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/*
Copyright (c) 2011 Cisco and/or its affiliates.
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at:
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <vppinfra/anneal.h>
/*
* Optimize an objective function by simulated annealing
*
* Here are a couple of short, easily-understood
* descriptions of simulated annealing:
*
* http://www.cs.sandia.gov/opt/survey/sa.html
* Numerical Recipes in C, 2nd ed., 444ff
*
* The description in the Wikipedia is not helpful.
*
* The algorithm tries to produce a decent answer to combinatorially
* explosive optimization problems by analogy to slow cooling
* of hot metal, aka annealing.
*
* There are (at least) three problem-dependent annealing parameters
* to consider:
*
* t0, the initial "temperature. Should be set so that the probability
* of accepting a transition to a higher cost configuration is
* initially about 0.8.
*
* ntemps, the number of temperatures to use. Each successive temperature
* is some fraction of the previous temperature.
*
* nmoves_per_temp, the number of configurations to try at each temperature
*
* It is a black art to set ntemps, nmoves_per_temp, and the rate
* at which the temperature drops. Go too fast with too few iterations,
* and the computation falls into a local minimum instead of the
* (desired) global minimum.
*/
void
clib_anneal (clib_anneal_param_t * p)
{
f64 t;
f64 cost, prev_cost, delta_cost, initial_cost, best_cost;
f64 random_accept, delta_cost_over_t;
f64 total_increase = 0.0, average_increase;
u32 i, j;
u32 number_of_increases = 0;
u32 accepted_this_temperature;
u32 best_saves_this_temperature;
int accept;
t = p->initial_temperature;
best_cost = initial_cost = prev_cost = p->anneal_metric (p->opaque);
p->anneal_save_best_configuration (p->opaque);
if (p->flags & CLIB_ANNEAL_VERBOSE)
fformat (stdout, "Initial cost %.2f\n", initial_cost);
for (i = 0; i < p->number_of_temperatures; i++)
{
accepted_this_temperature = 0;
best_saves_this_temperature = 0;
p->anneal_restore_best_configuration (p->opaque);
cost = best_cost;
for (j = 0; j < p->number_of_configurations_per_temperature; j++)
{
p->anneal_new_configuration (p->opaque);
cost = p->anneal_metric (p->opaque);
delta_cost = cost - prev_cost;
/* cost function looks better, accept this move */
if (p->flags & CLIB_ANNEAL_MINIMIZE)
accept = delta_cost < 0.0;
else
accept = delta_cost > 0.0;
if (accept)
{
if (p->flags & CLIB_ANNEAL_MINIMIZE)
if (cost < best_cost)
{
if (p->flags & CLIB_ANNEAL_VERBOSE)
fformat (stdout, "New best cost %.2f\n", cost);
best_cost = cost;
p->anneal_save_best_configuration (p->opaque);
best_saves_this_temperature++;
}
accepted_this_temperature++;
prev_cost = cost;
continue;
}
/* cost function worse, keep stats to suggest t0 */
total_increase += (p->flags & CLIB_ANNEAL_MINIMIZE) ?
delta_cost : -delta_cost;
number_of_increases++;
/*
* Accept a higher cost with Pr { e^(-(delta_cost / T)) },
* equivalent to rnd[0,1] < e^(-(delta_cost / T))
*
* AKA, the Boltzmann factor.
*/
random_accept = random_f64 (&p->random_seed);
delta_cost_over_t = delta_cost / t;
if (random_accept < exp (-delta_cost_over_t))
{
accepted_this_temperature++;
prev_cost = cost;
continue;
}
p->anneal_restore_previous_configuration (p->opaque);
}
if (p->flags & CLIB_ANNEAL_VERBOSE)
{
fformat (stdout, "Temp %.2f, cost %.2f, accepted %d, bests %d\n", t,
prev_cost, accepted_this_temperature,
best_saves_this_temperature);
fformat (stdout, "Improvement %.2f\n", initial_cost - prev_cost);
fformat (stdout, "-------------\n");
}
t = t * p->temperature_step;
}
/*
* Empirically, one wants the probability of accepting a move
* at the initial temperature to be about 0.8.
*/
average_increase = total_increase / (f64) number_of_increases;
p->suggested_initial_temperature = average_increase / 0.22; /* 0.22 = -ln (0.8) */
p->final_temperature = t;
p->final_metric = p->anneal_metric (p->opaque);
if (p->flags & CLIB_ANNEAL_VERBOSE)
{
fformat (stdout, "Average cost increase from a bad move: %.2f\n",
average_increase);
fformat (stdout, "Suggested t0 = %.2f\n",
p->suggested_initial_temperature);
}
}
/*
* fd.io coding-style-patch-verification: ON
*
* Local Variables:
* eval: (c-set-style "gnu")
* End:
*/
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