! E05SBF Example Program Text
! Mark 27.3 Release. NAG Copyright 2021.
Module e05sbfe_mod
! E05SBF Example Program Module:
! Parameters and User-defined Routines
! .. Use Statements ..
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: confun_non_linear, display_option, &
display_result, monmod, &
objfun_schwefel
! .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: f_target_c = &
-731.70709230672696_nag_wp
Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
Real (Kind=nag_wp), Parameter :: f_target_u = &
-837.9657745448674_nag_wp
Real (Kind=nag_wp), Parameter :: x_target = -420.9687463599820_nag_wp
Integer, Parameter :: detail_level = 0, report_freq = 100
Integer, Parameter, Public :: liopts = 100, liuser = 1, &
lopts = 100, lruser = 1, ncon = 3, &
ndim = 2, nout = 6
Real (Kind=nag_wp), Parameter :: c_scale(ncon) = (/2490.0_nag_wp, &
750000.0_nag_wp,0.1_nag_wp/)
Real (Kind=nag_wp), Parameter :: c_target_c(ncon) = 0._nag_wp
Real (Kind=nag_wp), Parameter :: c_target_u(ncon) = (/zero, &
31644.05623568455_nag_wp, &
0.07574889943398055_nag_wp/)
Real (Kind=nag_wp), Parameter :: x_target_c(ndim) = (/ &
-394.1470221120988_nag_wp, &
-433.48214189947606_nag_wp/)
Real (Kind=nag_wp), Parameter :: x_target_u(ndim) = (/x_target, &
x_target/)
Contains
Subroutine objfun_schwefel(mode,ndim,x,objf,vecout,nstate,iuser,ruser)
! Objfun routine for the Schwefel function for E05SBF.
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: objf
Integer, Intent (Inout) :: mode
Integer, Intent (In) :: ndim, nstate
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: ruser(*), vecout(ndim)
Real (Kind=nag_wp), Intent (In) :: x(ndim)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Logical :: evalobjf, evalobjg
! .. Intrinsic Procedures ..
Intrinsic :: abs, cos, sin, sqrt, sum
! .. Executable Statements ..
! Test NSTATE to indicate what stage of computation has been reached.
Select Case (nstate)
Case (2)
! OBJFUN is called for the very first time.
Case (1)
! OBJFUN is called on entry to a NAG local minimizer.
Case (0)
! This will be the normal value of NSTATE.
End Select
! Test MODE to determine whether to calculate OBJF and/or OBJGRD.
evalobjf = .False.
evalobjg = .False.
Select Case (mode)
Case (0,5)
! Only the value of the objective function is needed.
evalobjf = .True.
Case (1,6)
! Only the values of the NDIM gradients are required.
evalobjg = .True.
Case (2,7)
! Both the objective function and the NDIM gradients are required.
evalobjf = .True.
evalobjg = .True.
End Select
If (evalobjf) Then
! Evaluate the objective function.
objf = sum(x(1:ndim)*sin(sqrt(abs(x(1:ndim)))))
End If
If (evalobjg) Then
! Calculate the gradient of the objective function.
vecout = sqrt(abs(x))
vecout = sin(vecout) + 0.5E0_nag_wp*vecout*cos(vecout)
End If
Return
End Subroutine objfun_schwefel
Subroutine confun_non_linear(mode,ncon,ndim,ldcj,needc,x,c,cjac,nstate, &
iuser,ruser)
! Subroutine used to supply constraints
! .. Scalar Arguments ..
Integer, Intent (In) :: ldcj, ncon, ndim, nstate
Integer, Intent (Inout) :: mode
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: c(ncon)
Real (Kind=nag_wp), Intent (Inout) :: cjac(ldcj,ndim), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(ndim)
Integer, Intent (Inout) :: iuser(*)
Integer, Intent (In) :: needc(ncon)
! .. Local Scalars ..
Integer :: k
Logical :: evalc, evalcjac
! .. Intrinsic Procedures ..
Intrinsic :: cos
! .. Executable Statements ..
