Interactive Artificial Bee Colony (IABC) Optimization

Pei-Wei Tsai, Jeng-Shyang Pan, Bin-Yih Liao, and Shu-Chuan Chu

pwtsai@bit.kuas.edu.tw

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

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Introduction Swarm Intelligence employs the collective be

haviors 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

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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 em

ployed bees hit the limit. Update the memory Check the terminational condition

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Movement of the Onlookers

Probability of Selecting a nectar source:

(1)

Pi : The probability of selecting the ith employed bee

S : The number of employed beesθi : The position of the ith employed bee

: The fitness value

S

kk

ii

F

FP

1

iF

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Movement of the Onlookers (2)

Calculation of the new position:(2)

: The position of the onlooker bee. t : The iteration number : The randomly chosen employed bee. j : The dimension of the solution : A series of random variable in the range

.

ttttx kjijijij 1

ix

k

1 1,-

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Movement of the Scouts

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

(3)

r : A random number and

minmaxmin jjjij r

1,0r

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Artificial Bee Colony (ABC) (4)

The Employed Bee The Onlooker Bee The Scout

S

kk

ii

F

FP

1

Record the best solution found so far

ttttx kjijijij 1

minmaxmin jjjij r

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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.(4)

: The gravitational force heads from object 1 to 2.

G : The universal gravitational constant. m : The mass of the object. : The separation between the objects. : The unit vector in the form of equation.

^

21221

2112 r

rmm

GF

12F

21r^

21r

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Interactive Artificial Bee Colony

In Interactive Artificial Bee Colony (IABC), the mass in equation (4) is replaced by .

Euclidean distance is applied for calculating .

The normalization procedure is applied to the fitness values we used in equation (4) and the normalized fitness values are given as .

iF

21r

~

ikF

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Interactive Artificial Bee Colony (2)

After employing the universal gravitation into equation (2), it can be reformed as follows:

(5)

By applying equation (5) and simultaneously considering the gravitation between the picked employed bee and n selected employed bees, it can be reformed again into equation (6).

(6)

][1 ttFttx kjijikijij j

n

kkjijikijij ttFttx

j1

~][1

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Interactive Artificial Bee Colony (3)

1

2

i

1iF

2iF

2n

n

kkjijikijij ttFttx

j1

~][1

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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).

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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 is set to 4.

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Experimental Results

1100

cos1004000

111

21

n

i

in

ii i

xxxf

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Experimental Results (3)

n

iii xxxf

1

22 102cos10

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Experimental Results (2)

1

1

22213 1100

n

iiii xxxxf

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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?