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ga_routines.f
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module GA_m
use mpi
use type_m
use constants_m
use MM_types , only : LogicalKey
use MPI_definitions_m , only : master , world , myid , np , slave
use parameters_m , only : DP_Moment , CG_ , &
Pop_size , N_generations , &
Top_Selection , Pop_range , &
Mutation_rate , Mutate_Cross , &
Alpha_Tensor , OPT_parms , &
Adaptive_, selection_by
use Semi_Empirical_Parms , only : atom
use Structure_Builder , only : Extended_Cell
use OPT_Parent_class_m , only : GA_OPT
use FF_OPT_class_m , only : FF_OPT
use EH_CG_driver_m , only : CG_driver
use GA_QCModel_m , only : GA_eigen , &
GA_DP_Analysis , &
AlphaPolar , &
Adaptive_GA
use ziggurat , only : ziggurat_t , ziggurat_rnor
use cost_EH , only : evaluate_cost
use cost_MM , only : SetKeys , &
KeyHolder
public :: Genetic_Algorithm , Dump_OPT_parameters
interface Genetic_Algorithm
module procedure Genetic_Algorithm_EH
module procedure Genetic_Algorithm_MM
end interface
private
! module variables ...
type(GA_OPT) :: GA
! module parameters ...
logical, parameter :: T_ = .true. , F_ = .false.
contains
!
!
!
!=================================================
subroutine Genetic_Algorithm_EH( basis, OPT_basis)
!=================================================
implicit none
type(STO_basis) , intent(inout) :: basis(:)
type(STO_basis) , allocatable , intent(out) :: OPT_basis(:)
! local variables ...
real*8 :: BestCost
real*8 , allocatable :: Pop(:,:) , cost(:) , Old_Pop(:,:) , snd_cost(:)
real*8 :: GA_DP(3) , Alpha_ii(3)
integer , allocatable :: indx(:)
integer :: mpi_D_R = mpi_double_precision
integer :: i , generation , err , Pop_start , GeneSize , label
logical :: done = .false.
type(R_eigen) :: GA_UNI
type(STO_basis) , allocatable :: basis_local_min(:) , CG_basis(:) , GA_basis(:) , GA_Selection(:,:)
! reading input-GA key ...
CALL Read_GA_key( basis )
!-----------------------------------------------
! SETTING-UP initial populations
!-----------------------------------------------
GeneSize = GA%GeneSize
! Initial Populations ...
allocate( Pop(Pop_Size , GeneSize) )
Pop_start = 1
! only master handles this stuff ...
If( master ) then
open( unit=23, file='opt.trunk/GA_cost.dat', status='unknown' )
allocate( Old_Pop (Pop_Size , GeneSize) )
allocate( indx (Pop_Size) )
CALL generate_RND_Pop( Pop_start , Pop , distro_type='GAUSS' )
! this keeps the input EHT parameters in the population ...
Pop(1,:) = D_zero
indx = [ ( i , i=1,Pop_Size ) ]
end If
!-----------------------------------------------
! clone basis ...
allocate( GA_basis (size(basis)) )
allocate( basis_local_min (size(basis)) )
GA_basis = basis
basis_local_min = basis
allocate( cost (Pop_size), source=D_zero )
allocate( snd_cost(Pop_size) )
! enable on the fly evaluation cost ...
Adaptive_GA%mode = Adaptive_
do generation = 1 , N_generations
99 CALL MPI_BCAST( done , 1 , mpi_logical , 0 ,world , err )
If( done ) then ! <== slaves pack and stop here ...
deallocate( GA_basis , cost , snd_cost , Pop )
call MPI_FINALIZE(err)
STOP
end If
! for on_the_fly cost evaluation ...
