mo_sce Module Reference

Shuffled Complex Evolution optimization algorithm. More...

Functions/Subroutines
real(dp) function, dimension(size(pini, 1)), public	sce (eval, functn, pini, prange, mymaxn, mymaxit, mykstop, mypcento, mypeps, myseed, myngs, mynpg, mynps, mynspl, mymings, myiniflg, myprint, mymask, myalpha, mybeta, tmp_file, popul_file, popul_file_append, parallel, restart, restart_file, bestf, neval, history)
	Shuffled Complex Evolution (SCE) algorithm for global optimization.
subroutine	parstt (x, bound, peps, mask, xnstd, gnrng, ipcnvg)
subroutine	comp (ngs2, npg, a, af, b, bf)
subroutine	sort_matrix (rb, ra)
subroutine	chkcst (x, bl, bu, mask, ibound)
subroutine	getpnt (idist, bl, bu, std, xi, mask, save_state, x)
subroutine	cce (s, sf, bl, bu, maskpara, xnstd, icall, maxn, maxit, save_state_gauss, functn, eval, alpha, beta, history, idot ifdef mpi

Detailed Description

Shuffled Complex Evolution optimization algorithm.

Optimization algorithm using Shuffled Complex Evolution strategy. Original version 2.1 of Qingyun Duan (1992) rewritten in Fortran 90.

Authors

Juliane Mai

Date

Feb 2013

Copyright

Copyright 2005-2024, the CHS Developers, Sabine Attinger: All rights reserved. FORCES is released under the LGPLv3+ license

The UFZ (CHS) FORCES code is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the free Software Foundation either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You received a copy of the GNU Lesser General Public License along with the UFZ CHS FORCES code. It can be found in the files COPYING and COPYING.LESSER provided with this software. The complete GNU license text can also be found at http://www.gnu.org/licenses/.

Function/Subroutine Documentation

cce()

subroutine mo_sce::cce ( real(dp), dimension(:, :), intent(inout)  s, real(dp), dimension(:), intent(inout)  sf, real(dp), dimension(:), intent(in)  bl, real(dp), dimension(:), intent(in)  bu, logical, dimension(:), intent(in)  maskpara, real(dp), dimension(:), intent(in)  xnstd, integer(i8), intent(inout)  icall, integer(i8), intent(in)  maxn, logical, intent(in)  maxit, integer(i8), dimension(n_save_state), intent(inout)  save_state_gauss, procedure(objective_interface), intent(in), pointer  functn, procedure(eval_interface), intent(in), pointer  eval, real(dp), intent(in)  alpha, real(dp), intent(in)  beta, real(dp), dimension(maxn), intent(inout)  history, logical, intent(in)  idot,   ifdef,   mpi  )

private

Definition at line 1830 of file mo_sce.F90.

chkcst()

subroutine mo_sce::chkcst ( real(dp), dimension(:), intent(in)  x, real(dp), dimension(:), intent(in)  bl, real(dp), dimension(:), intent(in)  bu, logical, dimension(:), intent(in)  mask, integer(i4), intent(out)  ibound  )

private

Definition at line 1735 of file mo_sce.F90.

comp()

subroutine mo_sce::comp ( integer(i4), intent(in)  ngs2, integer(i4), intent(in)  npg, real(dp), dimension(:, :), intent(inout)  a, real(dp), dimension(:), intent(inout)  af, real(dp), dimension(size(a, 1), size(a, 2)), intent(out)  b, real(dp), dimension(size(af)), intent(out)  bf  )

private

Definition at line 1647 of file mo_sce.F90.

getpnt()

subroutine mo_sce::getpnt ( integer(i4), intent(in)  idist, real(dp), dimension(:), intent(in)  bl, real(dp), dimension(:), intent(in)  bu, real(dp), dimension(:), intent(in)  std, real(dp), dimension(:), intent(in)  xi, logical, dimension(:), intent(in)  mask, integer(i8), dimension(n_save_state), intent(inout)  save_state, real(dp), dimension(size(xi, 1)), intent(out)  x  )

private

Definition at line 1776 of file mo_sce.F90.

parstt()

subroutine mo_sce::parstt ( real(dp), dimension(:, :), intent(in)  x, real(dp), dimension(:), intent(in)  bound, real(dp), intent(in)  peps, logical, dimension(:), intent(in)  mask, real(dp), dimension(size(bound, 1)), intent(out)  xnstd, real(dp), intent(out)  gnrng, integer(i4), intent(out)  ipcnvg  )

private

Definition at line 1579 of file mo_sce.F90.

