper is
structured as follows. In Section II, the WD O technique will be
described in detail along with the un derlying physical equations
of atmo spheric motion, and i n Section III a param eter study will
be conducted to aid in tuning the W DO algorithm. Following
this, several optimization examples are presented, including a
linear antenna array optim ization comparing WDO w ith PSO
in Section IV, the design of a double-sided artificial magnetic
conductor (DSAMC) in Section V, and an E-shaped microstrip
patch antenna in Section VI. Final remarks and conclusions are
giveninSectionVII.
II. T
HE WIND DRIVEN OPTIMIZATION TECHNIQUE
The inspiration for WDO comes f ro m the earth’s atmosphere,
where w ind blows in an attempt to equalize horizontal imbal-
anc
es in the air pressure [38] . The t erm “wind” actually refers
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