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Additional subtour cuts

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This commit is contained in:
Alinson S. Xavier
2015-03-25 06:32:19 -04:00
parent 5fe42908b4
commit 8af349c106
7 changed files with 376 additions and 106 deletions
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22
src/branch_and_cut.c
View File

@@ -5,6 +5,8 @@
#include "branch_and_cut.h"
#include "util.h"
int BNC_NODE_COUNT = 0;
static int BNC_solve_node(struct BNC *bnc, int depth);
static int BNC_branch_node(struct BNC *bnc, double *x, int depth);
@@ -40,6 +42,7 @@ void BNC_free(struct BNC *bnc)
LP_free(bnc->lp);
free(bnc->lp);
}
if (bnc->best_x) free(bnc->best_x);
}
int BNC_init_lp(struct BNC *bnc)
@@ -72,6 +75,8 @@ static int BNC_solve_node(struct BNC *bnc, int depth)
struct LP *lp = bnc->lp;
double *best_val = &bnc->best_obj_val;
BNC_NODE_COUNT++;
int rval = 0;
double *x = (double *) NULL;
@@ -91,10 +96,12 @@ static int BNC_solve_node(struct BNC *bnc, int depth)
rval = LP_get_obj_val(lp, &objval);
abort_if(rval, "LP_get_obj_val failed\n");
log_debug(" objective value = %.2f\n", objval);
log_debug(" obj value = %.2f\n", objval);
if (objval > *best_val)
if (objval > *best_val + LP_EPSILON)
{
log_debug("Branch pruned by bound (%.2lf > %.2lf).\n", objval,
*best_val);
rval = 0;
@@ -128,17 +135,20 @@ static int BNC_solve_node(struct BNC *bnc, int depth)
{
log_debug(" solution is integral\n");
if (objval < *best_val)
if (objval + LP_EPSILON < *best_val)
{
if (bnc->best_x) free(bnc->best_x);
*best_val = objval;
bnc->best_x = x;
x = 0;
log_info("Found a better integral solution:\n");
log_info(" objval = %.2lf **\n", objval);
log_info(" obj val = %.2lf **\n", objval);
if (bnc->problem_solution_found)
bnc->problem_solution_found(bnc->problem_data, bnc->best_x);
}
}
else
} else
{
log_debug(" solution is fractional\n");
rval = BNC_branch_node(bnc, x, depth);

4
src/branch_and_cut.h
View File

@@ -17,6 +17,8 @@ struct BNC
int (*problem_init_lp)(struct LP *, void *);
int (*problem_add_cutting_planes)(struct LP *, void *);
int (*problem_solution_found)(void *data, double *x);
};
int BNC_init(struct BNC *bnc);
@@ -27,4 +29,6 @@ int BNC_init_lp(struct BNC *bnc);
void BNC_free(struct BNC *bnc);
extern int BNC_NODE_COUNT;
#endif //_PROJECT_BRANCH_AND_CUT_H_

6
src/flow.c
View File

@@ -4,6 +4,8 @@
#include "gtsp.h"
#include "util.h"
int FLOW_MAX_FLOW_COUNT = 0;
int flow_mark_reachable_nodes(
const struct Graph *graph, double *residual_caps, struct Node *from)
{
@@ -62,11 +64,13 @@ int flow_find_max_flow(
{
int rval = 0;
FLOW_MAX_FLOW_COUNT++;
for (int i = 0; i < digraph->node_count; i++)
digraph->nodes[i].mark = 0;
log_verbose("Input graph:\n");
graph_dump(digraph);
// graph_dump(digraph);
log_verbose("Solving flow problem:\n");

2
src/flow.h
View File

@@ -25,6 +25,8 @@ int flow_mark_reachable_nodes(
int flow_main(int argc, char **argv);
extern int FLOW_MAX_FLOW_COUNT;
#include "graph.h"
#endif //_PROJECT_FLOW_H_

9
src/graph.c
View File

@@ -17,6 +17,7 @@ void graph_free(struct Graph *graph)
{
if (!graph) return;
if (graph->edges) free(graph->edges);
if (graph->nodes) free(graph->nodes);
if (graph->adj) free(graph->adj);
}
@@ -201,7 +202,8 @@ int graph_dump(struct Graph *graph)
{
int rval = 0;
log_debug("node_count: %d edge_count: %d\n", graph->node_count, graph->edge_count);
log_debug("node_count: %d edge_count: %d\n", graph->node_count,
graph->edge_count);
for (int i = 0; i < graph->node_count; i++)
{
@@ -212,8 +214,9 @@ int graph_dump(struct Graph *graph)
for (int i = 0; i < graph->edge_count; i++)
{
struct Edge *e = &graph->edges[i];
log_debug("%3d (%d, %d) weight: %d ", e->index, e->from->index, e->to->index, e->weight);
#if LOG_LEVEL >= LOG_LEVEL_VERBOSE
log_debug("%3d (%d, %d) weight: %d ", e->index, e->from->index,
e->to->index, e->weight);
#if LOG_LEVEL >= LOG_LEVEL_DEBUG
if (e->reverse) printf("reverse: %d ", e->reverse->index);
printf("\n");
#endif

