A Global Multilevel Thresholding Using Differential Evolution Approach

Algorithm 3

DE with onlooker and ranking-based mutation.

(1)  Randomly generate the initial population

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

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

(4)     Sort and rank the fitness values of population according to (13)

(5)     Calculate the selection probability for each individual according to (14)

(6)   𝑟₁=0                                    ⇐

(7)   for 𝑖=1 to NP do

(8)       Select 𝑟₁, 𝑟₂, 𝑟₃ as shown in Algorithm 2 based on the current 𝑟₁ and 𝛽    ⇐

(9)       𝑗_rand=rndint[1,𝐷]

(10)      for 𝑗=1 to 𝐷 do

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

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

(13)          else

(14)            𝑢_𝑖,𝑗=𝑥_𝑖,𝑗

(15)          end if

(16)      end for

(17)    end for

(18)    for 𝑖=1 to NP do

(19)          Evaluate the offspring 𝑢_𝑖

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

(21)            Replace 𝑥_𝑖 with 𝑢_𝑖

(22)          end if

(23)    end for

(24) end while