sce()

real(dp) function, dimension(size(pini, 1)), public mo_sce::sce	(	procedure(eval_interface), intent(in), pointer	eval,
		procedure(objective_interface), intent(in), pointer	functn,
		real(dp), dimension(:), intent(in)	pini,
		real(dp), dimension(:, :), intent(in)	prange,
		integer(i8), intent(in), optional	mymaxn,
		logical, intent(in), optional	mymaxit,
		integer(i4), intent(in), optional	mykstop,
		real(dp), intent(in), optional	mypcento,
		real(dp), intent(in), optional	mypeps,
		integer(i8), intent(in), optional	myseed,
		integer(i4), intent(in), optional	myngs,
		integer(i4), intent(in), optional	mynpg,
		integer(i4), intent(in), optional	mynps,
		integer(i4), intent(in), optional	mynspl,
		integer(i4), intent(in), optional	mymings,
		integer(i4), intent(in), optional	myiniflg,
		integer(i4), intent(in), optional	myprint,
		logical, dimension(size(pini, 1)), intent(in), optional	mymask,
		real(dp), intent(in), optional	myalpha,
		real(dp), intent(in), optional	mybeta,
		character(len = *), intent(in), optional	tmp_file,
		character(len = *), intent(in), optional	popul_file,
		logical, intent(in), optional	popul_file_append,
		logical, intent(in), optional	parallel,
		logical, intent(in), optional	restart,
		character(len = *), intent(in), optional	restart_file,
		real(dp), intent(out), optional	bestf,
		integer(i8), intent(out), optional	neval,
		real(dp), dimension(:), intent(out), optional, allocatable	history
	)

Shuffled Complex Evolution (SCE) algorithm for global optimization.

Shuffled Complex Evolution method for global optimization – version 2.1

by Qingyun Duan
Department of Hydrology & Water Resources
University of Arizona, Tucson, AZ 85721
(602) 621-9360, email: duan@.nosp@m.hwr..nosp@m.arizo.nosp@m.na.e.nosp@m.du

Written by Qingyun Duan, Oct 1990.
Revised by Qingyun Duan, Aug 1991.
Revised by Qingyun Duan, Apr 1992.

Re-written by Juliane Mai, Feb 2013.

Statement by Qingyun Duan:

This general purpose global optimization program is developed at the Department of Hydrology & Water Resources of the University of Arizona. Further information regarding the SCE-UA method can be obtained from Dr. Q. Duan, Dr. S. Sorooshian or Dr. V.K. Gupta at the address and phone number listed above. We request all users of this program make proper reference to the paper entitled 'Effective and Efficient Global Optimization for Conceptual Rainfall-runoff Models' by Duan, Q., S. Sorooshian, and V.K. Gupta, Water Resources Research, Vol 28(4), pp.1015-1031, 1992.

The function to be minimized is the first argument of DDS and must be defined as

function functn(p)
     use mo_kind, only: dp
     implicit none
     real(dp), dimension(:), intent(in) :: p
     real(dp) :: functn
end function functn

Example

use mo_opt_functions, only: griewank
 
prange(:,1) = (/ -600.0, -600.0, -600.0, -600.0, -600.0, -600.0, -600.0, -600.0, -600.0, -600.0 /)
prange(:,2) = (/ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 /)
pini        = (/ -.226265e+01, -.130187e+01, -.151219e+01, 0.133983e+00, 0.988159e+00, &
                   -.495074e+01, -.126574e+02, 0.572684e+00, 0.303864e+01, 0.343031e+01 /)
 
opt = sce(griewank, pini, prange)

-> see also example in test directory

Literature

1. Duan, Q., S. Sorooshian, and V.K. Gupta - Effective and Efficient Global Optimization for Conceptual Rainfall-runoff Models Water Resources Research, Vol 28(4), pp.1015-1031, 1992.