361
src/gtsp.c
View File

@@ -32,11 +32,10 @@ int GTSP_init_data(struct GTSP *data)
void GTSP_free(struct GTSP *data)
{
if (!data) return;
if (data->graph)
{
graph_free(data->graph);
free(data->graph);
}
if (data->clusters) free(data->clusters);
if (data->x_coordinates) free(data->x_coordinates);
if (data->y_coordinates) free(data->y_coordinates);
@@ -106,9 +105,10 @@ int GTSP_create_random_problem(
data->y_coordinates = y_coords;
CLEANUP:
if (weights) free(weights);
if (edges) free(edges);
if (rval)
{
if (edges) free(edges);
if (clusters) free(clusters);
}
return rval;
@@ -202,10 +202,117 @@ int GTSP_add_subtour_elimination_cut(
rmatind[cut_edges_count + 1] = to->index;
rmatval[cut_edges_count + 1] = -2.0;
log_debug("Generated cut:\n");
log_verbose("Generated cut:\n");
for (int i = 0; i < newnz; i++)
log_debug("%8.2f x%d\n", rmatval[i], rmatind[i]);
log_debug(" %c %.2lf\n", sense, rhs);
log_verbose("%8.2f x%d\n", rmatval[i], rmatind[i]);
log_verbose(" %c %.2lf\n", sense, rhs);
if (OPTIMAL_X)
{
double sum = 0;
for (int i = 0; i < newnz; i++)
sum += rmatval[i] * OPTIMAL_X[rmatind[i]];
abort_if(sum <= rhs - LP_EPSILON, "cannot add invalid cut");
}
rval = LP_add_rows(lp, 1, newnz, &rhs, &sense, &rmatbeg, rmatind, rmatval);
abort_if(rval, "LP_add_rows failed");
CLEANUP:
if (rmatval) free(rmatval);
if (rmatind) free(rmatind);
return rval;
}
int GTSP_add_subtour_elimination_cut_2(
struct LP *lp,
struct Graph *graph,
struct Node *from,
struct Node *to,
struct Edge **cut_edges,
int cut_edges_count)
{
int rval = 0;
char sense = 'G';
double rhs = 0.0;
int newnz = cut_edges_count + 1;
int rmatbeg = 0;
int *rmatind = 0;
double *rmatval = 0;
rmatind = (int *) malloc(newnz * sizeof(int));
abort_if(!rmatind, "could not allocate rmatind");
rmatval = (double *) malloc(newnz * sizeof(double));
abort_if(!rmatval, "could not allocate rmatval");
for (int i = 0; i < cut_edges_count; i++)
{
rmatind[i] = cut_edges[i]->index + graph->node_count;
rmatval[i] = 1.0;
}
rmatind[cut_edges_count] = from->index;
rmatval[cut_edges_count] = -2.0;
log_verbose("Generated cut:\n");
for (int i = 0; i < newnz; i++)
log_verbose("%8.2f x%d\n", rmatval[i], rmatind[i]);
log_verbose(" %c %.2lf\n", sense, rhs);
if (OPTIMAL_X)
{
double sum = 0;
for (int i = 0; i < newnz; i++)
sum += rmatval[i] * OPTIMAL_X[rmatind[i]];
abort_if(sum <= rhs - LP_EPSILON, "cannot add invalid cut");
}
rval = LP_add_rows(lp, 1, newnz, &rhs, &sense, &rmatbeg, rmatind, rmatval);
abort_if(rval, "LP_add_rows failed");
CLEANUP:
if (rmatval) free(rmatval);
if (rmatind) free(rmatind);
return rval;
}
int GTSP_add_subtour_elimination_cut_3(
struct LP *lp,
struct Graph *graph,
struct Node *from,
struct Node *to,
struct Edge **cut_edges,
int cut_edges_count)
{
int rval = 0;
char sense = 'G';
double rhs = 2.0;
int newnz = cut_edges_count;
int rmatbeg = 0;
int *rmatind = 0;
double *rmatval = 0;
rmatind = (int *) malloc(newnz * sizeof(int));
abort_if(!rmatind, "could not allocate rmatind");
rmatval = (double *) malloc(newnz * sizeof(double));
abort_if(!rmatval, "could not allocate rmatval");
for (int i = 0; i < cut_edges_count; i++)
{
rmatind[i] = cut_edges[i]->index + graph->node_count;
rmatval[i] = 1.0;
}
log_verbose("Generated cut:\n");
for (int i = 0; i < newnz; i++)
log_verbose("%8.2f x%d\n", rmatval[i], rmatind[i]);
log_verbose(" %c %.2lf\n", sense, rhs);
if (OPTIMAL_X)
{
