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of GBA. The performance evaluation is expressed in this section. And, these simu-
lated results are compared with BA and HBA. Finally, the conclusions of this study
are summarized in Section 5.
2
Related Work
Bat Algorithm (BA) is a bio-inspired algorithm proposed by Xin-She Yang to solve
optimization problems of single objective and multi-objectives [6, 7]. And, BA is
investigated in depth and is applied [8]. All bats have an ability of echolocation. Bats
randomly fly in the velocity (
v
i
) with frequency (
f
min
), varying wavelength (
λ
), adjust-
able pulse emission rate (
r
i
) and changeable loudness (
A
0
) at position (
x
i
) to search the
prey. The frequency
f
i
in bat
i
is assumed to range from
f
min
to
f
max
. The loudness is
assumed between 1 and 2 as well as decreases from a large positive
A
0
to a minimum
constant value
A
min
. The pulse emission rate is set between 0 and 1.
The frequency only depends on a randomly vector from a uniform distribution. The
movement of bats is unable to adjust its velocity according to the distance between
bats and objective appropriately. The echo time is adopted to aid the more accurate
measurement of distance between bats and objective. This bat algorithm with echo-
aided is called as EABA [9]. In EABA, the velocity of each bat not only considers the
frequency of ultrasound but takes the echo time into account to properly adjust
movement of bats. The bats emit an ultrasound to the objective to calculate the echo
time between its position and the objective's position as Eq. (1). The longer echo time
is, the farther the distance is. At this moment, the bats should increase its velocity to
quickly approach to the objective. On the contrary, the bats should decrease its veloci-
ty to discover the better position near the objective when the echo time is shorter. The
velocity is adjusted by the measured echo time as shown in Eq. (2).
,340/
(1)
(2)
where
is the echo time between the
i
th
bat and current global best solution,
V
is the
propagation of sound in temperature is
25
. The velocity (
is from frequency.
Then, the velocity (
is obtained by velocity (
and echo time (
. The echo
time is used to measure the distance from bat to objective. The bats can accurately
move by the echo-aided to reduce the error caused by random frequency. This pro-
posed EABA improves the performance of the original bat algorithm.
Echolocation is an important feature of bat behavior. That means, bats emit an ul-
trasound and listen to the echo bouncing back from obstacles while flying. This algo-
rithm obtained good results in dealing with lower-dimensional optimization problems,
but may become problematic for higher-dimensional problems because it tends to
converge very fast initially. In order to improve bat algorithm behavior for higher-
dimensional problems, the original bat algorithm was hybridized with the strategies of
differential evolutions (DE), called hybrid bat algorithm (HBA) [10]. HBA has been
proved on a standard set of benchmark functions taken from literatures. And, the
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