module data_type
implicit none
integer(kind=4), parameter :: IB=4, RP=8
end module data_type
module data_Rosen
use data_type
implicit none
integer(kind=IB), parameter :: Dim_XC=10
end module data_Rosen
module data_HDE
use data_type
use data_Rosen
implicit none
integer(kind=IB), parameter :: NP=20, itermax=20000, strategy=6, &
refresh=500, iwrite=7
integer(kind=IB), dimension(3), parameter :: method=(/0, 1, 0/)
real(kind=RP), parameter :: VTR=-1.0e-4_RP, CR_XC=0.5_RP
real(kind=RP) :: F_XC=0.8_RP, F_CR=0.8_RP
real(kind=RP), dimension(Dim_XC), parameter :: XCmin=-10.0_RP, XCmax=10.0_RP
real(kind=RP), dimension(Dim_XC) :: bestmem_XC
integer(kind=IB) :: nfeval
real(kind=RP) :: bestval
end module data_HDE
program Rosen
use data_type
use data_Rosen
use data_HDE
implicit none
integer(kind=IB) :: i
integer (kind=IB), dimension(8) :: time
intrinsic date_and_time
external FTN
open(iwrite,file='Rosen.txt')
call date_and_time(values=time)
write(unit=iwrite, FMT=11) time(1:3), time(5:7)
call DE_Fortran90(FTN, Dim_XC, XCmin, XCmax, VTR, NP, itermax, F_XC,&
CR_XC, strategy, refresh, iwrite, bestmem_XC, &
bestval, nfeval, F_CR, method)
write(iwrite,205) NP, nfeval, method(1:3)
write(iwrite,FMT=201) F_XC, CR_XC, F_CR
write(iwrite,FMT=200) bestval
do i=1,Dim_XC
write(iwrite,FMT=202) i,bestmem_XC(i)
end do
200 format(/2x, 'Bestval=', ES14.7)
201 format(2x, 'F_XC =',F6.3, 2x, 'CR_XC =', F6.3, 2x, 'F_CR =', F6.3)
202 format(2x, 'best_XC(',I3,') =',ES14.7)
205 format(2x, 'NP=', I4, 4x, 'No. function call =', I9, &
/2x, 'mehtod(1:3) =',3I3)
call date_and_time(values=time)
write(unit=iwrite, FMT=10)time(1:3), time(5:7)
10 format(/1x, 'End of Program. Date:', I4, '/', I2,'/', I2, ', Time: ', I2,':',I2,':',I2)
11 format(1x, 'Beginning of Program. Date:', I4, '/', I2,'/', I2, ', Time: ', I2,':',I2,':',I2)
end program Rosen
subroutine FTN(X, objval)
use data_type
use data_Rosen
implicit none
real(kind=RP), dimension(Dim_XC), intent(in) :: X
real(kind=RP), intent(out) :: objval
integer(kind=IB) :: i
i=Dim_XC
objval=sum(100.0*(x(1:i-1)**2-x(2:i))**2+(1.0-x(1:i-1))**2)
end subroutine FTN
subroutine DE_Fortran90(obj, Dim_XC, XCmin, XCmax, VTR, NP, itermax, F_XC, &
CR_XC, strategy, refresh, iwrite, bestmem_XC, bestval, nfeval, &
F_CR, method)
!.......................................................................
!
! Differential Evolution for Optimal Control Problems
!
!.......................................................................
! This Fortran 90 program translates from the original MATLAB
! version of differential evolution (DE). This FORTRAN 90 code
! has been tested on Compaq Visual Fortran v6.1.
! Any users new to the DE are encouraged to read the article of Storn and Price.
!
! Refences:
! Storn, R., and Price, K.V., (1996). Minimizing the real function of the
! ICEC'96 contest by differential evolution. IEEE conf. on Evolutionary
! Comutation, 842-844.
!
! This Fortran 90 program written by Dr. Feng-Sheng Wang
! Department of Chemical Engineering, National Chung Cheng University,
! Chia-Yi 621, Taiwan, e-mail: chmfsw@ccunix.ccu.edu.tw
!.........................................................................
! obj : The user provided file for evlauting the objective function.
! subroutine obj(xc,fitness)
! where "xc" is the real decision parameter vector.(input)
! "fitness" is the fitness value.(output)
! Dim_XC : Dimension of the real decision parameters.
! XCmin(Dim_XC) : The lower bound of the real decision parameters.
! XCmax(Dim_XC) : The upper bound of the real decision parameters.
! VTR : The expected fitness value to reach.
! NP : Population size.
! itermax : The maximum number of iteration.
! F_XC : Mutation scaling factor for real decision parameters.
! CR_XC : Crossover factor for real decision parameters.
! strategy : The strategy of the mutation operations is used in HDE.
! refresh : The intermediate output will be produced after "refresh"
! iterations. No intermediate output will be produced if
! "refresh < 1".
! iwrite : The unit specfier for writing to an external data file.
