The document summarizes the artificial bee colony (ABC) algorithm, which was introduced in 2005 and is inspired by the foraging behavior of honeybee swarms. The ABC algorithm simulates three groups of bees - employed bees, onlookers, and scouts - to solve optimization problems. It involves phases of employed bee search, onlooker bee choice, and scout bee recruitment to balance exploration and exploitation. The ABC algorithm has few parameters and fast convergence but is limited by its initial solutions. Variations include multi-objective ABC algorithms and parameter studies on swarm size, limit, and dimension.

2.  Introduced in 2005 by Dervis Karaboga
 Honey bee foraging behavior

3.  Types of foraging bee
◦ Employed bees
◦ Unemployed bees
 Scout
 Onlooker bees
Picture form www.acclaimclipart.com

4. Hive
Dancing
area for A
Dancing
area for B
Picture form www.acclaimclipart.com , www.computerclipart.com

5. 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

6. Foraging bee
employed bee
onlookers
Scout

7. Food source initialize
(Number of solutions = Employed bees)
xi , j = xmin, j + rand (0,1)( xmax, j − xmin, j )
Where
i = 1,2,…,n
n = Food source
j = Dimension

8.  Send to each solutions (Can be done with Initial phase)
◦ Number of solutions = Employed bees
 Calculate fitness
f ( x1 )
f ( x2 )
f ( x3 )
f ( x4 )
f ( x5 )

9.  Evolve Solution to neighborhood Where
φij= rand(-1,1)
vij = xij + φij ( xij − xkj ) i = 1,2,…,n
n = Food source
j = Dimension
Evolved k = rand(1,n)!=i
Solution Solution
Xi Vi
j=6
 Select better solution

10.  Calculate probability for each solution
f ( xi )
P{xi } = n
∑ f (x )
i =1
i
 Select solution due to probability
Employed bee 1 2 3 4 5
Ri<P(xi) ?
No
1 2 3 4 5 Ri =rand(0,1)
Onlooker
Modify from G. Yan et al. “” An Effective Refinement Artificial Bee Colony Optimization Algorithm
Based On Chaotic Search and Application for PID Control Tuning,Journal of Computational Information Systems 7:9 (2011) 3309-3316

11.  Evolve Solution to neighborhood
Where
φij= rand(-1,1)
vij = xij + φij ( xij − xkj ) i = 1,2,…,n
n = Food source
j = Dimension
k = rand(1,n)!=i
 Select better solution
(Same as Employed bee phase)
Modify from G. Yan et al. “” An Effective Refinement Artificial Bee Colony Optimization Algorithm
Based On Chaotic Search and Application for PID Control Tuning,Journal of Computational Information Systems 7:9 (2011) 3309-3316

12. No of food source visited = “limit”
Send scouts to find new
source
 xmin + rand (0,1)( xmax − xmin ) , counter ≥ limit
xi (G + 1) = 
 xi (G ) , else

13.  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

14.  Advantages
◦ Few control parameters
◦ Fast convergence
◦ Both exploration & exploitation
 Disadvantages
◦ Search space limited by initial solution (normal
distribution sample should use in initialize step)

15.  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

16.  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

17.  De Jong
◦ Function
D
∑ xi2
i =1
◦ Decision space
[ − 5.12,5.12] D
 Griewangk
◦ Function
1 D 2 D xi
∑ xi − ∏ cos( i ) + 1
4000 i =1 i =1
◦ Decision space
[ − 600,600] D
M. Molga, C. Smutnicki, “Test functions for optimization needs”,
http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

18.  Rastrigin
◦ Function
D
10 D + ∑ ( xi2 − 10 cos(2πxi ))
i =0
◦ Decision space
[ − 5.12,5.12] D
 Rosenbrock
◦ Function
∑ [100( x ]
D −1
i +1 − xi2 ) 2 + (1 − xi ) 2
i =0
◦ Decision space
[ − 2.048,2.048] D
M. Molga, C. Smutnicki, “Test functions for optimization needs”,
http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

19.  De Jong ◦ Swarm size = 10
◦ Swarm size = 50
5
10
◦ Swarm size = 100
0
10
Best function value
-5
10
-10
10
-15
10
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Cycle

20.  Griewangk ◦ Swarm size = 10
◦ Swarm size = 50
4
10
2
10 ◦ Swarm size = 100
0
10
Best function value
-2
10
-4
10
-6
10
-8
10
-10
10
-12
10
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Cycle

21.  Rastrigin ◦ Swarm size = 10
◦ Swarm size = 50
5
10
◦ Swarm size = 100
0
10
Best function value
-5
10
-10
10
-15
10
0 500 1000 1500 2000 2500 3000 3500 4000
Cycle

22.  Rosenbrock ◦ Swarm size = 10
◦ Swarm size = 50
5
10
◦ Swarm size = 100
4
10
Best function value
3
10
2
10
1
10
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Cycle

23. Effect of “limit”
Function 0.1*D*n e 0.5*D*n e D*n e 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
ne is number of employed bee
Swarm size = 50, D = 50, 30 runs, 5000 evaluations