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// Copyright (C) 2004, 2006 Michael Creel <michael.creel@uab.es>
//
// This program 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 should have received a copy of the GNU General Public License along with
// this program; if not, see <http://www.gnu.org/licenses/>.
// References:
//
// The code follows the article
// Goffe, William L. (1996) "SIMANN: A Global Optimization Algorithm
// using Simulated Annealing " Studies in Nonlinear Dynamics & Econometrics
// Oct96, Vol. 1 Issue 3.
//
// The code uses the same names for control variables,
// for the most part. A notable difference is that the initial
// temperature is found automatically to ensure that the active
// bounds when the temperature begins to reduce cover the entire
// parameter space (defined as a n-dimensional
// rectangle that is the Cartesian product of the
// (lb_i, ub_i), i = 1,2,..n
//
// Also of note:
// Corana et. al., (1987) "Minimizing Multimodal Functions of Continuous
// Variables with the "Simulated Annealing" Algorithm",
// ACM Transactions on Mathematical Software, V. 13, N. 3.
//
// Goffe, et. al. (1994) "Global Optimization of Statistical Functions
// with Simulated Annealing", Journal of Econometrics,
// V. 60, N. 1/2.
#include <oct.h>
#include <octave/parse.h>
#include <octave/Cell.h>
#include <octave/lo-mappers.h>
#include <octave/oct-rand.h>
#include <float.h>
#include "error-helpers.h"
// define argument checks
static bool any_bad_argument(const octave_value_list& args)
{
// objective function name is a string?
if (!args(0).is_string())
{
_p_error("samin: first argument must be string holding objective function name");
return true;
}
// are function arguments contained in a cell?
if (!args(1).OV_ISCELL ())
{
_p_error("samin: second argument must cell array of function arguments");
return true;
}
// is control a cell?
Cell control;
bool err;
SET_ERR (control =args(2).cell_value(), err);
if (err)
{
_p_error("samin: third argument must cell array of algorithm controls");
return true;
}
// does control have proper number of elements?
if (!(control.numel () == 11))
{
_p_error("samin: third argument must be a cell array with 11 elements");
return true;
}
// now check type of each element of control
if (!(control(0).is_real_matrix()) && !(control(0).is_real_scalar()))
{
_p_error("samin: 1st element of controls must be LB: a vector of lower bounds");
return true;
}
if ((control(0).is_real_matrix()) && (control(0).columns() != 1))
{
_p_error("samin: 1st element of controls must be LB: a vector of lower bounds");
return true;
}
if (!(control(1).is_real_matrix()) && !(control(1).is_real_scalar()))
{
_p_error("samin: 1st element of controls must be UB: a vector of lower bounds");
return true;
}
if ((control(1).is_real_matrix()) && (control(1).columns() != 1))
{
_p_error("samin: 2nd element of controls must be UB: a vector of lower bounds");
return true;
}
int tmp;
SET_ERR (tmp = control(2).int_value(), err);
if (err || tmp < 1)
{
_p_error("samin: 3rd element of controls must be NT: positive integer\n\
loops per temperature reduction");
return true;
}
SET_ERR (tmp = control(3).int_value(), err);
if (err || tmp < 1)
{
_p_error("samin: 4th element of controls must be NS: positive integer\n\
loops per stepsize adjustment");
return true;
}
double tmp2;
SET_ERR (tmp2 = control(4).double_value(), err);
if (err || tmp < 0)
{
_p_error("samin: 5th element of controls must be RT:\n\
temperature reduction factor, RT > 0");
return true;
}
SET_ERR (tmp2 = control(5).double_value(), err);
if (err || tmp < 0)
{
_p_error("samin: 6th element of controls must be integer MAXEVALS > 0 ");
return true;
}
SET_ERR (tmp = control(6).int_value(), err);
if (err || tmp < 0)
{
_p_error("samin: 7th element of controls must be NEPS: positive integer\n\
number of final obj. values that must be within EPS of eachother ");
return true;
}
SET_ERR (tmp2 = control(7).double_value(), err);