! bestmen_XC(Dim_XC) : The best real decision parameters.
! bestval : The best objective function.
! nfeval : The number of function call.
! method(1) = 0, Fixed mutation scaling factors (F_XC)
! = 1, Random mutation scaling factors F_XC=[0, 1]
! = 2, Random mutation scaling factors F_XC=[-1, 1]
! method(2) = 1, Random combined factor (F_CR) used for strategy = 6
! in the mutation operation
! = other, fixed combined factor provided by the user
! method(3) = 1, Saving results in a data file.
! = other, displaying results only.
use data_type, only : IB, RP
implicit none
integer(kind=IB), intent(in) :: NP, Dim_XC, itermax, strategy, &
iwrite, refresh
real(kind=RP), intent(in) :: VTR, CR_XC
real(kind=RP) :: F_XC, F_CR
real(kind=RP), dimension(Dim_XC), intent(in) :: XCmin, XCmax
real(kind=RP), dimension(Dim_XC), intent(inout) :: bestmem_XC
real(kind=RP), intent(out) :: bestval
integer(kind=IB), intent(out) :: nfeval
real(kind=RP), dimension(NP,Dim_XC) :: pop_XC, bm_XC, mui_XC, mpo_XC, &
popold_XC, rand_XC, ui_XC
integer(kind=IB) :: i, ibest, iter
integer(kind=IB), dimension(NP) :: rot, a1, a2, a3, a4, a5, rt
integer(kind=IB), dimension(4) :: ind
real(kind=RP) :: tempval
real(kind=RP), dimension(NP) :: val
real(kind=RP), dimension(Dim_XC) :: bestmemit_XC
real(kind=RP), dimension(Dim_XC) :: rand_C1
integer(kind=IB), dimension(3), intent(in) :: method
external obj
intrinsic max, min, random_number, mod, abs, any, all, maxloc
interface
function randperm(num)
use data_type, only : IB
implicit none
integer(kind=IB), intent(in) :: num
integer(kind=IB), dimension(num) :: randperm
end function randperm
end interface
!!-----Initialize a population --------------------------------------------!!
pop_XC=0.0_RP
do i=1,NP
call random_number(rand_C1)
pop_XC(i,:)=XCmin+rand_C1*(XCmax-XCmin)
end do
!!--------------------------------------------------------------------------!!
!!------Evaluate fitness functions and find the best member-----------------!!
val=0.0_RP
nfeval=0
ibest=1
call obj(pop_XC(1,:), val(1))
bestval=val(1)
nfeval=nfeval+1
do i=2,NP
call obj(pop_XC(i,:), val(i))
nfeval=nfeval+1
if (val(i) < bestval) then
ibest=i
bestval=val(i)
end if
end do
bestmemit_XC=pop_XC(ibest,:)
bestmem_XC=bestmemit_XC
!!--------------------------------------------------------------------------!!
bm_XC=0.0_RP
rot=(/(i,i=0,NP-1)/)
iter=1
!!------Perform evolutionary computation------------------------------------!!
do while (iter <= itermax)
popold_XC=pop_XC
!!------Mutation operation--------------------------------------------------!!
ind=randperm(4)
a1=randperm(NP)
rt=mod(rot+ind(1),NP)
a2=a1(rt+1)
rt=mod(rot+ind(2),NP)
a3=a2(rt+1)
rt=mod(rot+ind(3),NP)
a4=a3(rt+1)
rt=mod(rot+ind(4),NP)
a5=a4(rt+1)
bm_XC=spread(bestmemit_XC, DIM=1, NCOPIES=NP)
!----- Generating a random sacling factor--------------------------------!
select case (method(1))
case (1)
call random_number(F_XC)
case(2)
call random_number(F_XC)
F_XC=2.0_RP*F_XC-1.0_RP
end select
!---- select a mutation strategy-----------------------------------------!
select case (strategy)
case (1)
ui_XC=bm_XC+F_XC*(popold_XC(a1,:)-popold_XC(a2,:))
case default
ui_XC=popold_XC(a3,:)+F_XC*(popold_XC(a1,:)-popold_XC(a2,:))
case (3)
ui_XC=popold_XC+F_XC*(bm_XC-popold_XC+popold_XC(a1,:)-popold_XC(a2,:))
case (4)
ui_XC=bm_XC+F_XC*(popold_XC(a1,:)-popold_XC(a2,:)+popold_XC(a3,:)-popold_XC(a4,:))
case (5)
ui_XC=popold_XC(a5,:)+F_XC*(popold_XC(a1,:)-popold_XC(a2,:)+popold_XC(a3,:) &
-popold_XC(a4,:))
case (6) ! A linear crossover combination of bm_XC and popold_XC
if (method(2) == 1) call random_number(F_CR)
ui_XC=popold_XC+F_CR*(bm_XC-popold_XC)+F_XC*(popold_XC(a1,:)-popold_XC(a2,:))
end select
!!---------------------------------------
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