A Design Optimization Method with Sparse Scattered Data and Evolutionary Computation

Algorithm 1

Nondominant sorting- and crowding distance selection-based ergodic evolution algorithm. PS: population size; Dim: dimension; : direction factor; DR: direction factor rate; EP: ergodic parameter; : generation; maxIter: maximum generation; : index of individual; : index of dimension; Cr: mutant rate; targeti,j: individual to generate offspring.

Generate an initial population. Evaluate the fitness for each individual.

/DandEPinitialization/ fori =1 to PSdo

forj =1 to Dimdo

/DRas a random value/ ifrand [0, 1) < DRthen

D_i,j = −1

else

D_i,j = +1

end if

EP_i,j = rand(0,1)

end for end for

Evaluate the fitness for each offspring individual

Select n individuals as target individuals

/Ergodic Search/forG =1 to maxIterdo

fori =1 to PSdo

k=rand(1,Dim)

forj =1 to Dimdo

ifrand[0, 1) < Crorj == kthenmutant_i,j = target_i,j (1 + D_i,jEP_i,j) ergodic_i,j = mutant_i,j

else

ergodic_i,j = target_i,j

end if end for

/Selection/

Nondominant sort target vectors of G_th and G −1_th generations Apply crowding distance

Select n individuals as target individual

end for

/DandEPupdate/ fori =1 to PSdo

forj =1 to Dimdo

EP_i,j = logistic map(EP_i,j)

ifrand[0, 1) < DRthen

D_i,j = −1

else

D_i,j = +1

end if end for

end for end for

return the optimum