The document summarizes the bat algorithm, which is inspired by the echolocation of bats. It describes how bats use echolocation to detect prey and avoid obstacles. The bat algorithm models this behavior mathematically to solve optimization problems. Key aspects covered include the idealized rules of the bat algorithm, the mathematical equations governing how solutions are generated and updated, examples of its application in image segmentation and other domains, comparisons to other algorithms, and advantages such as automatic zooming and parameter control.

1. BAT ALGORITHM
Presented by :
Ayushi Gagneja
Priya Kaushal

2. INTRODUCTION
• The BA algorithm is proposed by Xin-She Yang in
2010.
• The algorithm exploits the so-called echolocation
of the bats.
• The bat use sonar echoes to detect and avoid
obstacles. It’s generally known that sound pulses are
transformed into a frequency which reflects from
obstacles. The bats navigate by using the time delay
from emission to reflection.

3. INTRODUCTION
• After hitting and reflecting, the bats transform their own pulse into useful information to
explore how far away the prey is.
• The pulse rate can be simply determined in the range from 0 to 1, where 0 means that there
is no emission and 1 means that the bat’s emitting is their maximum. The bat behaviour can
be used to formulate a new BAT.
Bat sends signal with frequency f Echo signal used to calculate the distance

4. IDEALIZED RULES OF BA
All bats use echolocation to sense distance, and they also ‘know’ the difference
between food/prey and background barriers in some magical way.
Bats fly randomly with velocity vi at position xi with a fixed frequency fmin, varying
wavelength λ and loudness A0 to search for prey. They can automatically adjust the
wavelength of their emitted pulses and adjust the rate of pulse emission r λ [0,1],
depending on the proximity of their target.
Although the loudness can vary in many ways, we assume that the loudness varies
from a large (positive) A0 to a minimum constant value Amin.
1
2
3

5. MATHEMATICAL EQUATIONS
• Generating new solutions is performed by moving virtual bats according to the following equations:
• where β∈ [0,1] is a random vector drawn from a uniform distribution.
• Here x* is the current global best location (solution) which is located after comparing all the solutions
among all the bats.

6. • The current best solution according the equation:
where 𝜕 ∈[-1,1] is a random number, while At is the average loudness of all the best at this time
step.
• As the loudness usually decreases once a bat has found its pray, while the rate of pulse
emission increases, the loudness can be chosen as any value of convenience.
Frequency [20KHZ-500KHZ] Wavelength [0.7mm-17mm]

7. LOUDNESS AND PULSE EMISSION VS ITERATION

8. FLOW CHART

10. EXAMPLE- SEGMENTATION
where
The multilevel thresholding problem can be configured as a
k-dimensional optimization problem, for determination of k
optimal thresholds [t1, t2 ,..., tk ] which optimizes an objective
function.
L gray levels in a given image I having M pixels and these
grey levels are in the range {0,1,...L-1}.
The objective function is determined from the histogram of
the image, denoted by h(i) , i= 0, 1,2, …. L-1 , where h(i)
represents the number of pixels having the gray level i.
The normalized probability at level i is defined by the ratio
Pi = h(i) /M .

11. ADVANCEMENTS
Fuzzy Logic Bat Algorithm (FLBA): By introducing fuzzy logic into the bat algorithm, they called their variant fuzzy bat
algorithm.
Multi objective bat algorithm (MOBA): Extended BA to deal with multi objective optimization, which has demonstrated its
effectiveness for solving a few design benchmarks in engineering.
K-Means Bat Algorithm (KMBA): Presented a combination of K-means and bat algorithm (KMBA) for efficient clustering.
Chaotic Bat Algorithm (CBA): Presented a chaotic bat algorithm using L´evy flights and chaotic maps to carry out parameter
estimation in dynamic biological systems.
Binary bat algorithm (BBA): Developed a discrete version of bat algorithm to solve classifications and feature selection
problems.
Differential Operator and L´evy flights Bat Algorithm (DLBA): Presented a variant of bat algorithm using differential
operator and L´evy flights to solve function optimization problems.
Improved bat algorithm (IBA): Extended the bat algorithm with a good combination of L´evy flights and subtle variations of
loudness and pulse emission rates. They tested the IBA versus over 70 different test functions and proved to be very efficient.

12. APPLICATIONS
Applications
Image
processing
Continuous
optimization in
engineering
design
Combinatorial
optimization
and scheduling
Inverse
problems and
parameter
Estimation
Classifications,
clustering and
data mining
Fuzzy Logic
and Other
Application

13. COMPARATIVE ANALYSIS

14. WHY BAT ALGORITHM BETTER?
Automatic zooming
BAT has a capability of automatically
zooming into a region where
promising solutions have been found.
Parameter control
BAT uses parameter control, which
can vary the values of parameters (A
and r) as the iterations proceed. This
provides a way to automatically
switch from exploration to
exploitation when the optimal
solution is approaching.
Frequency tuning
BA uses echolocation and frequency
tuning to solve problems. Though
echolocation is not directly used to
mimic the true function in reality,
frequency variations are used.

15. ADVANTAGES OF BAT
Simple, Flexible and Easy to implement.
Solve a wide range of problems and highly non linear problems efficiently.
Give best solution in quick time.
The loudness and pulse emission rates essentially provide a mechanism for automatic
control and auto-zooming into the region.
It gives promising optimal solutions.
Works well with complicated problems

16. DISADVANTAGES OF BAT
Bat algorithm converge very quickly at the early stage and then convergence
rate slow down
There is no mathematical analysis to link the parameters with convergence
rates.
Accuracy may be limited if the number of function evaluations is not high.
Not clear what the best values are for most applications.
It is highly needed that large-scale application shoulds be tested.