! Test NSTATE to determine whether the local minimizer is being called
! for the first time from a new start point
If (nstate==1) Then
! Set any constant elements of the Jacobian matrix.
cjac(1,1) = 3.0_nag_wp
cjac(1,2) = -2.0_nag_wp
End If
! MODE: are constraints, derivatives, or both are required?
evalc = mode == 0 .Or. mode == 2
evalcjac = mode == 1 .Or. mode == 2
loop_constraints: Do k = 1, ncon
! Only those for which needc is nonzero need be set.
If (needc(k)<=0) Then
Cycle loop_constraints
End If
If (evalc) Then
! Constraint values are required.
Select Case (k)
Case (1)
c(k) = 3.0_nag_wp*x(1) - 2.0_nag_wp*x(2)
Case (2)
c(k) = x(1)**2 - x(2)**2 + 3.0_nag_wp*x(1)*x(2)
Case (3)
c(k) = cos((x(1)/200.0_nag_wp)**2+(x(2)/100.0_nag_wp))
Case Default
! This constraint is not coded (there are only three).
! Terminate.
mode = -1
Exit loop_constraints
End Select
End If
If (evalcjac) Then
! Constraint derivatives (CJAC) are required.
Select Case (k)
Case (1)
! Constant derivatives set when NSTATE=1 remain throughout
! the local minimization.
Continue
Case (2)
! If the constraint derivatives are known and are readily
! calculated, populate CJAC when required.
cjac(k,1) = 2.0_nag_wp*x(1) + 3.0_nag_wp*x(2)
cjac(k,2) = -2.0_nag_wp*x(2) + 3.0_nag_wp*x(1)
Case Default
! Any elements of CJAC left unaltered will be approximated
! using finite differences when required.
Continue
End Select
End If
End Do loop_constraints
Return
End Subroutine confun_non_linear
Subroutine monmod(ndim,ncon,npar,x,xb,fb,cb,xbest,fbest,cbest,itt,iuser, &
ruser,inform)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: fb
Integer, Intent (Inout) :: inform
Integer, Intent (In) :: ncon, ndim, npar
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: cb(ncon), cbest(ncon,npar), &
fbest(npar), xb(ndim), &
xbest(ndim,npar)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*), x(ndim,npar)
Integer, Intent (In) :: itt(7)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Integer :: indent, j
! .. Intrinsic Procedures ..
Intrinsic :: modulo, repeat
! .. Executable Statements ..
If (detail_level>=2) Then
! Report on the first iteration, and every report_freq iterations.
If (itt(1)==1 .Or. modulo(itt(1),report_freq)==0) Then
Write (nout,*) '* Locations of particles'
indent = 2
Do j = 1, npar
Write (nout,99999) repeat(' ',indent), j
Write (nout,99998) repeat(' ',indent), x(1:ndim,j)
End Do
Write (nout,*) '* Cognitive memory'
Do j = 1, npar
Write (nout,99999) repeat(' ',indent), j
Write (nout,*) repeat(' ',indent*2), '* Best position'
Write (nout,99998) repeat(' ',indent*2), xbest(1:ndim,j)
Write (nout,*) repeat(' ',indent*2), &
'* Function value at best position'
Write (nout,99997) repeat(' ',indent*2), fbest(j)
Write (nout,*) repeat(' ',indent*2), &
'* Best constraint violations'
Write (nout,99998) repeat(' ',indent*2), cbest(1:ncon,j)
End Do
Write (nout,*) '* Current global optimum candidate'
Write (nout,99998) repeat(' ',indent), xb(1:ndim)
Write (nout,*) '* Current global optimum value'
Write (nout,99997) repeat(' ',indent), fb
Write (nout,*) '* Constraint violations of candidate'
Write (nout,99998) repeat(' ',indent), cb(1:ncon)
End If
End If
! If required set INFORM<0 to force exit
inform = 0
Return
99999 Format (1X,A,'* Particle ',I3)
99998 Format (1X,A,(6F13.5))
99997 Format (1X,A,F13.5)
End Subroutine monmod
Subroutine display_option(optstr,optype,ivalue,rvalue,cvalue)
! Subroutine to query optype and print the appropriate option values
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: rvalue
Integer, Intent (In) :: ivalue, optype
Character (*), Intent (In) :: cvalue, optstr
! .. Executable Statements ..