@@ -252,19 +359,23 @@ int GTSP_find_exact_subtour_elimination_cuts(
struct Graph digraph;
graph_init(&digraph);
digraph_edges = (int *) malloc(8 * graph->edge_count * sizeof(int));
flow = (double *) malloc(4 * graph->edge_count * sizeof(double));
capacities = (double *) malloc(4 * graph->edge_count * sizeof(double));
int digraph_edge_count = 4 * graph->edge_count + 2 * graph->node_count;
int digraph_node_count = node_count + data->cluster_count;
digraph_edges = (int *) malloc(2 * digraph_edge_count * sizeof(int));
flow = (double *) malloc(digraph_edge_count * sizeof(double));
capacities = (double *) malloc(digraph_edge_count * sizeof(double));
cut_edges =
(struct Edge **) malloc(
4 * graph->edge_count * sizeof(struct Edge *));
(struct Edge **) malloc(digraph_edge_count * sizeof(struct Edge *));
abort_if(!digraph_edges, "could not allocate digraph_edges");
abort_if(!flow, "could not allocate flow");
abort_if(!capacities, "could not allocate capacities");
abort_if(!cut_edges, "could not allocate cut_edges");
// Create four directed edges for each edge of the original graph.
// Create four directed edges for each edge of the original graph
int ke = 0;
int kc = 0;
for (int i = 0; i < graph->edge_count; i++)
{
assert(node_count + i < num_cols);
@@ -273,39 +384,56 @@ int GTSP_find_exact_subtour_elimination_cuts(
int from = e->from->index;
int to = e->to->index;
digraph_edges[8 * i] = from;
digraph_edges[8 * i + 1] = to;
capacities[4 * i] = x[node_count + i];
digraph_edges[ke++] = from;
digraph_edges[ke++] = to;
capacities[kc++] = x[node_count + i];
digraph_edges[8 * i + 2] = to;
digraph_edges[8 * i + 3] = from;
capacities[4 * i + 1] = 0;
digraph_edges[ke++] = to;
digraph_edges[ke++] = from;
capacities[kc++] = 0;
digraph_edges[8 * i + 4] = to;
digraph_edges[8 * i + 5] = from;
capacities[4 * i + 2] = x[node_count + i];
digraph_edges[ke++] = to;
digraph_edges[ke++] = from;
capacities[kc++] = x[node_count + i];
digraph_edges[8 * i + 6] = from;
digraph_edges[8 * i + 7] = to;
capacities[4 * i + 3] = 0;
digraph_edges[ke++] = from;
digraph_edges[ke++] = to;
capacities[kc++] = 0;
}
rval = graph_build(node_count, 4 * graph->edge_count, digraph_edges, 1, &digraph);
// Create an extra node for each cluster and connect it to the vertices
// of the cluster through some edge with very high capacity
for (int i = 0; i < node_count; i++)
{
struct Node *n = &graph->nodes[i];
int cl = data->clusters[n->index];
digraph_edges[ke++] = n->index;
digraph_edges[ke++] = node_count + cl;
capacities[kc++] = 1e100;
digraph_edges[ke++] = node_count + cl;
digraph_edges[ke++] = n->index;
capacities[kc++] = 1e100;
}
assert(ke == 2 * digraph_edge_count);
assert(kc == digraph_edge_count);
rval = graph_build(digraph_node_count, digraph_edge_count, digraph_edges, 1,
&digraph);
abort_if(rval, "graph_build failed");
for (int i = 0; i < graph->edge_count; i++)
for (int i = 0; i < digraph_edge_count; i += 2)
{
digraph.edges[4 * i].reverse = &digraph.edges[4 * i + 1];
digraph.edges[4 * i + 1].reverse = &digraph.edges[4 * i];
digraph.edges[4 * i + 2].reverse = &digraph.edges[4 * i + 3];
digraph.edges[4 * i + 3].reverse = &digraph.edges[4 * i + 2];
digraph.edges[i].reverse = &digraph.edges[i + 1];
digraph.edges[i + 1].reverse = &digraph.edges[i];
}
int max_x_index = 0;
double max_x = DBL_MIN;
for (int i = 0; i < graph->node_count; i++)
for (int i = 0; i < node_count; i++)
{
struct Node *n = &graph->nodes[i];