if (err || tmp2 < 0)
{
_p_error("samin: 8th element of controls must must be FUNCTOL (> 0)\n\
used to compare the last NEPS obj values for convergence test");
return true;
}
SET_ERR (tmp2 = control(8).double_value(), err);
if (err || tmp2 < 0)
{
_p_error("samin: 9th element of controls must must be PARAMTOL (> 0)\n\
used to compare the last NEPS obj values for convergence test");
return true;
}
SET_ERR (tmp = control(9).int_value(), err);
if (err || tmp < 0 || tmp > 2)
{
_p_error("samin: 9th element of controls must be VERBOSITY (0, 1, or 2)");
return true;
}
SET_ERR (tmp = control(10).int_value(), err);
if (err || tmp < 0)
{
_p_error("samin: 10th element of controls must be MINARG (integer)\n\
position of argument to minimize wrt");
return true;
}
// make sure that minarg points to an existing element
if ((tmp > args(1).length ()) || (tmp < 1))
{
_p_error("bfgsmin: 4th argument must be a positive integer that indicates \n\
which of the elements of the second argument is the one minimization is over");
return true;
}
return false;
}
//-------------- The annealing algorithm --------------
DEFUN_DLD(samin, args, , "samin: simulated annealing minimization of a function. See samin_example.m\n\
\n\
samin will be removed from a future version of the optim package.\n\
Equivalent functionality is now in the samin backend of nonlin_min.\n\
\n\
usage: [x, obj, convergence, details] = samin(\"f\", {args}, {control})\n\
\n\
Arguments:\n\
* \"f\": function name (string)\n\
* {args}: a cell array that holds all arguments of the function,\n\
* {control}: a cell array with 11 elements\n\
* LB - vector of lower bounds\n\
* UB - vector of upper bounds\n\
* nt - integer: # of iterations between temperature reductions\n\
* ns - integer: # of iterations between bounds adjustments\n\
* rt - (0 < rt <1): temperature reduction factor\n\
* maxevals - integer: limit on function evaluations\n\
* neps - integer: number of values final result is compared to\n\
* functol - (> 0): the required tolerance level for function value\n\
comparisons\n\
* paramtol - (> 0): the required tolerance level for parameters\n\
* verbosity - scalar: 0, 1, or 2.\n\
* 0 = no screen output\n\
* 1 = only final results to screen\n\
* 2 = summary every temperature change\n\
* minarg - integer: which of function args is minimization over?\n\
\n\
Returns:\n\
* x: the minimizer\n\
* obj: the value of f() at x\n\
* convergence:\n\
0 if no convergence within maxevals function evaluations\n\
1 if normal convergence to a point interior to the parameter space\n\
2 if convergence to point very near bounds of parameter space\n\
(suggest re-running with looser bounds)\n\
* details: a px3 matrix. p is the number of times improvements were found.\n\
The columns record information at the time an improvement was found\n\
* first: cumulative number of function evaluations\n\
* second: temperature\n\
* third: function value\n\
\n\
Example: see samin_example\n\
")
{
static bool warned = false;
if (! warned)
{
warned = true;
warning_with_id ("Octave:deprecated-function",
"samin will be removed from a future version of the optim package, equivalent functionality is now in the samin backend of nonlin_min");
}
int nargin = args.length();
if (!(nargin == 3))
{
error("samin: you must supply 3 arguments");
return octave_value_list();
}
// check the arguments
if (any_bad_argument (args))
{
error ("error in samin");
return octave_value_list();
}
std::string obj_fn (args(0).string_value());
Cell f_args_cell = args(1).cell_value (); // args to obj fn come in as a cell to allow arbitrary number
Cell control (args(2).cell_value());
octave_value_list f_args;
octave_value_list f_return; // holder for feval returns
int m, i, j, k, h, n, nacc, func_evals;
int nup, nrej, nnew, ndown, lnobds;
int converge, test, coverage_ok;
// user provided controls
const ColumnVector lb (control(0).column_vector_value());
const ColumnVector ub (control(1).column_vector_value());
const int nt (control(2).int_value());
