Analysis Of The Genetic Artificial Bee Colony Algorithm

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4.1 The GABC Approach for Image Segmentation
The GABC is the Genetic Artificial Bee Colony Algorithm. The proposed algorithm is the implementation of ABC algorithm with the key concept of GA technique.The GABC is actually the hybrid approach of Artificial Bee Colony Algorithm and the Genetic Algorithm.In this method we extend Genetic Algorithm with Artificial Bee Colony operators i:e Employed Bees and Onlooker Bees to improve the solution space named as Genetic Artificial Bee Colony Algorithm (GABCA). Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions using techniques inspired by natural evolution to optimization problems. Artificial Bee Colony (ABC) is an optimization algorithm based on
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The ABC algorithm defines ith fitness value fitnessi as,

fitnessi= {(1/(1+fi ))/(1+abs(fi))┤ (2)
Candidate food source position from old one in memory can be generated as, vij=xij+ Φij( xij+ xkj) (3) where k={1,2,……,SN} and jϵ{1,2,…..,D} are randomly chosen indexes. Φijϵ [-1, 1] is a random number. The comparison between viand xi positions is done and the remaining one is a better solution. If the food source is abandoned by bees, the old food source is replaced with a new food source by the scout bees which exploit it with the new one as, xi j= xjmin + rand(0,1) (xjmax - xjm (4) where xi is abandoned source, jϵ{1,2,….,D}, xjmin and xjmax are the lower and upper bounds of jth dimension of problem space.
Form the above study, it shows that ABC is a well-suited and well-performed algorithm for various optimization problems and also for segmentation of images, there are still some limitations. For some problems, convergent speed of ABC is quite slower. It is also not well suited for some complex multimodal problems as it get slowly trapped in local optima. To overcome this limitation issues, a hybrid approach of Genetic ABC is
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In general, gray information doesn’t include average gray value of pixels which is spatial information of pixels. Thus in order to better utilize the gray information and spatial information of grey scale images, the improved computation method of 2D entropy came into existence.

4.4.1 GREY NUMBER IN GREY THEORY
An effective mathematical method for solving problems like uncertainty and indetermination developed by Deng in 1982 called as Grey theory [29]. It’s a multidisciplinary and generic theory that is designed to deal with systems containing poor information. Grey theory, the random process is treated as grey process within certain range and a random variable is regarded as a grey number.
Definition : A grey number can be defined as an unknown value in an interval with known lower and upper bounds of x, where x denote a closed and bounded set of real numbers.
( ⊗) ̅x є [▁(⊗)x,⊗ ̅x] where ▁(⊗)x and ¯(⊗)x are lower and upper bounds of ⊗x

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