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was run with simulated binary crossover (with
η
c
= 20), polynomial mutation
(with
η
m
= 20), crossover probability of 0.8 and mutation probability of 1
/n
(where
n
is the number of variables) for all problems. The population size and
number of iterations depends on the problem and will be given in what follows.
In all simulations in Subsections 6.3 and 6.4, omni-aiNet has always been run
with the number of generations and individuals in the initial population smaller
than or equal to the ones adopted for the DT omni-optimizer.
6.1
Single-Objective Uni-global Problem
The omni-aiNet algorithm was applied to the following single objective uni-global
constrained test problem:
Minimize
f
(
x
)=exp(
x
)
,
Subject to
g
(
x
)=exp(
x
)
−
5
≥
0
,
(3)
0
≤
x
≤
3
,
This problem has a single optima located at
x
=1
.
609.The omni-aiNet could
successfully find this global solution. The simulation was made with the following
parameters: initial population of 20 individuals, 20 generations, 10 generations
between suppressions, 5 individuals in Random Insertion, a suppression thresh-
old of 0
.
01, 5 clones per individual and
δ
=0.
The main aspect to be emphasized here is that the population converges to
a single individual (global solution), indicating that the algorithm is capable of
automatically adjusting the amount of computational resources to the kind of
problem being treated.
6.2
Single-Objective Multi-global Problems
In this section, two single-objective multi-global problems were considered. The
first problem is a single variable problem having 21 different global optimal
solutions and given by:
Minimize
f
(
x
)=sin
2
(
πx
)
,x
∈
[0
,
20]
.
(4)
For this problem, eight simulations were made with an initial population of
60 individuals, for 50 generations (being 10 the number of generations between
suppressions), with 20 individuals in Random Insertion, a suppression threshold
of 0
.
01, 10 clones per individual and
δ
=0
.
05. The final
-nondominated solutions
for one of these simulations (24 solutions in the final population) are presented
in Figure 3-a. The omni-aiNet algorithm found an average of 19
.
75
0
.
71 of
the 21 global optimal solutions of this problem, and kept in the final population
an average of 22
.
63
±
1
.
93 individuals. The average number of individuals in
the final populations were higher than the average number of global solutions
found because some non-optimal individuals presented distances from the other
elements in the population greater than the defined suppression threshold, which
prevented their suppression.
±
