Automatic Circle Detection on Images Based on an Evolutionary Algorithm That Reduces the Number of Function Evaluations

Algorithm 3

Exploration operation of APRE algorithm.

(1)    Input: Current population 𝐏^𝑘

(2)   for 𝑖=1 to 𝑁^𝑘_𝑒 do

(3)    𝐩_𝑟1,𝐩_𝑟2,𝐩_𝑟3← SelectElements()   % Considering that 𝑟1≠𝑟2≠𝑟3≠𝑖

(4)    for 𝑗=1 to 𝑛  do

(5)    if (rand(0,1)<=MR) then

(6)      ℎ_𝑖,𝑗← DEMutation(𝐩_𝑟1,𝐩_𝑟2,𝐩_𝑟3) % (7)

(7)    else

(8)      ℎ_𝑖,𝑗← TrigonometricMutation(𝐩_𝑟1,𝐩_𝑟2,𝐩_𝑟3) % (8)

(9)    end if

(10)     if (rand(0,1)<=CH) then

(11)     𝑡_𝑖,𝑗←ℎ_𝑖,𝑗

(12)     else

(13)     𝑡_𝑖,𝑗←𝑝_𝑖,𝑗

(14)     end if

(15)    end for

(16)   end for

(17)   Output: Population 𝐓^𝑘