BAT ALGORITHM

Presented by :

Ayushi Gagneja

Priya Kaushal

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.

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

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.

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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.

• 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]

LOUDNESS AND PULSE EMISSION VS ITERATION

FLOW CHART

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 .

ADVANCEMENTSFuzzy 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.

APPLICATIONS

Applications

Image processingContinuous optimization

in engineering design

Combinatorial optimization and

scheduling

Inverse problems and parameter Estimation

Classifications, clustering and data

mining Fuzzy Logic and Other Application

COMPARATIVE ANALYSIS

WHY BAT ALGORITHM BETTER?

Automatic zoomingBAT has a capability of

automatically zooming into a region where promising solutions

have been found.

Parameter controlBAT 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 tuningBA 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.

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

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.