CALL MPI_BCAST( generation , 1 , mpi_Integer , 0 , world , err )
CALL MPI_BCAST( N_generations , 1 , mpi_Integer , 0 , world , err )
CALL MPI_BCAST( Pop , Pop_Size*GeneSize , mpi_D_R , 0 , world , err )
! optimized basis becomes basis_local_min ...
if( (mod(generation,30) == 0) ) &
then
CALL modify_EHT_parameters( basis_local_min , GA_basis , Pop(1,:) )
basis_local_min = GA_basis
Pop(1,:) = D_zero
if( master ) Print 164
end if
! sharing these variables with ga_QCModel ...
Adaptive_GA%gen = generation ; Adaptive_GA%Ngen = N_generations
snd_cost = D_zero
! Mutation_&_Crossing preserves the top-selections ...
! evaluate cost only for new Pop outside top_selection ...
do i = myid + 1 , Pop_Size , np
! search around basis_local_min ...
! intent(in):basis_local_min ; intent(inout):GA_basis ...
CALL modify_EHT_parameters( basis_local_min , GA_basis , Pop(i,:) )
CALL GA_eigen( Extended_Cell , GA_basis , GA_UNI )
If( DP_Moment ) CALL GA_DP_Analysis( Extended_Cell , GA_basis , GA_UNI%L , GA_UNI%R , GA_DP )
If( Alpha_Tensor ) CALL AlphaPolar( Extended_Cell , GA_basis , Alpha_ii )
! gather data and evaluate population cost ...
snd_cost(i) = evaluate_cost( Extended_Cell , GA_UNI , GA_basis , GA_DP , Alpha_ii )
end do
! gather data ...
CALL MPI_reduce( snd_cost , cost , Pop_Size , MPI_D_R , mpi_SUM , 0 , world , err )
If ( slave ) goto 99
! select the fittest ...
CALL SelectTheFittest( cost , Pop , Pop_Size , GeneSize , BestCost)
! Mutation_&_Crossing preserves the top-selections ...
If( Mutate_Cross .AND. (mod(generation,5) /= 0) ) then
CALL Mutation_and_Crossing( Pop )
assign 159 to label
else
Pop_start = Pop_size/4 + 1
CALL generate_RND_Pop( Pop_start , Pop , distro_type='GAUSS' )
assign 163 to label
end If
indx = [ ( i , i=1,Pop_Size ) ]
If( Adaptive_ ) then
Print label , generation , N_generations
else
Print 160 , generation , N_generations
EndIf
Print*, BestCost
write(23,*) generation , BestCost
! saving the temporary optimized parameters ...
! intent(in):basis_local_min ; intent(inout):GA_basis ...
CALL modify_EHT_parameters( basis_local_min , GA_basis , Pop(1,:) )
CALL Dump_OPT_parameters( GA_basis , output = "tmp" )
If( generation == N_generations ) then
done = .true.
CALL MPI_Bcast( done , 1 , mpi_logical , 0 ,world , err )
end If
end do
close(23)
! switch-off on the fly evaluation cost ...
Adaptive_GA%mode = .false.
deallocate( cost , snd_cost , indx , Old_Pop )
!----------------------------------------------------------------
! Prepare grid of parameters for CG fine tuning optimization ...
!----------------------------------------------------------------
If( CG_ ) then
allocate( GA_Selection( size(basis) , Top_Selection ) )
do i = 1 , Top_Selection
! optimized parameters by GA method : intent(in):basis ; intent(inout):GA_basis ...
CALL modify_EHT_parameters( basis_local_min , GA_basis , Pop(i,:) )
GA_Selection(:,i) = GA_basis
end do
CALL CG_driver( GA , GA_Selection , CG_basis )
! create OPT basis ...
allocate( OPT_basis (size(basis)) )
OPT_basis = CG_basis
deallocate( GA_basis , CG_basis , GA_Selection , basis_local_min )
else
! optimized parameters by GA method : intent(in):basis ; intent(inout):GA_basis ...
CALL modify_EHT_parameters( basis_local_min , GA_basis , Pop(1,:) )
! create OPT basis ...
allocate( OPT_basis (size(basis)) )
OPT_basis = GA_basis
deallocate( GA_basis , basis_local_min )
end if
! saving the optimized parameters ...
