Interactive Artificial Bee Colony (IABC) Optimization Pei-Wei Tsai, Jeng-Shyang Pan, Bin-Yih Liao, and Shu-Chuan Chu [email protected]

Outline

 Introduction  Artificial Bee Colony (ABC) Algorithm  Interactive Artificial Bee Colony (IABC)  Experiments and Experimental Results  Conclusions 2

Introduction

 Swarm Intelligence employs the collective behaviors in the animal societies to design algorithms.

 In 2005, Karaboga proposed an Artificial Bee Colony (ABC), which is based on a particular intelligent behavior of honeybee swarms.

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Artificial Bee Colony (ABC)

 ABC is developed based on inspecting the behaviors of real bees on finding nectar and sharing the information of food sources to the bees in the hive.

 Agents in ABC:  The Employed Bee  The Onlooker Bee  The Scout 4

Artificial Bee Colony (ABC) (2)

 The Employed Bee : It stays on a food source and provides the neighborhood of the source in its memory.

 The Onlooker Bee : It gets the information of food sources from the employed bees in the hive and select one of the food source to gathers the nectar.

 The Scout : It is responsible for finding new food, the new nectar, sources.

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Artificial Bee Colony (ABC) (3)

 Procedures of ABC:  Initialize (Move the scouts).

 Move the onlookers.

 Move the scouts only if the counters of the employed bees hit the

limit

.

 Update the memory  Check the terminational condition 6

Movement of the Onlookers

 Probability of Selecting a nectar source:

P i



F

 

i k S

  1

F

 

k

(1)

P i

: The probability of selecting the bee

i th

employed

S

: The number of employed bees

θ i F

 : The position of the

i th

 

i

: The fitness value employed bee 7

Movement of the Onlookers (2)

 Calculation of the new position:

x ij



t

 1   

ij

   

ij

 

kj

 

x i

: The position of the onlooker bee.



t

: The iteration number  

k

: The randomly chosen employed bee.



j

: The dimension of the solution   : A series of random variable in the   (2) 8

Movement of the Scouts

 The movement of the scout bees follows equation (3).



ij

 

j

min 

r

  

j

max  

j

min  (3) 

r

: A random number and

r

 9

Artificial Bee Colony (ABC) (4)

   

ij

 

j

min 

r

  

j

max  

j

min  The Employed Bee The Onlooker Bee The Scout

x ij P i

 

k

 1

F



F

 

i



k ij

   

ij

 

kj

 Record the best solution found so far 10

Discussion

 The movement of the onlookers is limited to the selected nectar source and the randomly selected source.

 Suppose we find a way to consider more relations between the employed bees and the onlookers, we may extend the exploitation capacity of the ABC algorithm.

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Universal Gravitation

 Universal Gravitation is an invisible force between objects.

F

12 

G m

1

m

2 2

r

21 ^

r

21 (4) 

F

12 : The gravitational force heads from object

1

to

2.



G

: The universal gravitational constant.



m

: The mass of the object.



r

21 : The separation between the objects.

 ^

r

21 : The unit vector in the form of equation.

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Interactive Artificial Bee Colony

 In Interactive Artificial Bee Colony (IABC), the  

i

 Euclidean distance is applied for

r

 The normalization procedure is applied to the fitness values we used in equation (4) and

F

~ the normalized fitness values are given as .

ik

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Interactive Artificial Bee Colony (2)  After employing the universal gravitation into equation (2), it can be reformed as follows:

x ij t

  

ij t

  

F ik j

 [ 

ij t

   

kj t

  ] (5)  By applying equation (5) and simultaneously considering the gravitation between the picked employed bee and equation (6).

n

selected employed bees, it can be reformed again into

x ij



t

 1   

ij



k n

  1 ~

F ik j

 [ 

ij

 

kj

] (6) 14

Interactive Artificial Bee Colony (3)

x ij n

 2 1  

ij



k n

  1 ~

F ik j

 [ 

ij

 

kj

  ] 1

F i

1 2

F i

2

i

15

Experiments

 To analyze the performances, the experiments are made with three well-known benchmark functions, and the results are compared with ABC and Particle Swarm Optimization (PSO).

16

Experiments (2)

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Experiments (3)

 Conditions:  Dimension of the solution:

50

 Runs for average:

30

 Iteration number:

5000

 Population size:

100

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Experiments (4)

 To apply IABC for solving problems related to optimization, the number of the considered employed bee

n

should be predetermined.

 In these experiments, the number of

n

to

4

.

is set 19

Experimental Results

f

1

x

   1 4000  

i n

  1 

x i

 100  2     

i n

  1 cos 

i

100      1 20

Experimental Results (3)

f

2

x

  

i n

  1 

x i

2  10 cos  2 

x i

  10  21

Experimental Results (2)

f

3 

i

 1

n

  1 100 

x i

 1 

x i

2  2  

x i

 1  2 22

Conclusions

 IABC is proposed in this paper.

 It leads in the concept of universal gravitation to the movement of onlooker bees in ABC, and it successfully increases the exploitation ability of ABC.

 The performance of IABC, ABC and PSO are compared in the experiments, and the value of

n

with the best reaction is also discussed and analyzed.

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Thank You for Your Attention.

 Any Question?

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