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

Algorithm 5

Exploitation operation of APRE.

(1)   Input: New memory 𝐌(𝑘+1), current iteration 𝑘

(2)   ME ← SortElementsFitness(𝐌(𝑘+1))

(3)   𝑁_𝑒←ceil(0.1⋅𝑁_𝑝)

(4)   E ← SelectTheFirstElements(𝐌𝐄,𝑁_𝑒)

(5)   for 𝑖=1 to 𝑁_𝑒 do

(6)   𝑝_𝑖←(𝑁_𝑒+1−𝑖)/𝑁_𝑒

(7)   if (rand(0, 1) <= 𝑝_𝑖) then

(8)     for 𝑗=1 to 𝑛  do

(9)       𝑚𝑒^new_𝑖,𝑗←𝑚𝑒_𝑖,𝑗+𝐷𝑛𝑔−𝑘/𝑛𝑔(2⋅rand(0,1)−1)

(10)   end for

(11)      𝐽(𝐦𝐞^new_𝑖)←𝑓(𝐦𝐞^new_𝑖)

(12)      if (𝐽(𝐦𝐞^new_𝑖)>𝐽(𝐦𝐞_𝑖)) then

(13)       𝐌(𝑘+1)← MemoryIsUpdated(𝐦𝐞^new_𝑖)

(14)      end if

(15)   end if

(16) end for

(17) Output: Memory 𝐌(𝑘+1)