CALL Dump_OPT_parameters( OPT_basis )
deallocate( GA_UNI%L , GA_UNI%R , GA_UNI%erg )
deallocate( Pop )
include 'formats.h'
end subroutine Genetic_Algorithm_EH
!
!
!
!
!============================================================
subroutine generate_RND_Pop( Pop_start , Pop , distro_type )
!============================================================
use :: ziggurat
implicit none
integer , intent(in) :: Pop_start
real*8 , allocatable , intent(inout) :: Pop(:,:)
character(len=*) , intent(in) :: distro_type
! local variables ...
integer :: i , j , GeneSize
real :: x
real*8 :: a , seed
real*8 , allocatable :: pot(:,:)
type(ziggurat_t) :: rng_Zig
! local parameters ...
integer , parameter :: iii = 123456789 !< The RNG seed for Ziggurat method.
real*8 , parameter :: mean = 0.d0 , std_dev = 0.3d0
!-----------------------------------------------
! SETTING-UP populations
!-----------------------------------------------
GeneSize = size(Pop(1,:))
allocate( pot(Pop_Size , GeneSize) )
select case (distro_type)
case ('RNG')
! Generates a UNIFORMLY DISTRIBUTED pseudo-random value in the range [-1,+1]*Pop_range
CALL random_seed ! <== distribution within the range 0 <= x < 1.
do i = Pop_start , Pop_size
do j = 1 , GeneSize
CALL random_number( a )
CALL random_number( seed )
pot(i,j) = int( 2*seed ) ! <== bimodal function (-1)^pot = -1 , +1
Pop(i,j) = ((-1)**pot(i,j)) * a * Pop_range
end do
end do
case ('GAUSS')
! Generates a UNIFORMLY DISTRIBUTED pseudo-random value in the range [-1,+1]*Pop_range
! Seed the RNG.
call ziggurat_seed (rng_Zig, iii)
do i = Pop_start , Pop_size
do j = 1 , GeneSize
! Generate random numbers ...
x = ziggurat_rnor(rng_Zig)
! Transform to desired mean and variance ...
x = mean + std_dev * x
Pop(i,j) = x * Pop_range
end do
end do
end select
! truncate variations to 1.d-5 ...
Pop = Pop * 1.d5 ; Pop = int(Pop) ; Pop = Pop * 1.d-5
deallocate( pot )
!-----------------------------------------------
end subroutine generate_RND_Pop
!
!
!
!
!=======================================
subroutine Mutation_and_Crossing( Pop )
!=======================================
implicit none
real*8 , intent(inout) :: Pop(:,:)
! local variables ...
real*8 , allocatable :: aux(:,:), a(:), b(:), seed(:), pot(:)
real*8 :: rn, rp
integer , allocatable :: p(:), n(:)
integer :: i, j, MT, HALF_MT, NX, XP, GeneSize, odd, even, ind1, ind2
GeneSize = size(Pop(1,:))
!N_crossings and XingPoint ...
NX = Pop_Size / 2
XP = NX / 2
! Start Xing ...
!---------------------------------------------------------------------------
! random population pointer ...
allocate( n(NX) )
do i = 1 , NX
call random_number( rn ) ! <== distribution within the range 0 <= x < 1.
n(i) = int(Pop_Size*rn) + 1
end do
! random gene pointer ...
allocate( p(XP) )
do i = 1 , XP
call random_number( rp )
p(i) = min( int(GeneSize*rp) + 1 , GeneSize-1 )
end do
allocate( aux(Pop_Size,GeneSize) , source=Pop )
j=0
do odd = 1 , 2*XP-1 , 2
even = odd + 1
j=j+1
Pop( NX + odd , 1:p(j) ) = aux( n(odd) , 1:p(j) )
Pop( NX + odd , p(j)+1:GeneSize ) = aux( n(even) , p(j)+1 : GeneSize )
Pop( NX + even, 1:p(j) ) = aux( n(even) , 1:p(j) )
Pop( NX + even, p(j)+1:GeneSize ) = aux( n(odd) , p(j)+1 : GeneSize )
end do
deallocate( n , p , aux )
!---------------------------------------------------------------------------
! End Xing...
