Algorithm 2 Pseudo code of the HEHO algorithm

Initialization. Generate the individuals in population; divide population into n clans; calculate fitness for each individual; set generation counter $t=1$, maximum generation $MaxGen$, and the initial value of the $limit$ parameter

while $t<MaxGen$ do

Arrange all solutions according to their fitness

for all clans $ci$ do

for all solution j in the clan $ci$ do

Update $x_{ci,j}$ and generate $x_{new,ci,j}$ using Equation (10)

Select and obtain better solution between $x_{ci,j}$ and $x_{new,ci,j}$

Update $x_{best,ci}$ and generate $x_{new,ci,j}$ using Equation (11)

Select and retain better solution between $x_{best,ci}$ and $x_{new,ci,j}$

end for

end for

for all clans $ci$ in the population do

Replace the worst solution in clan $ci$ using Equation (13)

Replace the solutions that violate $limit$ value by using Equation (13)

end for

Analyze population and calculate fitness

Recalculate the value of the $limit$ parameter

end while

return the best solution among all clans