artificial bee colony (abc)

Introduced in 2005 by Dervis Karaboga Honey bee foraging behavior

Types of foraging bee◦ Employed bees

◦ Unemployed bees Scout

Onlooker bees

Picture form www.acclaimclipart.com

Picture form www.acclaimclipart.com , www.computerclipart.com

HiveHive

Dancing area for A

Dancing area for B

Modify from Parmaksızoğlu, S.; Alçı, M. A Novel Cloning Template Designing Method by Using an Artificial Bee Colony Algorithm for Edge Detection of CNN Based Imaging Sensors. Sensors 2011, 11, 5337-5359

Foraging bee

employed bee

Scout

onlookers

Food source initialize(Number of solutions = Employed bees)

Where i = 1,2,…,nn = Food sourcej = Dimension

))(1,0( min,max,min,, jjjji xxrandxx

Send to each solutions (Can be done with Initial phase)◦ Number of solutions = Employed bees

Calculate fitness

)( 1xf)( 2xf

)( 4xf)( 5xf

)( 3xf

Evolve Solution to neighborhood

)( kjijijijij xxxv ijWhere = rand(-1,1)i = 1,2,…,nn = Food sourcej = Dimensionk = rand(1,n)!=i

SolutionXi

j=6

Evolved Solution

Vi

Select better solution

Calculate probability for each solution

Select solution due to probability

Modify from G. Yan et al. “” An Effective Refinement Artificial Bee Colony Optimization AlgorithmBased On Chaotic Search and Application for PID Control Tuning,Journal of Computational Information Systems 7:9 (2011) 3309-3316

n

ii

ii

xf

xfxP

1

)(

)(}{

1Employed bee

Onlooker

2 3 4 5

2 3 4 5 Ri =rand(0,1)1

Ri<P(xi) ?No

Evolve Solution to neighborhood

Select better solution(Same as Employed bee phase)

Modify from G. Yan et al. “” An Effective Refinement Artificial Bee Colony Optimization AlgorithmBased On Chaotic Search and Application for PID Control Tuning,Journal of Computational Information Systems 7:9 (2011) 3309-3316

)( kjijijijij xxxv Where = rand(-1,1)i = 1,2,…,nn = Food sourcej = Dimensionk = rand(1,n)!=i

ij

)(

))(1,0()1( minmaxmin

Gx

xxrandxGx

ii

, counter ≥ limit

, else

No of food source visited = “limit”

Send scouts to find new source

Swarm size Employed bees(50% of swarm) Onlookers(50% of swarm) Scouts(1) Limit Dimension

Modify from D. Karaboga, An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005

Advantages◦ Few control parameters◦ Fast convergence◦ Both exploration & exploitation

Disadvantages◦ Search space limited by initial solution (normal

distribution sample should use in initialize step)

VEABC◦ Multi-objective ABC◦ Inspired by VEGA, BEPSO

◦ Separate in to k swarm◦ Due to number of objective

◦ Evaluate each swarm to each objective

◦ Position of each swarm -> update neighbor solution

S.N. Omkar, J. Senthilnath, R. Khandelwal, G. Nrayana Naik, S. Gopalakrishnan “Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures

,” Applied Soft Computing, Volume 11, Issue 1, January, 2011

Design composite structure◦ Objectives

Minimize weight Minimize total cost Specified strength

◦ Variables Number of layers Stacking sequence Thickness of each layer

◦ Evaluation Stresses of component Failure criteria

◦ Comparison PSO, AIS, GA

De Jong

M. Molga, C. Smutnicki, “Test functions for optimization needs”,http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

◦ Function

◦ Decision space

D

iix

1

2

D12.5,12.5 Griewangk

◦ Function

◦ Decision space

1)cos(4000

1

11

2

D

i

iD

ii

i

xx

D600,600

Rastrigin

M. Molga, C. Smutnicki, “Test functions for optimization needs”,http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

◦ Function

◦ Decision space D12.5,12.5

Rosenbrock

◦ Function

◦ Decision space

D

iii xxD

0

2 ))2cos(10(10

21

0

221 )1()(100 i

D

iii xxx

D048.2,048.2

◦ Swarm size = 10◦ Swarm size = 50◦ Swarm size = 100

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-15

10-10

10-5

100

105

Cycle

Bes

t fu

nctio

n va

lue

De Jong

◦ Swarm size = 10◦ Swarm size = 50◦ Swarm size = 100

Griewangk

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-12

10-10

10-8

10-6

10-4

10-2

100

102

104

Cycle

Bes

t fu

nctio

n va

lue

◦ Swarm size = 10◦ Swarm size = 50◦ Swarm size = 100

Rastrigin

0 500 1000 1500 2000 2500 3000 3500 400010

-15

10-10

10-5

100

105

Cycle

Bes

t fu

nctio

n va

lue

◦ Swarm size = 10◦ Swarm size = 50◦ Swarm size = 100

Rosenbrock

0 500 1000 1500 2000 2500 3000 3500 4000 450010

1

102

103

104

105

Cycle

Bes

t fu

nctio

n va

lue

ne is number of employed bee

Swarm size = 50, D = 50, 30 runs, 5000 evaluations

Function

0.1*D*ne 0.5*D*ne D*ne No scouts

De Jong 1.40E-15 9.97E-16 9.86E-16 1.11E-15

Griewank 2.53E-14 2.52E-16 1.44E-16 0.000350

Rastrigin 5.25E-11 6.07E-16 2.31E-16 0.000336

Rosenbrock 58.310518 58.444032 51.074693 48.912436

Effect of “limit”