! Start Mutation ...
!---------------------------------------------------------------------------
! integer # of genes to mutate
MT = int( NX * GeneSize * Mutation_rate )
HALF_MT = MT / 2
allocate( b(MT), a(HALF_MT), seed(HALF_MT), pot(HALF_MT) )
do i = 1 , MT
call random_number( b(i) ) ! <== distribution within the range 0 <= x < 1.
end do
do i = 1 , HALF_MT
call random_number( a (i) )
call random_number( seed(i) )
pot(i) = int( two * seed(i) ) ! <== bimodal function (-1)^pot = -1 , +1
ind1 = int( NX * b(i) )
ind2 = int( GeneSize * b(HALF_MT+i) )
Pop( NX+1+ind1 , ind2+1) = (-1)**pot(i) * a(i) * Pop_range
end do
! truncate variations to 1.d-5 ...
Pop = Pop * 1.d5 ; Pop = int(Pop) ; Pop = Pop * 1.d-5
deallocate( b , a , seed , pot )
!---------------------------------------------------------------------------
! End Mutation ...
end subroutine Mutation_and_Crossing
!
!
!
!==========================================================
subroutine modify_EHT_parameters( basis , GA_basis , Pop )
!==========================================================
implicit none
type(STO_basis) , intent(in) :: basis(:)
type(STO_basis) , intent(inout) :: GA_basis(:)
real*8 , intent(in) :: Pop(:)
! local variables ...
integer :: L , gene , EHS , N_of_EHSymbol
integer :: indx(size(basis)) , k , i
real*8 :: zeta(2) , coef(2)
! -----------------------------------------------
! changing basis: editting functions ...
! -----------------------------------------------
! GA%key storage
!
! EHSymbol --->
! | 1 - S
! | 2 - P
! V 3 - D
! 4 - IP
! 5 - zeta1
! 6 - zeta2
! 7 - k_WH
! -----------------------------------------------
indx = [ ( i , i=1,size(basis) ) ]
N_of_EHSymbol = size(GA%EHSymbol)
gene = 0
do EHS = 1 , N_of_EHSymbol
! S , P , D orbitals ...
do L = 0 , 2
If( GA%key(L+1,EHS) == 1 ) then
! changes VSIP; defined as negative, only bound states ...
gene = gene + GA%key(4,EHS)
If( GA%key(4,EHS) == 1 ) then
where( (GA_basis%EHSymbol == GA%EHSymbol(EHS)) .AND. (GA_basis%l == L) ) GA_basis%IP = Pop(gene) + basis%IP
where( GA_basis%IP >= d_zero ) GA_basis%IP = -1.d-2
end If
! single STO orbitals; positive by definition ...
gene = gene + GA%key(5,EHS) - GA%key(6,EHS)
If( (GA%key(5,EHS) == 1) .AND. (GA%Key(6,EHS) == 0) ) &
where( (GA_basis%EHSymbol == GA%EHSymbol(EHS)) .AND. (GA_basis%l == L) ) GA_basis%zeta(1) = abs( Pop(gene) + basis%zeta(1) )
! double STO orbitals ...
If( (GA%key(5,EHS) == 1) .AND. (Ga%key(6,EHS) ==1) ) then
! finds the first EHT atom ...
k = minloc( indx , dim=1 , MASK = (GA_basis%EHSymbol == GA%EHSymbol(EHS)) .AND. (GA_basis%l == L) )
! calculate coef(1)[ zeta(1) , zeta(2) , coef(2) ] ...
