Aerospace and Electronic Systems - July 2019 - 27

Moreno et al.

Figure 18.
Antenna parameters optimization.

multiobjective optimization together with a simulation
software of antenna radiation, MONURBS, as previously
described.

Figure 16.
Electromagnetic simulation stage block diagram.

Algorithm 2: NSGA-II Algorithm [2]
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:
15:

Figure 17.
Electromagnetic suite newFASANT.

be applied if the resources of the machine are not high. To
overcome this, several techniques have been implemented
to speed up the simulation while using less memory:
(i) Fast Multipole Multilevel Method [12], [24] and (ii) the
Characteristics Basis Function Method [25], [26]. Also, the
Message Passing Interface (MPI) and OpenMP paradigms
have also been implemented to solve the problem using
less CPU time with multiprocessor machines [27].

LOOKING FOR THE OPTIMAL PARAMETERS
In this paper, we used the implementation of NSGA-II and
SPEA-2 provided in the jMetal2 framework [28] for
2

https://github.com/jMetal/

JULY 2019

P
makeInitalRandomPopulation()
" Call to evaluate P
P
antennaSimulator(P )
t
0
while t max generations do
Q
makeNewPopulationðP Þ
Q
antennaSimulator(Q) " Call to evaluate Q
" Combine parents and offsprings
R
P [Q
F fastNonDominatedSortðRÞ " Calculate Fronts
P
;^i
1
while jP j þ jF i j N do
" Add ith rank to population
P
P [ Fi
i
iþ1
end while
if jP j 6¼ N then
" Calc. crowding
crowdingDistance(F i )
measure in F i

16:
P
P [ bestCrowdingSolutionsðF i ; jP j À NÞ
17: end if
18: t
tþ1
19: end while
20: F
fastNonDominatedSortðRÞ
21: return F 1 " Return first front; i.e., Pareto-optimal
Front

As jMetal is being developed in Java, the communication is also handled using the Java runtime API to
simulate the antenna radiation using the antenna
parameters generated by the multiobjective algorithms.
Therefore, to perform the data exchange between
jMetal and MONURBS, it was necessary to implement a specific method, called AntennaSimulation(P )
(Algorithm 4) to perform the population evaluation.
The calls are carried out in lines 2 and 6 in the
NSGA-II (Algorithm 2), and lines 4 and 5 in the
SPEA-2 (Algorithm 3). Figure 18 illustrates the communication between jMetal and MONURBS implemented in Algorithm 4.

IEEE A&E SYSTEMS MAGAZINE

27



https://www.github.com/jMetal/

Aerospace and Electronic Systems - July 2019

Table of Contents for the Digital Edition of Aerospace and Electronic Systems - July 2019

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