A Global Multilevel Thresholding Using Differential Evolution Approach

Algorithm 1

The DE algorithm with “DE/rand/1/bin” strategy.

(1)  Generate the initial population randomly

(2)  Evaluate the fitness for each individual in the population

(3)  while the maximum generation G is not reached do

(4)   for 𝑖=1 to NP do

(5)     Select uniform randomly 𝑟₁≠𝑟₂≠𝑟₃≠𝑖

(6)     𝑗_rand=rndint[1,𝐷]

(7)     for 𝑗=1 to 𝐷 do

(8)        if rndreal_𝑗[0,1)≤CR or 𝑗 is equal to 𝑗_rand then

(9)        𝑢_𝑖,𝑗=𝑥_𝑟1,𝑗+𝐹⋅𝑥_𝑟2,𝑗−𝑥_𝑟3,𝑗

(10)      else

(11)      𝑢_𝑖,𝑗=𝑥_𝑖,𝑗

(12)      end if

(13)    end for

(14)  end for

(15)  for 𝑖=1 to NP do

(16)      Evaluate the offspring 𝑢_𝑖

(17)       if 𝑓(𝑢_𝑖) is better than or equal to 𝑓(𝑥_𝑖) then

(18)      Replace 𝑥_𝑖 with 𝑢_𝑖

(19)      end if

(20)    end for

(21) end while