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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:
+ */