Select Case (optype)
Case (1)
Write (nout,99999) optstr, ivalue
Case (2)
Write (nout,99998) optstr, rvalue
Case (3)
Write (nout,99997) optstr, cvalue
Case (4)
Write (nout,99996) optstr, ivalue, cvalue
Case (5)
Write (nout,99995) optstr, rvalue, cvalue
End Select
Flush (nout)
Return
99999 Format (3X,A39,' : ',I13)
99998 Format (3X,A39,' : ',F13.4)
99997 Format (3X,A39,' : ',16X,A16)
99996 Format (3X,A39,' : ',I13,3X,A16)
99995 Format (3X,A39,' : ',F13.4,3X,A16)
End Subroutine display_option
Subroutine display_result(ndim,ncon,xb,fb,cb,itt,inform)
! Display final results in comparison to known global optimum.
! .. Use Statements ..
Use nag_library, Only: x04cbf
! .. Parameters ..
Integer, Parameter :: indent = 1, ncols = 79
Character (11), Parameter :: clabs(1:6) = (/'x_target_u ', &
'x_target_c ','xb ', &
'c_target_u ','c_target_c ', &
'cb '/)
Character (1), Parameter :: diag = 'D', labcol = 'C', &
labrow = 'I', matrix = 'G'
Character (5), Parameter :: fmtc = 'f12.5', fmtx = 'f12.2'
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: fb
Integer, Intent (In) :: inform, ncon, ndim
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: cb(ncon), xb(ndim)
Integer, Intent (In) :: itt(7)
! .. Local Scalars ..
Integer :: ifail, ldcom
Character (ncols) :: titlec, titlex
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: ccom(:,:), xcom(:,:)
! .. Executable Statements ..
! Display final counters.
Write (nout,*) ' Algorithm Statistics'
Write (nout,*) ' --------------------'
Write (nout,99994) 'Total complete iterations ', itt(1)
Write (nout,99994) 'Complete iterations since improvement ', itt(2)
Write (nout,99994) 'Total particles converged to xb ', itt(3)
Write (nout,99994) 'Total improvements to global optimum ', itt(4)
Write (nout,99994) 'Total function evaluations ', itt(5)
Write (nout,99994) 'Total particles re-initialized ', itt(6)
Write (nout,99994) 'Total constraints violated ', itt(7)
! Display why finalization occurred.
Write (nout,*)
Select Case (inform)
Case (1)
Write (nout,99999) 'Target value achieved'
Case (2)
Write (nout,99999) 'Minimum swarm standard deviation obtained'
Case (3)
Write (nout,99999) 'Sufficient particles converged'
Case (4)
Write (nout,99999) 'No improvement in preset iteration limit'
Case (5)
Write (nout,99999) 'Maximum complete iterations attained'
Case (6)
Write (nout,99999) 'Maximum function evaluations exceeded'
Case (7)
Write (nout,99999) 'Constrained point located'
Case (:-1)
Write (nout,99998) inform
Go To 100
End Select
! Display final objective value and location.
Write (nout,*)
Write (nout,99997) f_target_u
Write (nout,99996) f_target_c
Write (nout,99995) fb
ldcom = ndim
Allocate (xcom(ldcom,3))
xcom(1:ndim,1) = x_target_u(1:ndim)
xcom(1:ndim,2) = x_target_c(1:ndim)
xcom(1:ndim,3) = xb(1:ndim)
Write (nout,*)
Flush (nout)
titlex = 'Comparison between known and achieved optima.'
ifail = 0
Call x04cbf(matrix,diag,ndim,3,xcom,ldcom,fmtx,titlex,labrow,clabs, &
labcol,clabs,ncols,indent,ifail)
Deallocate (xcom)
If (ncon>0) Then
ldcom = ncon
Allocate (ccom(ldcom,3))
ccom(1:ncon,1) = c_target_u(1:ncon)/c_scale(1:ncon)
ccom(1:ncon,2) = c_target_c(1:ncon)/c_scale(1:ncon)
ccom(1:ncon,3) = cb(1:ncon)/c_scale(1:ncon)
Write (nout,*)
Flush (nout)
titlec = 'Comparison between scaled constraint violations.'
