Amazingly, the emitted pulse could be as loud as 110 dB, and, fortunately, they
are in the ultrasonic region. The loudness also varies from the loudest when sear ching
for pre y and to a quieter base when homing towards the prey. The travelling range of
such short pulses are typically a few metres, depending on the actual frequencies [12].
Microbats can manage to avoid obstacles as small as thin human hairs.
Studies show that microbats use the time delay from the emission and detection of
the echo, the time differenc e between their two ears, and the loudness variations of the
echoes to build up three dimensional scenario of the surr ounding. They can detect the
distance and orientation of the target, the type of prey, and even the moving speed of
the pr e y such as small insects . Indeed, studies suggested that bats seem to be able to
discriminate targets by the variations of the Doppler effect induced by the wing -flutter
rates of the target insects [1].
Obviously, some bats have good eyesight, and most bats also have very sensitive
smell sense. In reality, they will use all the senses as a combination to maximize the
efficient detection of prey and smooth navigation. However, here we are only interested
in the echolocation and the ass ociated behaviour.
Such echolocation behaviour of microbats can be formulated in such a way that it
can be associated with the objective function to be optimized, and this make it possible
to formulate new optimization algorithms. In the rest of this paper, we will first outline
the ba sic formulation of the Bat Algorithm (BA) and then discuss the implementation
and comparison in detail.
3 Bat Algorithm
If we idealize some of the echolocation characteristics of microbats, we can develop var-
ious ba t- inspired algo rithms or bat algorithms. For simplicity, we now use the following
approximate or idealized rules :
1. All bats use echolocation to sense distance, and they also ‘know’ the difference
between food/prey and background barrie rs in some magical way;
2. B ats fly randomly with velocity v
i
at position x
i
with a fixed frequency f
min
,
varying wavelength λ and loudness A
0
to search for prey. They can automatically
adjust the wavelength (o r frequency) of their emitted pulses and adjust the rate
of pulse emission r ∈ [0, 1], depending on the proximity of their target;
3. Although the loudness can vary in many ways, we assume that the loudness varies
from a large (positive) A
0
to a minimum constant va lue A
min
.
Another obvious simplification is that no ray tracing is used in estimating the time
delay and three dimensional topography. Though this might be a good feature for
the a pplication in computationa l geometry, however, we will not use this as it is more
computationally extensive in multidimensional cases.
In addition to these simplified assumptions, we also use the following approxima-
tions, fo r simplicity. In general the frequency f in a range [f
min
, f
max
] corresponds to
a range of wavelengths [λ
min
, λ
max
]. For example a frequency r ange of [20kHz, 500kHz]
corres ponds to a range of wavelengths from 0.7mm to 17mm.
For a given problem, we can also use any wavelength for the ease of implementation.
In the actual implementation, we can adjust the range by adjusting the wavelengths
(or frequencies), and the detectable range (or the larg est wavelength) should be chosen
3