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Step 1. Initialization
The parameters are specified including iteration, population size and dimension of
search space for algorithm. Then, for the properties of bat such as the frequency, ve-
locity, previous position, current position, location, loudness and emission pulse rate
are initialized. In GBA, the position of bats represents a potential solution in a solu-
tion space. Then, the fitness function is designed for the target problem and used to
evaluate the quality of position. Each bat has its fitness evaluated by the defined fit-
ness function. In this study, the proposed algorithm is used to discover the minimum
solution of continuous functions. Hence, the smaller the fitness value is, the better the
position is.
Step 2. Guidable Search
Doppler Effect is employed to establish a regular rule of bat movement in GBA. The
bats governed by GBA are able to adjust their velocity by frequency shift with Dopp-
ler Effect. This frequency shift depends on Doppler Effect caused by velocity between
the bats and the current best bat. When the bats are close to the current best bat, the
bats should receive the ultrasound with higher frequency. The bats use this higher
frequency of the ultrasound to accelerate the velocity. The acceleration is able to as-
sist the bats quickly flying toward the direction of the current best bat. The bats at-
tempt to find a better position than the current best bat according to this direction. On
the contrary, when the bats run away from the current best bat, the bats will receive an
ultrasound with lower frequency. The bats should use this frequency to derive the
velocity. The bats slowly move to explore a better position than their own position
along the path of the current best bat. In guidable search, the velocity of bats is ad-
justed by frequency shift of the received ultrasound wave to approach to a better posi-
tion. This novel movement benefits the bats to quickly and accurately explore the
global optimal solution to improve the solving efficiency of the proposed algorithm.
In additional, this proposed GBA is employed to solve the optimal solution of conti-
nuous function during evolution. The bats use their own previous positions and
current position to ascertain close to or away from the current best bat according to
Eq. (6) and Eq. (7).
(6)
(7)
where
and
are the distances of the previous position (
) and the current
position (
) between bat
i
and the current best bat (
) respectively. The bats ob-
tain a frequency of received ultrasound as shown in Eq. (8). Then, a low filter is uti-
lized to filter out the LF noise of frequency caused by background noise as shown in
Eq. (9). Hence, the bats can accurately adjust the velocity given by Eq. (10). If
, the bats fly toward the current best bat. The bats should receive the ultra-
sound with higher frequency. The bats will quickly fly toward the direction of the
current best bat to find a better position than the current best bat according to this
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