ifail = 0
Call x04cbf(matrix,diag,ncon,3,ccom,ldcom,fmtc,titlec,labrow,clabs, &
labcol,clabs(4:6),ncols,indent,ifail)
Deallocate (ccom)
End If
100 Continue
Write (nout,*)
Return
99999 Format (2X,'Solution Status : ',A38)
99998 Format (' User termination case : ',I13)
99997 Format (' Known unconstrained objective minimum : ',F13.3)
99996 Format (' Best Known constrained objective minimum : ',F13.3)
99995 Format (' Achieved objective value : ',F13.3)
99994 Format (2X,A40,' :',I13)
End Subroutine display_result
End Module e05sbfe_mod
Program e05sbfe
! E05SBF Example Main Program
! This example program demonstrates how to use E05SBF in standard
! execution, and with E04UCF as a coupled local minimizer.
! The non-default option 'REPEATABILITY ON' is used here, giving
! repeatable results.
! .. Use Statements ..
Use e05sbfe_mod, Only: confun_non_linear, display_option, &
display_result, f_target_c, liopts, liuser, &
lopts, lruser, monmod, ncon, ndim, nout, &
objfun_schwefel, zero
Use nag_library, Only: e05sbf, e05zkf, e05zlf, nag_wp, x06acf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: fb, rvalue
Integer :: ifail, inform, ivalue, npar, optype
Character (16) :: cvalue
Character (80) :: optstr
! .. Local Arrays ..
Real (Kind=nag_wp) :: bl(ndim+ncon), bu(ndim+ncon), &
cb(ncon), opts(lopts), &
ruser(lruser), xb(ndim)
Real (Kind=nag_wp), Allocatable :: cbest(:,:), fbest(:,:), xbest(:,:)
Integer :: iopts(liopts), itt(7), iuser(liuser)
! .. Intrinsic Procedures ..
Intrinsic :: max
! .. Executable Statements ..
! Print advisory information.
Write (nout,*) 'E05SBF Example Program Results'
Write (nout,*)
Write (nout,*) 'Minimization of the Schwefel function.'
Write (nout,*) 'Subject to one linear and two nonlinear constraints.'
Write (nout,*)
! Determine the number of particles to be used in the simulation.
npar = 10*max(x06acf(),ndim)
Allocate (xbest(ndim,npar),cbest(ncon,npar),fbest(ndim,npar))
xbest = zero
fbest = zero
cbest = zero
! Set problem specific values.
! Set box bounds.
bl(1:ndim) = -500.0_nag_wp
bu(1:ndim) = 500.0_nag_wp
! Set constraint bounds.
bl((ndim+1):(ndim+ncon)) = (/-1.0E6_nag_wp,-1.0_nag_wp,-0.9_nag_wp/)
bu((ndim+1):(ndim+ncon)) = (/10.0_nag_wp,5.0E5_nag_wp,0.9_nag_wp/)
! Initialize the option arrays for E05SBF.
ifail = 0
Call e05zkf('Initialize = E05SBF',iopts,liopts,opts,lopts,ifail)
! Set the option SMP Callback Thread Safe to indicate the callback functions
! are indeed threadsafe. This must be done if using multiple threads.
ifail = 0
Call e05zkf('SMP Callback Thread Safe = Yes',iopts,liopts,opts,lopts, &
ifail)
! Query some default option values.
Write (nout,*) ' Default Option Queries:'
Write (nout,*)
ivalue = 0
rvalue = 0.0_nag_wp
ifail = 0
optstr = 'Constraint Norm'
Call e05zlf(optstr,ivalue,rvalue,cvalue,optype,iopts,opts,ifail)
Call display_option(optstr,optype,ivalue,rvalue,cvalue)
ifail = 0
optstr = 'Maximum Iterations Completed'
Call e05zlf(optstr,ivalue,rvalue,cvalue,optype,iopts,opts,ifail)
Call display_option(optstr,optype,ivalue,rvalue,cvalue)
ifail = 0
optstr = 'Distance Tolerance'
Call e05zlf(optstr,ivalue,rvalue,cvalue,optype,iopts,opts,ifail)
Call display_option(optstr,optype,ivalue,rvalue,cvalue)
! ------------------------------------------------------------------
Write (nout,*)
Write (nout,*) '1. Solution without using coupled local minimizer'
Write (nout,*)
! Set various options to non-default values if required.