const int ns (control(3).int_value());
const double rt (control(4).double_value());
const int maxevals (control(5).int_value());
const int neps (control(6).int_value());
const double functol (control(7).double_value());
const double paramtol (control(8).double_value());
const int verbosity (control(9).int_value());
const int minarg (control(10).int_value());
// type checking for minimization parameter done here, since we don't know minarg
// until now
if (!(f_args_cell(minarg - 1).is_real_matrix() || (f_args_cell(minarg - 1).is_real_scalar())))
{
error("samin: minimization must be with respect to a column vector");
return octave_value_list();
}
if ((f_args_cell(minarg - 1).is_real_matrix()) && (f_args_cell(minarg - 1).columns() != 1))
{
error("samin: minimization must be with respect to a column vector");
return octave_value_list();
}
double f, fp, p, fopt, rand_draw, ratio, t;
Matrix details(1,3); // record function evaluations, temperatures and function values
RowVector info(3);
// copy cell contents over to octave_value_list to use feval()
k = f_args_cell.numel ();
f_args(k); // resize only once
for (i = 0; i<k; i++) f_args(i) = f_args_cell(i);
ColumnVector x = f_args(minarg - 1).column_vector_value();
ColumnVector bounds = ub - lb;
n = x.rows();
ColumnVector xopt = x;
ColumnVector xp(n);
ColumnVector nacp(n);
// Set initial values
nacc = 0; // total accepted trials
t = 1000.0; // temperature - will initially rise or fall to cover parameter space. Then it will fall
converge = 0; // convergence indicator 0 (failure), 1 (normal success), or 2 (convergence but near bounds)
coverage_ok = 0; // has parameter space been covered? When turns to 1, temperature starts to fall
// most recent values, to compare to when checking convergend
ColumnVector fstar(neps,1);
fstar.fill(DBL_MAX);
octave_rand::distribution("uniform"); // we'll be using draws from U(0,1)
// check for out-of-bounds starting values
for(i = 0; i < n; i++)
{
if(( x(i) > ub(i)) || (x(i) < lb(i)))
{
error("samin: initial parameter %d out of bounds", i+1);
return octave_value_list();
}
}
// Initial obj_value
f_return = OCTAVE__FEVAL (obj_fn, f_args);
f = f_return(0).double_value();
fopt = f; // give it something to compare to
func_evals = 0; // total function evaluations (limited by maxeval)
details(0,0) = func_evals;
details(0,1) = t;
details(0,2) = fopt;
// main loop, first increase temperature until parameter space covered, then reduce until convergence
while(converge==0)
{
// statistics to report at each temp change, set back to zero
nup = 0;
nrej = 0;
nnew = 0;
ndown = 0;
lnobds = 0;
// repeat nt times then adjust temperature
for(m = 0;m < nt;m++)
{
// repeat ns times, then adjust bounds
for(j = 0;j < ns;j++)
{
// generate new point by taking last and adding a random value
// to each of elements, in turn
for(h = 0;h < n;h++)
{
// new Sept 2011, if bounds are same, skip the search for that vbl. Allows restrictions without complicated programming
if (lb(h) != ub(h))
{
xp = x;
rand_draw = octave_rand::scalar();
xp(h) = x(h) + (2.0 * rand_draw - 1.0) * bounds(h);
if ((xp(h) < lb(h)) || (xp(h) > ub(h)))
{
rand_draw = octave_rand::scalar(); // change 07-Nov-2007: avoid correlation with hitting bounds
xp(h) = lb(h) + (ub(h) - lb(h)) * rand_draw;
lnobds = lnobds + 1;
}
// Evaluate function at new point
f_args(minarg - 1) = xp;
f_return = OCTAVE__FEVAL (obj_fn, f_args);
fp = f_return(0).double_value();
func_evals = func_evals + 1;
// Accept the new point if the function value decreases
if(fp <= f)
{
x = xp;
f = fp;
nacc = nacc + 1; // total number of acceptances
nacp(h) = nacp(h) + 1; // acceptances for this parameter
nup = nup + 1;
// If lower than any other point, record as new optimum
if(fp < fopt)
{
xopt = xp;
fopt = fp;
nnew = nnew + 1;
info(0) = func_evals;
info(1) = t;
info(2) = fp;
details = details.stack(info);
}
}
// If the point is higher, use the Metropolis criteria to decide on
// acceptance or rejection.
