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25.3.1 Trivial example

The first example, in one dimensional Cartesian space, sets up an energy function which is a damped sine wave; this has many local minima, but only one global minimum, somewhere between 1.0 and 1.5. The initial guess given is 15.5, which is several local minima away from the global minimum.

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_siman.h>

/* set up parameters for this simulated annealing run */

/* how many points do we try before stepping */
#define N_TRIES 200             

/* how many iterations for each T? */
#define ITERS_FIXED_T 1000

/* max step size in random walk */
#define STEP_SIZE 1.0            

/* Boltzmann constant */
#define K 1.0                   

/* initial temperature */
#define T_INITIAL 0.008         

/* damping factor for temperature */
#define MU_T 1.003              
#define T_MIN 2.0e-6

gsl_siman_params_t params 
  = {N_TRIES, ITERS_FIXED_T, STEP_SIZE,
     K, T_INITIAL, MU_T, T_MIN};

/* now some functions to test in one dimension */
double E1(void *xp)
{
  double x = * ((double *) xp);

  return exp(-pow((x-1.0),2.0))*sin(8*x);
}

double M1(void *xp, void *yp)
{
  double x = *((double *) xp);
  double y = *((double *) yp);

  return fabs(x - y);
}

void S1(const gsl_rng * r, void *xp, double step_size)
{
  double old_x = *((double *) xp);
  double new_x;

  double u = gsl_rng_uniform(r);
  new_x = u * 2 * step_size - step_size + old_x;

  memcpy(xp, &new_x, sizeof(new_x));
}

void P1(void *xp)
{
  printf ("%12g", *((double *) xp));
}

int
main(int argc, char *argv[])
{
  const gsl_rng_type * T;
  gsl_rng * r;

  double x_initial = 15.5;

  gsl_rng_env_setup();

  T = gsl_rng_default;
  r = gsl_rng_alloc(T);

  gsl_siman_solve(r, &x_initial, E1, S1, M1, P1,
                  NULL, NULL, NULL, 
                  sizeof(double), params);

  gsl_rng_free (r);
  return 0;
}

Here are a couple of plots that are generated by running siman_test in the following way:

$ ./siman_test | awk '!/^#/ {print $1, $4}' 
 | graph -y 1.34 1.4 -W0 -X generation -Y position 
 | plot -Tps > siman-test.eps
$ ./siman_test | awk '!/^#/ {print $1, $5}' 
 | graph -y -0.88 -0.83 -W0 -X generation -Y energy 
 | plot -Tps > siman-energy.eps

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