Parameters

[in]	real(dp) :: functn(p)	Function on which to search the optimum
[in]	real(dp) :: pini(:)	inital value of decision variables
[in]	real(dp) :: prange(size(pini),2)	Min/max range of decision variables
[in]	integer(i8), optional :: mymaxn	max no. of trials allowed before optimization is terminated DEFAULT: 1000_i8
[in]	logical, optional :: mymaxit	maximization (.true.) or minimization (.false.) of function DEFAULT: false
[in]	integer(i4), optional :: mykstop	number of shuffling loops in which the criterion value must change by given percentage before optimiz. is terminated DEFAULT: 10_i4
[in]	real(dp), optional :: mypcento	percentage by which the criterion value must change in given number of shuffling loops DEFAULT: 0.0001_dp
[in]	real(dp), optional :: mypeps	optimization is terminated if volume of complex has converged to given percentage of feasible space DEFAULT: 0.001_dp
[in]	integer(i8), optional :: myseed	initial random seed DEFAULT: get_timeseed
[in]	integer(i4), optional :: myngs	number of complexes in the initial population DEFAULT: 2_i4
[in]	integer(i4), optional :: mynpg	number of points in each complex DEFAULT: 2*n+1
[in]	integer(i4), optional :: mynps	number of points in a sub-complex DEFAULT: n+1
[in]	integer(i4), optional :: mynspl	number of evolution steps allowed for each complex before complex shuffling DEFAULT: 2*n+1
[in]	integer(i4), optional :: mymings	minimum number of complexes required, if the number of complexes is allowed to reduce as the optimization proceeds DEFAULT: ngs = number of complexes in initial population
[in]	integer(i4), optional :: myiniflg	flag on whether to include the initial point in population 0, not included 1, included (DEFAULT)
[in]	integer(i4), optional :: myprint	flag for controlling print-out after each shuffling loop 0, print information on the best point of the population 1, print information on every point of the population 2, no printing (DEFAULT) 3, same as 0 but print progress '.' on every function call 4, same as 1 but print progress '.' on every function call
[in]	logical, optional :: mymask(size(pini))	parameter included in optimization (true) or discarded (false) DEFAULT: .true.
[in]	real(dp), optional :: myalpha	parameter for reflection of points in complex DEFAULT: 0.8_dp
[in]	real(dp), optional :: mybeta	parameter for contraction of points in complex DEFAULT: 0.45_dp
[in]	character(len=*), optional :: tmp_file	if given: write results after each evolution loop to temporal output file of that name # of headlines: 7 format: '# nloop icall ngs1 bestf worstf ... ... gnrng (bestx(j),j=1,nn)'
[in]	character(len=*), optional :: popul_file	if given: write whole population to file of that name # of headlines: 1 format: #_evolution_loop, xf(i), (x(i,j),j=1,nn) total number of lines written <= neval <= mymaxn
[in]	logical, optional :: popul_file_append	if true, append to existing population file (default: false)
[in]	logical, optional :: parallel	sce runs in parallel (true) or not (false) parallel sce should only be used if model/ objective is not parallel DEFAULT: .false.
[in]	logical, optional :: restart	if .true.: restart former sce run from restart_file
[in]	character(len=*), optional :: restart_file	file name for read/write of restart file (default: mo_sce.restart)
[out]	real(dp), optional :: bestf	the best value of the function.
[out]	integer(i8), optional :: neval	number of function evaluations needed.
[out]	real(dp), optional, allocatable :: history(:)	the history of best function values, history(neval)=bestf

Returns

real(dp) :: bestx(size(pini)) — The parameters of the point which is estimated to minimize/maximize the function.

Note

Maximal number of parameters is 1000.
SCE is OpenMP enabled on the loop over the complexes.
OMP_NUM_THREADS > 1 does not give reproducible results even when seeded!

Author

Juliane Mai, Matthias Cuntz

Date

Feb 2013

• first version

Jul 2013

• OpenMP
• NaN and Inf in objective function

Oct 2013

• added peps as optional argument
• allow for masked parameters
• write population to file --> popul_file
• write intermediate results to file --> tmp_file
• flag parallel introduced

Nov 2013

• progress dots (MC)
• use iso_fortran_env
• treat functn=NaN as worse function value in cce

May 2014

• sort -> orderpack (MC)
• popul_file_append (MC)
• sort with NaNs (MC)

Feb 2015

• restart (MC, JM)

Mar 2015

• use is_finite and special_value from mo_utils (MC)

Apr 2015

• handling of array-like variables in restart-namelists (JM)

Definition at line 212 of file mo_sce.F90.

References mo_string_utils::compress(), mo_kind::dp, mo_kind::i4, mo_kind::i8, and mo_xor4096::n_save_state.

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sort_matrix()

subroutine mo_sce::sort_matrix ( real(dp), dimension(:, :), intent(inout)  rb, real(dp), dimension(:), intent(inout)  ra  )

private

Definition at line 1703 of file mo_sce.F90.