[Retracted] Image Encryption Algorithm Based on Artificial Bee Colony Algorithm and Chaotic System

Algorithm 2

Artificial bee colony optimization algorithm based on crossover operator.

	Require: Population: , Maximum number of iterations: , investigationsize, observationsize
	Ensure: Optimal encrypted image and its position
(1)	According to equation (13)
(2)
(3)	Rearrange according
(4)	fordo
(5)	/Hiring bee stage/
(6)	fordo
(7)
(8)
(9)
(10)
(11)
(12)	Substitute into equation (4) to update its position
(13)	Boundary value processing
(14)	Search for the corresponding encrypted image according to
(15)	equation (13) which in
(16)	According to equation (5) for select the better individuals
(17)	end for
(18)	/Introducing crossover operator/
(19)	Sort and save the top in
(20)	The remaining according to Figure 2 to cross other images
(21)	Calculate the fitness According to equation (13), select the better individuals according to equation (5)
(22)	/Observation bee stage/
(23)	fordo
(24)	according to equation (6)
(25)
(26)
(27)
(28)
(29)
(30)
(31)	repeat 11–16
(32)	end for
(33)	/Investigation bee stage/
(34)	fordo
(35)	Judge whether to give up the honey source
(36)	end for
(37)	end for
(38)	Calculate the fitness of each encrypted image in , select the encrypted image with the maximum fitness, and return its corresponding position