if (x[n->index] > max_x)
@@ -315,8 +443,11 @@ int GTSP_find_exact_subtour_elimination_cuts(
}
}
// Constraints (2.3)
{
int i = max_x_index;
for (int j = 0; j < digraph.node_count; j++)
for (int j = 0; j < node_count; j++)
{
if (i == j) continue;
@@ -326,8 +457,8 @@ int GTSP_find_exact_subtour_elimination_cuts(
struct Node *from = &digraph.nodes[i];
struct Node *to = &digraph.nodes[j];
log_verbose("Calculating max flow from %d to %to\n", from->index,
to->index);
log_verbose("Calculating max flow from node %d to node %to\n",
from->index, to->index);
double flow_value;
rval = flow_find_max_flow(&digraph, capacities, from, to, flow,
&flow_value);
@@ -342,25 +473,118 @@ int GTSP_find_exact_subtour_elimination_cuts(
2 * (x[i] + x[j] - 1));
int cut_edges_count;
rval = get_cut_edges_from_marks(&digraph, &cut_edges_count, cut_edges);
rval = get_cut_edges_from_marks(&digraph, &cut_edges_count,
cut_edges);
abort_if(rval, "get_cut_edges_from_marks failed");
log_verbose("Adding cut for i=%d j=%d, cut edges:\n", i, j);
for (int k = 0; k < cut_edges_count/2; k++)
for (int k = 0; k < cut_edges_count / 2; k++)
{
cut_edges[k] = &graph->edges[cut_edges[k*2]->index / 4];
log_verbose(" %d %d\n", cut_edges[k*2]->from->index,
cut_edges[k*2]->to->index);
cut_edges[k] = &graph->edges[cut_edges[k * 2]->index / 4];
log_verbose(" %d %d\n", cut_edges[k * 2]->from->index,
cut_edges[k * 2]->to->index);
}
rval = GTSP_add_subtour_elimination_cut(lp, graph, from, to, cut_edges,
cut_edges_count/2);
rval = GTSP_add_subtour_elimination_cut(lp, graph, from, to,
cut_edges, cut_edges_count / 2);
abort_if(rval, "GTSP_add_subtour_elimination_cut failed");
(*added_cuts_count)++;
goto CLEANUP;
}
}
// Constraints (2.2)
for (int i = 0; i < node_count; i++)
{
for (int j = 0; j < data->cluster_count; j++)
{
if (clusters[i] == j) continue;
if (x[i] < LP_EPSILON) continue;
struct Node *from = &digraph.nodes[i];
struct Node *to = &digraph.nodes[node_count + j];
log_verbose("Calculating max flow from node %d to cluster %to\n", i,
j);
double flow_value;
rval = flow_find_max_flow(&digraph, capacities, from, to, flow,
&flow_value);
abort_if(rval, "flow_find_max_flow failed");
log_verbose(" %.2lf\n", flow_value);
if (flow_value >= 2 * x[i] - LP_EPSILON) continue;
log_verbose("violation: %.2lf >= %.2lf\n", flow_value, 2 * x[i]);
int cut_edges_count;
rval = get_cut_edges_from_marks(&digraph, &cut_edges_count,
cut_edges);
abort_if(rval, "get_cut_edges_from_marks failed");
log_verbose("Adding cut for i=%d j=%d, cut edges:\n", i, j);
for (int k = 0; k < cut_edges_count / 2; k++)
{
cut_edges[k] = &graph->edges[cut_edges[k * 2]->index / 4];
log_verbose(" %d %d\n", cut_edges[k * 2]->from->index,
cut_edges[k * 2]->to->index);
}
rval = GTSP_add_subtour_elimination_cut_2(lp, graph, from, to,
cut_edges, cut_edges_count / 2);
abort_if(rval, "GTSP_add_subtour_elimination_cut failed");
(*added_cuts_count)++;
goto CLEANUP;
}
}
// Constraints (2.1)
for (int i = 0; i < data->cluster_count; i++)
{
for (int j = i + 1; j < data->cluster_count; j++)
{
struct Node *from = &digraph.nodes[node_count + i];
struct Node *to = &digraph.nodes[node_count + j];
log_verbose("Calculating max flow from cluster %d to cluster %to\n",
i, j);
double flow_value;
rval = flow_find_max_flow(&digraph, capacities, from, to, flow,
&flow_value);
abort_if(rval, "flow_find_max_flow failed");
log_verbose(" %.2lf\n", flow_value);