gene = gene + 1
zeta(1) = abs( Pop(gene) + basis(k)%zeta(1) )
gene = gene + 1
zeta(2) = abs( Pop(gene) + basis(k)%zeta(2) )
coef(2) = abs( Pop(gene) )
CALL normalization( basis , zeta , coef , GA_basis(k)%n , k , 1 , 2 )
where( (GA_basis%EHSymbol == GA%EHSymbol(EHS)) .AND. (GA_basis%l == L) )
GA_basis % zeta(1) = zeta(1)
GA_basis % zeta(2) = zeta(2)
GA_basis % coef(1) = coef(1)
GA_basis % coef(2) = coef(2)
end where
End If
! changes k_WH ; defined as positive paramter, to guarantee E(bonding) < E(anti-bonding) ...
gene = gene + GA%key(7,EHS)
If( GA%key(7,EHS) == 1 ) then
where( (GA_basis%EHSymbol == GA%EHSymbol(EHS)) .AND. (GA_basis%l == L) ) GA_basis%k_WH = Pop(gene) + basis%k_WH
where( GA_basis%k_WH < d_zero ) GA_basis%k_WH = +1.d-2
end If
end If
end do
end do
end subroutine modify_EHT_parameters
!
!
!
!===============================
subroutine Read_GA_key( basis )
!===============================
implicit none
type(STO_basis) , intent(inout) :: basis(:)
! local variables ...
integer :: i , j , ioerr , n , N_of_EHSymbol , err , size_EHSymbol
character(1) :: dumb
OPEN(unit=3,file='input-GA.dat',status='old',iostat=ioerr,err=10)
n = 0
do
read(3,*,IOSTAT=ioerr) dumb
if(ioerr < 0) EXIT
n = n + 1
end do
N_of_EHSymbol = n - 1
! allocatting EH_keys: [s,p,d,IP,zeta,coef,k_WH] ...
allocate( GA%EHSymbol ( N_of_EHSymbol) )
allocate( GA%key (7 , N_of_EHSymbol) )
! future use in bcasting ...
size_EHSymbol = len(GA%EHSymbol(1)) * N_of_EHSymbol
! read the input-GA ...
rewind 3
read(3,*) dumb
If( master ) then
Print 40
Print 41
do j = 1 , N_of_EHSymbol
read(3,42) GA%EHSymbol(j) , ( GA%key(i,j) , i=1,7 )
write(*,421) GA%EHSymbol(j) , ( GA%key(i,j) , i=1,7 )
end do
CLOSE(3)
Print 43
end If
CALL MPI_BCAST( GA%EHSymbol , size_EHSymbol , mpi_CHARACTER , 0 , world , err )
CALL MPI_BCAST( GA%key , 7*N_of_EHSymbol , mpi_INTEGER , 0 , world , err )
GA%GeneSize = sum( [ ( count(GA%key(1:3,j)==1) * count(GA%key(4:7,j)==1) , j=1,N_of_EHSymbol ) ] )
do j = 1 , N_of_EHSymbol
If( GA%key(1,j) /= 0 ) & ! <== optimizing s orbital ...
where( adjustl(basis% EHSymbol) == adjustl(GA% EHSymbol(j)) .AND. basis%L == 0 ) basis%Nzeta = max( GA% key(5,j)+GA% key(6,j) , basis%Nzeta )
If( GA%key(2,j) /= 0 ) & ! <== optimizing p orbital ...
where( adjustl(basis% EHSymbol) == adjustl(GA% EHSymbol(j)) .AND. basis%L == 1 ) basis%Nzeta = max( GA% key(5,j)+GA% key(6,j) , basis%Nzeta )
If( GA%key(3,j) /= 0 ) & ! <== optimizing d orbital ...
where( adjustl(basis% EHSymbol) == adjustl(GA% EHSymbol(j)) .AND. basis%L == 2 ) basis%Nzeta = max( GA% key(5,j)+GA% key(6,j) , basis%Nzeta )
end do
If(master) then
If( OPT_parms ) then
Print*, ">> OPT_parms being used as input <<"
else
Print*, ">> OPT_parms were not used <<"
end if
call sleep(4) ! waits 4 seconds ...
end If
10 if( ioerr > 0 ) stop "input-GA.dat file not found; terminating execution"
include 'formats.h'
end subroutine Read_GA_key
!
