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

Algorithm 4

Fitness estimation strategy.

(1)    Input: Population 𝐓^𝑘 and memory 𝐌(𝑘)

(2)   for 𝑖=1 to 𝑁^𝑘_𝑒 do

(3)    𝐦^ne← FindNearestElementOfM(𝐭_𝑖)

(4)   distance ← FindTheDistance(𝐭_𝑖,𝐦^ne)

(5)   if (distance < 𝐷) then

(6)    if (rand(0, 1) <= 𝑄(𝐦^ne)) then

(7)        𝐽(𝐭_𝑖)←𝑓(𝐭_𝑖)  % Evaluation

(8)       else              (Rule  1)

(9)        𝐽(𝐭_𝑖)←𝐽(𝐦^ne)  % Estimation

(10)     end if

(11)     else

(12)      𝐽(𝐭_𝑖)←𝑓(𝐭_𝑖)  % Evaluation  (Rule  2)

(13)  end if

(14)   end for

(15)   Output: fitness values of  𝐓^𝑘