else
{
p = exp(-(fp - f) / t);
rand_draw = octave_rand::scalar();
if(rand_draw < p)
{
x = xp;
f = fp;
nacc = nacc + 1;
nacp(h) = nacp(h) + 1;
ndown = ndown + 1;
}
else nrej = nrej + 1;
}
}
// If maxevals exceeded, terminate the algorithm
if (func_evals >= maxevals)
{
if (verbosity >= 1)
{
printf("\n================================================\n");
printf("SAMIN results\n");
printf("NO CONVERGENCE: MAXEVALS exceeded\n");
printf("================================================\n");
printf("Convergence tolerances: Func. tol. %e Param. tol. %e\n", functol, paramtol);
printf("Obj. fn. value %f\n\n", fopt);
printf(" parameter search width\n");
for(i = 0; i < n; i++) printf("%20f%20f\n", xopt(i), bounds(i));
}
f_return(3) = details;
f_return(2) = 0;
f_return(1) = fopt;
f_return(0) = xopt;
return octave_value_list(f_return);
}
}
}
// Adjust bounds so that approximately half of all evaluations are accepted
test = 0;
for(i = 0;i < n;i++)
{
if (lb(i) != ub(i))
{
ratio = nacp(i) / ns;
if(ratio > 0.6) bounds(i) = bounds(i) * (1.0 + 2.0 * (ratio - 0.6) / 0.4);
else if (ratio < .4)
bounds(i) = bounds(i) / (1.0 + 2.0 * ((0.4 - ratio) / 0.4));
// keep within initial bounds
if(bounds(i) >= (ub(i) - lb(i)))
{
bounds(i) = ub(i) - lb(i);
test = test + 1;
}
}
else
test = test + 1; // make sure coverage check passes for the fixed parameters
}
nacp.fill(0.0);
// check if we cover parameter space. if we have yet to do so
if (!coverage_ok) coverage_ok = (test == n);
}
// intermediate output, if desired
if(verbosity == 2)
{
printf("\nsamin: intermediate results before next temperature change\n");
printf("\ntemperature %e", t);
printf("\ncurrent best function value %f", fopt);
printf("\ntotal evaluations so far %d", func_evals);
printf("\ntotal moves since last temperature reduction %d", nup + ndown + nrej);
printf("\ndownhill %d", nup);
printf("\naccepted uphill %d", ndown);
printf("\nrejected uphill %d", nrej);
printf("\nout of bounds trials %d", lnobds);
printf("\nnew minima this temperature %d", nnew);
printf("\n\n parameter search width\n");
for(i = 0; i < n; i++) printf("%20f%20f\n", xopt(i), bounds(i));
printf("\n");
}
// Check for convergence, if we have covered the parameter space
if (coverage_ok)
{
// last value close enough to last neps values?
fstar(0) = f;
test = 0;
for (i = 1; i < neps; i++) test = test + fabs(f - fstar(i)) > functol;
test = (test > 0); // if different from zero, function conv. has failed
// last value close enough to overall best?
if (((fopt - f) <= functol) && (!test))
{
// check for bound narrow enough for parameter convergence
for (i = 0;i < n;i++)
{
if (bounds(i) > paramtol)
{
converge = 0; // no conv. if bounds too wide
break;
}
else
converge = 1;
}
}
// check if optimal point is near boundary of parameter space, and change convergence message if so
if (converge && lnobds > 0) converge = 2;
// Like to see the final results?
if (converge > 0)
{
if (verbosity >= 1)
{
printf("\n================================================\n");
printf("SAMIN results\n\n");
if (converge == 1) printf("==> Normal convergence <==\n\n");
if (converge == 2)
{
printf("==> WARNING <==: Last point satisfies convergence criteria,\n");
printf("but is near boundary of parameter space.\n");
printf("%d out of %d evaluations were out-of-bounds in the last round.\n", lnobds, (nup+ndown+nrej));
printf("Expand bounds and re-run, unless this is a constrained minimization.\n\n");
}
printf("Convergence tolerances:\nFunction: %e\nParameters: %e\n", functol, paramtol);
printf("\nObjective function value at minimum: %f\n\n", fopt);
printf(" parameter search width\n");
for(i = 0; i < n; i++) printf("%20f%20f\n", xopt(i), bounds(i));
printf("================================================\n");
}
f_return(3) = details;
f_return(2) = converge;
f_return(1) = fopt;
f_return(0) = xopt;
return f_return; // this breaks out, if we get here
}
// Reduce temperature, record current function value in the
// list of last "neps" values, and loop again
t = rt * t;
for(i = neps-1; i > 0; i--) fstar(i) = fstar(i-1);
f = fopt;
x = xopt;
}
else
{
// coverage not ok - increase temperature quickly to expand search area, to cover parameter space
t = t*t;
for(i = neps-1; i > 0; i--) fstar(i) = fstar(i-1);
f = fopt;
x = xopt;
}
}
// silence compiler warning
return octave_value_list ();
}
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