!
!
!====================================================
subroutine Dump_OPT_parameters( OPT_basis , output )
!====================================================
implicit none
type(STO_basis) , intent(inout) :: OPT_basis(:)
character(len=*), optional , intent(in) :: output
! local variables ...
integer :: i , j , L , AngMax ,n_EHS , N_of_EHSymbol , unit_tag
integer , allocatable :: aux(:)
integer , save , allocatable :: indx_EHS(:)
character(len=:) , allocatable :: string(:)
logical :: done = .false.
! local parameters ...
character(1) , parameter :: Lquant(0:3) = ["s","p","d","f"]
integer , parameter :: DOS (0:3) = [ 1 , 4 , 9 , 16]
!-------------------------------------------------------------------------------------
If( .not. done ) then
allocate( character( len=len(OPT_basis%EHSymbol)+len(OPT_basis%residue)) :: string(size(OPT_basis)) )
allocate( aux(size(OPT_basis)) , source = 0 )
j = 0
do i = 1 , size(OPT_basis)
string(i) = OPT_basis(i)% EHSymbol//OPT_basis(i)% residue
! find different (EHSymbol,residue) pairs ...
if( .NOT. any( string(1:i-1) == string(i) ) ) then
If( any( GA% EHSymbol == OPT_basis(i)% EHSymbol ) ) then
j = j + 1
aux(j) = i
end If
end If
end do
allocate( indx_EHS(j) , source = aux(1:j) )
deallocate( aux , string )
done = .true.
end If
N_of_EHSymbol = size( indx_EHS )
!-------------------------------------------------------------------------------------
If( present(output) .AND. output=="STDOUT" ) then
Print*,""
Print*,""
unit_tag = 6
elseIf( present(output) .AND. output=="tmp" ) then
! creating file opt_eht_parms.output with the optimized parameters ...
open( unit=13, file='opt.trunk/opt_eht_parms.output', status='unknown' )
unit_tag = 13
else
! creating file opt_eht_parms.output with the optimized parameters ...
open( unit=13, file='opt_eht_parms.output', status='unknown' )
unit_tag = 13
end If
! print heading ...
write(unit_tag,48)
do n_EHS = 1 , N_of_EHSymbol
i = indx_EHS(n_EHS)
AngMax = atom(OPT_basis(i)%AtNo)%AngMax
do L = 0 , AngMax
j = (i-1) + DOS(L)
write(unit_tag,17) OPT_basis(j)%Symbol , &
OPT_basis(j)%EHSymbol , &
OPT_basis(j)%residue , &
OPT_basis(j)%AtNo , &
atom(OPT_basis(j)%AtNo)%Nvalen , &
OPT_basis(j)%Nzeta , &
OPT_basis(j)%n , &
Lquant(OPT_basis(j)%l) , &
OPT_basis(j)%IP , &
OPT_basis(j)%zeta(1)*a_Bohr , & ! <== zetas of opt_eht_parms.output are written in units of a0^{-1} ...
OPT_basis(j)%zeta(2)*a_Bohr , & ! <== zetas of opt_eht_parms.output are written in units of a0^{-1} ...
OPT_basis(j)%coef(1) , &
OPT_basis(j)%coef(2) , &
OPT_basis(j)%k_WH , &
OPT_basis(j)%V_shift
enddo
enddo
If( unit_tag == 13 ) close(13)
17 format(t1,A2,t13,A3,t26,A3,t36,I3,t45,I3,t57,I3,t65,I3,t72,A3,t80,F9.5,t90,F9.6,t100,F9.6,t110,F9.6,t120,F9.6,t130,F9.6,t142,F6.2)
include 'formats.h'
end subroutine Dump_OPT_parameters
!
!
!
