Aerospace and Electronic Systems - July 2019 - 26

Design of a TTC Antenna Using Simulation and Multiobjective Evolutionary Algorithms
Algorithm 1: Evolutionary Algorithm
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:

solutions (from both the population and the archive) are
copied into a new generation population. If its size is larger
than the population size, the algorithm applies a truncation
operator to discard solutions. It is based on the distances to
the kth nearest neighbors (a crowding measure), so that
those solutions having the largest distances to the other solutions (i.e., the most isolated ones) are selected. Algorithm 3
presents a pseudocode of SPEA-2. Note that lines 4 and 5
are calls to the simulator to evaluate each solution parameters. SPEA-2 sends the parameters of the solution to the
simulator and the simulator returns the objective values for
that solution.

Create random initial population P
Evaluate population P
while Stopping criteria not reached do
Select population P
Create empty population Q
for Population size/2 times do
Select two parents from P
Perform crossover & Mutation
Insert children into Q
end for
Evaluate population Q
P
Q
end while
return P

DESIGNING THE ANTENNA

THE NONDOMINATED SORTING GENETIC ALGORITHM-II
(NSGA-II)
This algorithm was developed by Deb et al. [2] as an
extension of an earlier proposal by Srinivas and Deb [21].
The population individuals (solutions) are evaluated (i.e.,
they are assigned fitness values) in relation to how close they
are to the Pareto-optimal Front and a crowding measure.
The NSGA-II algorithm also considers the sparsity
(density) of the individuals belonging to the same rank using
a crowding measure (the Manhattan distance among individuals), with the idea of promoting diversity within the fronts
(the larger the sparsity, the better). In addition, the NSGA-II
includes elitism in order to maintain the best solutions from
the Pareto-optimal Front found. The rank of each individual
is based on the level of nondomination. Therefore, each
solution has two attributes: i) nondomination rank (front to
which the solution belongs) and ii) crowding distance. In
other words, between two solutions with differing nondomination ranks, the solution with the lower rank is preferred.
Otherwise, if both solutions belong to the same front, then
the solution that is located in a less crowded region is
preferred. The pseudocode of NSGA-II is shown in
Algorithm 2. Note that lines 2 and 6 are calls to the simulator
to evaluate the solution parameters. NSGA-II sends the
parameters of the solution to the simulator and the simulator
returns the objective values for that solution.

STRENGTH PARETO EVOLUTIONARY ALGORITHM-2 (SPEA-2)
This algorithm was proposed by Zitzler et al. [3]. In this
algorithm, the strength of an individual is defined in terms
of the number of solutions it dominates in the population. A
fitness value is assigned to every individual, and it is defined
as the sum of its strength raw fitness and a density estimation. The algorithm evolves the population through the
iterative application of the variation operators on the solutions. All generated nondominated solutions are stored in
an external archive. After every iteration, all nondominated
26

In order to obtain the radiation patterns of the antenna
shown in Figure 2, it is necessary to use a simulation computer program with the input of the four parameters of the
antenna, then does:
(1) builds the geometrical model of the antenna;
(2) discretize the model according the wavelength;
(3) simulates the antenna to obtain the radiation patterns for both frequencies in order to be processed
by the multiobjective algorithms.
Figure 16 shows the block diagram of the electromagnetic simulation stage.
The geometrical model is built using a software by
which the previously stated parameters can create a
geometrical file in AutoCAD DXF (Drawing Interchange
Format) [22] with the surfaces that define the antenna.
This file must be previously processed to be simulated
with a mesher that discretize the antenna parameters as
input to the simulator that calculates the radiation pattern
using a simulation software called MONURBS [1].
This simulation software is being developed by the
Electromagnetic Computing Group, University of Alcala,
and it is included in as part of an electromagnetic suite,
newFASANT [23]. This suite can be used in many
applications like electromagnetic field analysis of any
complex 3-D structures such as reflectors, horns, microstrip passive devices, periodical structures, antenna on
board, etc. Also, the RCS of complex platforms with arbitrary materials and the compatibility between different
devices mounted on the same platform. Figure 17 shows
the User Interface of the code with all the modules that
can be used for several electromagnetic applications.
From this suite, the MONURBS and mesher code have
been extracted and used as a black box to implement the
procedure of Figure 16. The MONURBS code is based on
the Moment Method Technique (MoM) that is a full-wave
solution. When the object to be analyzed is large, this
technique is both CPU and memory consuming and cannot

IEEE A&E SYSTEMS MAGAZINE

JULY 2019

Aerospace and Electronic Systems - July 2019

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