ifail = 0
Write (optstr,99999) 'Distance Tolerance', rvalue*0.1_nag_wp
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
ifail = 0
Write (optstr,99999) 'Constraint Tolerance', 1.0E-4_nag_wp
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
ifail = 0
Call e05zkf('Constraint Norm = Euclidean',iopts,liopts,opts,lopts,ifail)
ifail = 0
Call e05zkf('Repeatability = On',iopts,liopts,opts,lopts,ifail)
ifail = 0
Write (optstr,99999) 'Target Objective Value', f_target_c
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
ifail = 0
Write (optstr,99999) 'Target Objective Tolerance', 1.0E-4_nag_wp
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
! Call E05SBF to search for the global optimum.
! Non-zero IFAIL expected on exit here, so use IFAIL=1 (quiet) on entry.
ifail = 1
Call e05sbf(ndim,ncon,npar,xb,fb,cb,bl,bu,xbest,fbest,cbest, &
objfun_schwefel,confun_non_linear,monmod,iopts,opts,iuser,ruser,itt, &
inform,ifail)
! It is essential to test IFAIL on exit.
Select Case (ifail)
Case (0,1)
! No errors, best found optimum at xb returned in fb.
Call display_result(ndim,ncon,xb,fb,cb,itt,inform)
Case (3)
! Exit flag set in OBJFUN, CONFUN or MONMOD and returned in INFORM.
Call display_result(ndim,ncon,xb,fb,cb,itt,inform)
Case Default
! An error was detected. Print message since IFAIL=1 on entry.
Write (nout,99998) '** E05SBF returned with an error, IFAIL = ', ifail
Continue
End Select
! ------------------------------------------------------------------
Write (nout,*) '2. Solution using coupled local minimizer E04UCF'
Write (nout,*)
! Set the local minimizer to be E04UCF and set corresponding options.
ifail = 0
Call e05zkf('Local Minimizer = E04UCF',iopts,liopts,opts,lopts,ifail)
ifail = 0
Call e05zkf('Local Interior Major Iterations = 15',iopts,liopts,opts, &
lopts,ifail)
ifail = 0
Call e05zkf('Local Interior Minor Iterations = 5',iopts,liopts,opts, &
lopts,ifail)
ifail = 0
Call e05zkf('Local Exterior Major Iterations = 50',iopts,liopts,opts, &
lopts,ifail)
ifail = 0
Call e05zkf('Local Exterior Minor Iterations = 15',iopts,liopts,opts, &
lopts,ifail)
! Query the option Distance Tolerance
ifail = 0
optstr = 'Distance Tolerance'
Call e05zlf(optstr,ivalue,rvalue,cvalue,optype,iopts,opts,ifail)
! Adjust Distance Tolerance dependent upon its current value
Write (optstr,99999) 'Distance Tolerance', rvalue*10.0_nag_wp
ifail = 0
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
ifail = 0
Write (optstr,99999) 'Local Interior Tolerance', rvalue
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
ifail = 0
Write (optstr,99999) 'Local Exterior Tolerance', rvalue*1.0E-4_nag_wp
Call e05zkf(optstr,iopts,liopts,opts,lopts,ifail)
! Call E05SBF to search for the global optimum.
ifail = 1
Call e05sbf(ndim,ncon,npar,xb,fb,cb,bl,bu,xbest,fbest,cbest, &
objfun_schwefel,confun_non_linear,monmod,iopts,opts,iuser,ruser,itt, &
inform,ifail)
! It is essential to test IFAIL on exit.
Select Case (ifail)
Case (0,1)
! E05SBF encountered no errors during operation,
! and will have returned the best found optimum.
Call display_result(ndim,ncon,xb,fb,cb,itt,inform)
Case (3)
! Exit flag set in OBJFUN, CONFUN or MONMOD and returned in INFORM.
Call display_result(ndim,ncon,xb,fb,cb,itt,inform)
Case Default
! An error was detected. Print message since IFAIL=1 on entry.
Write (nout,99998) '** E05SBF returned with an error, IFAIL = ', ifail
Continue
End Select
99999 Format (A,' = ',E32.16)
99998 Format (1X,A,I6)
End Program e05sbfe