!===============================================================
subroutine normalization( basis , zeta , coef , n , k , i , j )
!===============================================================
implicit none
type(STO_basis) , intent(in) :: basis(:)
real*8 , intent(inout) :: zeta(:)
real*8 , intent(inout) :: coef(:)
integer , intent(in) :: n
integer , intent(in) :: k
integer , intent(in) :: i
integer , intent(in) :: j
! local variables ...
real*8 :: zeta_tmp(size(zeta)) , coef_tmp(size(coef))
real*8 :: alpha , prod , soma
zeta_tmp = zeta
coef_tmp = coef
prod = zeta_tmp(1) * zeta_tmp(2)
soma = zeta_tmp(1) + zeta_tmp(2)
alpha = ( four*prod )**n * two*sqrt( prod )
alpha = alpha / soma**(two*n + 1)
coef_tmp(i) = - coef_tmp(j)*alpha + sqrt( 1.d0 + coef_tmp(j)*coef_tmp(j)*(alpha*alpha - 1.d0) )
! if coef > 1 go back to original non-optimized STO parameters ...
If( coef_tmp(i) >= 1.d0 ) then
zeta(1) = basis(k)%zeta(1)
zeta(2) = basis(k)%zeta(2)
coef(1) = basis(k)%coef(1)
coef(2) = basis(k)%coef(2)
else
coef(i) = coef_tmp(i)
end If
end subroutine normalization
!
!
!
!==========================================================================
subroutine SelectTheFittest( cost , Pop , Pop_Size , GeneSize , BestCost )
!==========================================================================
implicit none
real*8 , allocatable , intent(inout) :: cost(:)
real*8 , allocatable , intent(inout) :: Pop(:,:)
integer , intent(in) :: Pop_size
integer , intent(in) :: GeneSize
real*8 , intent(out) :: BestCost
! local variables ...
integer :: i , j
integer , allocatable :: indx(:)
real*8 :: normalization , rn
real*8 , allocatable :: Old_Pop(:,:) , Prob_Selection(:) , fitness(:), wheel(:)
select case ( selection_by )
case( "roullete" )
allocate( fitness(Pop_Size) )
fitness = 1.d0/cost
normalization = sum(fitness)
allocate( Prob_Selection(Pop_Size) )
Prob_Selection = fitness / normalization
allocate( indx (Pop_Size) )
allocate( wheel(0:Pop_size) )
wheel(0:) = d_zero
do i = 1 , Pop_size
wheel(i) = wheel(i-1) + Prob_Selection(i)
end do
do j = 1 , Pop_size
call random_number(rn)
i_loop:do i = 1 , Pop_size
if( rn > wheel(i-1) .AND. rn <= wheel(i) ) &
then
indx(j) = i
exit i_loop
end if
end do i_loop
end do
! just double-checking ...
forall(j=1:Pop_size) indx(j) = merge( Pop_size , j , indx(j) > Pop_size )
print*, minloc(cost) , cost(minloc(cost))
allocate( Old_Pop(Pop_Size,GeneSize) , source = Pop )
Pop( 1:Pop_Size , : ) = Old_pop( indx(1:Pop_Size) , : )
Pop( 1 , : ) = Old_pop( minloc(cost,dim=1) , : )
BestCost = cost(minloc(cost,dim=1))
deallocate( fitness , Prob_Selection , wheel )
case( "ranking" )
normalization = two/((Pop_size+1)*Pop_size)
allocate( Prob_Selection(Pop_Size) )
forall( i=1:Pop_size ) Prob_Selection(i) = i*normalization
allocate( wheel(0:Pop_size) )
allocate( indx (Pop_Size) )
do j = 1 , Pop_size
wheel(0:) = d_zero
call random_number(rn)
do i = 1 , Pop_size
wheel(i) = wheel(i-1) + Prob_Selection(i)
if( rn > wheel(i-1) .AND. rn <= wheel(i) ) then
indx(j) = i
cycle
end if
end do
end do
print*, minloc(cost) , cost(minloc(cost))
allocate( Old_Pop(Pop_Size,GeneSize) , source = Pop )
Pop( 1:Pop_Size , : ) = Old_pop( indx(1:Pop_Size) , : )
Pop( 1 , : ) = Old_pop( minloc(cost,dim=1) , : )
BestCost = cost(minloc(cost,dim=1))
deallocate( Prob_Selection , wheel )
case( "sorting" )
allocate( indx(Pop_Size) )
indx = [ ( i , i=1,Pop_Size ) ]
CALL sort2(cost,indx)
BestCost = cost(1)
allocate( Old_Pop(Pop_Size,GeneSize) , source = Pop )
Pop( 1:Pop_Size , : ) = Old_pop( indx(1:Pop_Size) , : )
case default
CALL warning("execution stopped, check your 'selection_by' options in parameters.f")
stop
end select
deallocate( indx , Old_Pop )
end subroutine SelectTheFittest
!
