Differential Evolution Algorithm with Self-Adaptive Population Resizing Mechanism

Algorithm 2

The SapsDE algorithm.

(1): Begin

(2):  𝐺=0

(3):  Randomly initialize a population of 𝑁𝑃 vectors uniformly distributed in the

(4):  range 𝑋_min,𝑋_max

(5):  Evaluate the fitness values of the population

(6):  while termination criterion is not satisfied do

(7):   for  𝑖=1 to 𝑁𝑃  do

(8):    Generate donor vector 𝑋^→𝐺_𝑖

(9):    if  𝑅𝑛<𝜃  then

(10):     𝐯^𝐺_𝑖=𝐱^𝐺_𝑖+𝐹_𝑖⋅(𝐱^𝐺_best−𝐱^𝐺_𝑖)+𝐹_𝑖⋅(𝐱^𝐺_𝑟1−𝐱^𝐺_𝑟2)

(11):     // mutate with DE/rand-to-best/1 strategy

(12):    else

(13):     𝐯^𝐺_𝑖=𝐱^𝐺_𝑖+𝐹_𝑖⋅(𝐱^𝐺_best,𝑝−𝐱^𝐺_𝑖)+𝐹_𝑖⋅(𝐱^𝐺_𝑟1−𝐱^𝐺_𝑟2)

(14):     // mutate with DE/current-to-𝑝best/1 strategy (JADE)

(15):    end if

(16):    Through crossover operation to generate trial vector

(17):    𝑈^→𝐺_𝑖= Strategy (𝑖,pop)

(18):    Evaluate the trial vector 𝑈^→𝐺_𝑖

(19):    if 𝑓(𝑈^→𝐺_𝑖)≤𝑓(𝑋^→𝐺_𝑖)   then

(20):     𝑋^→_𝑖^𝐺+1=𝑈^→𝐺_𝑖// Save index for replacement

(21):    end if

(22):   end for

(23):   //𝜙 is the minimum value of function evaluations in the last generation

(24):   //𝐿𝑏 is the low bound of population size

(25):   if min(𝑓(𝑋^→𝐺_𝑖))<𝜙  then

(26):    𝐵=1;

(27):    𝜙 = min(𝑓(𝑋^→𝐺_𝑖))

(28):   else

(29):    𝑊=1;

(30):    𝑆𝑡 = 𝑆𝑡 + 1;

(31):   end if

(32):   if  popsize ≤ Lbound then

(33):     𝐿𝑏 = 𝐿𝑏 + 1

(34):   end if

(35):   if (𝑊 == 1) and (𝑆𝑡 ≤ 𝑅) then

(36):    Population_Reducing_Strategy()

(37):    𝑊 = 0

(38):   end if

(39):   if (𝐵 == 1) then

(40):    Population_Augmenting_Strategy1()

(41):    Evaluate the new additional individuals

(42):    𝐵 = 0

(43):    𝑆𝑡=0

(44):   end if

(45):   if (𝑆𝑡>𝑅) or  (𝐿𝑏>𝑅) then

(46):    Population_Augmenting_Strategy2()

(47):    Evaluate the new additional individuals

(48):    𝑆𝑡=0

(49):    𝐿𝑏=0

(50):   end if

(51):   𝐺 = 𝐺 + 1

(52):  end while

(53): End