!
!
!=========================
subroutine sort2(ra,ira)
!=========================
implicit none
real*8 , intent(inout) :: ra(:)
integer , intent(inout) :: ira(:)
! local variables ...
integer :: irra, l, n, ir, i, j
real*8 :: rra
!----------------------------------------------------------
! SORT A(I) , SO THAT THE ELEMENTS IA(I) FOLLOW TOGETHER
!----------------------------------------------------------
n = size(ra)
l = n/2+1
ir = n
10 continue
if(l .gt. 1) then
l = l -1
rra = ra(l)
irra = ira(l)
else
rra = ra(ir)
irra = ira(ir)
ra(ir) = ra(1)
ira(ir) = ira(1)
ir = ir - 1
if(ir .eq. 1) then
ra(1) = rra
ira(1) = irra
return
endif
endif
i = l
j = l + l
20 if(j .le. ir) then
if(j .lt. ir)then
if(ra(j) .lt. ra(j+1)) j = j + 1
endif
if(rra .lt. ra(j)) then
ra(i) = ra(j)
ira(i) = ira(j)
i = j
j = j + j
else
j = ir + 1
endif
goto 20
endif
ra(i) = rra
ira(i) = irra
goto 10
end subroutine sort2
!
!
!
!
!=========================================================
!
!
!
!
!=======================================================================
subroutine Genetic_Algorithm_MM( MM_parms , GA_Selection , directives )
!=======================================================================
implicit none
type(FF_OPT) , intent(inout) :: MM_parms
real*8 , allocatable , intent(out) :: GA_Selection(:,:)
character(*) , intent(in) :: directives
! local variables ...
real*8 , allocatable :: Pop(:,:) , Old_Pop(:,:) , cost(:) , p0(:)
integer , allocatable :: indx(:)
integer :: i , generation , Pop_start , GeneSize
type(LogicalKey) :: key
!-----------------------------------------------
! SETTING-UP MM_parms object
!-----------------------------------------------
CALL SetKeys
key = KeyHolder( size(KeyHolder) )
MM_parms = FF_OPT( key , kernel = "NormalModes" , directives = directives )
GeneSize = MM_parms % N_of_freedom
! creating reference copy of FF vector ...
allocate( p0(GeneSize) , source = MM_parms % p )
!-----------------------------------------------
! SETTING-UP initial populations
!-----------------------------------------------
! Initial Populations ...
allocate( Pop (Pop_Size , GeneSize) )
allocate( Old_Pop (Pop_Size , GeneSize) )
allocate( indx (Pop_Size) )
CALL random_seed
Pop_start = 1
CALL generate_RND_Pop( Pop_start , Pop , distro_type='RNG' )
! the input parameters constitute one of the genes of Pop ...
Pop(1,:) = D_zero
indx = [ ( i , i=1,Pop_Size ) ]
!-----------------------------------------------
! setting normal mode data in FF_OPT_class ...
allocate( cost(Pop_size) )
do generation = 1 , N_generations
do i = Pop_start , Pop_Size
! virtual displacements in the FF parameter space ...
MM_parms % p(:) = p0(:) * (D_one + Pop(i,:))
! evaluate Pop(i,:)'s cost ...
cost(i) = MM_parms % cost()
end do