if (flow_value >= 2 - LP_EPSILON) continue;
log_verbose("violation: %.2lf >= 2\n", flow_value);
int cut_edges_count;
rval = get_cut_edges_from_marks(&digraph, &cut_edges_count,
cut_edges);
abort_if(rval, "get_cut_edges_from_marks failed");
log_verbose("Adding cut for i=%d j=%d, cut edges:\n", i, j);
for (int k = 0; k < cut_edges_count / 2; k++)
{
cut_edges[k] = &graph->edges[cut_edges[k * 2]->index / 4];
log_verbose(" %d %d\n", cut_edges[k * 2]->from->index,
cut_edges[k * 2]->to->index);
}
rval = GTSP_add_subtour_elimination_cut_3(lp, graph, from, to,
cut_edges, cut_edges_count / 2);
abort_if(rval, "GTSP_add_subtour_elimination_cut failed");
(*added_cuts_count)++;
goto CLEANUP;
}
}
CLEANUP:
graph_free(&digraph);
if (digraph_edges) free(digraph_edges);
if (flow) free(flow);
if (cut_edges) free(cut_edges);
@@ -421,8 +645,7 @@ int GTSP_add_cutting_planes(struct LP *lp, struct GTSP *data)
{
log_debug("Found %d subtour elimination cuts using exact "
"separation\n", added_cuts_count);
}
else break;
} else break;
}
CLEANUP:
@@ -534,15 +757,15 @@ int GTSP_read_x(char *filename, double **p_x)
edge = get_edge_num(node_count, from, to);
abort_if(edge > num_cols, "invalid edge");
x[from] = x[
to] = 1.0;
x[from] += 0.5;
x[to] += 0.5;
x[edge] = 1;
}
for (int i = 0; i < num_cols; i++)
{
if (x[i] <= LP_EPSILON) continue;
log_verbose(" x%-3d = %.2f\n", i, x[i]);
log_debug(" x%-3d = %.2f\n", i, x[i]);
}
*p_x = x;
@@ -552,14 +775,13 @@ int GTSP_read_x(char *filename, double **p_x)
return rval;
}
static const struct option options_tab[] = {
{"help", no_argument, 0, 'h'}, {"nodes", required_argument, 0, 'n'},
static const struct option options_tab[] =
{{"help", no_argument, 0, 'h'}, {"nodes", required_argument, 0, 'n'},
{"clusters", required_argument, 0, 'm'},
{"grid-size", required_argument, 0, 'g'},
{"optimal", required_argument, 0, 'x'},
{"seed", required_argument, 0, 's'},
{(char *) 0, (int) 0, (int *) 0, (int) 0}
};
{(char *) 0, (int) 0, (int *) 0, (int) 0}};
static int input_node_count = 20;
static int input_cluster_count = 5;
@@ -623,6 +845,18 @@ static int GTSP_parse_args(int argc, char **argv)
return rval;
}
int GTSP_solution_found(struct GTSP *data, double *x)
{
int rval = 0;
log_info("Writting solution to file gtsp.out\n");
rval = GTSP_write_solution(data, "gtsp.out", x);
abort_if(rval, "GTSP_write_solution failed");
CLEANUP:
return rval;
}
int GTSP_main(int argc, char **argv)
{
int rval = 0;
@@ -630,7 +864,7 @@ int GTSP_main(int argc, char **argv)
struct BNC bnc;
struct GTSP data;
SEED = (unsigned int) get_real_time() % 10000;
SEED = (unsigned int) get_real_time() % 1000000;
rval = GTSP_init_data(&data);
abort_if(rval, "GTSP_init_data failed");
@@ -650,8 +884,7 @@ int GTSP_main(int argc, char **argv)
log_info(" grid_size = %d\n", grid_size);
rval = GTSP_create_random_problem(input_node_count, input_cluster_count,
grid_size,
&data);
grid_size, &data);
abort_if(rval, "GTSP_create_random_problem failed");
log_info("Writing random instance to file gtsp.in\n");
@@ -663,10 +896,23 @@ int GTSP_main(int argc, char **argv)
bnc.problem_init_lp = (int (*)(struct LP *, void *)) GTSP_init_lp;
bnc.problem_add_cutting_planes =
(int (*)(struct LP *, void *)) GTSP_add_cutting_planes;
bnc.problem_solution_found =
(int (*)(void *, double *)) GTSP_solution_found;
if (OPTIMAL_X)
{
log_info("Optimal solution is available. Cuts will be checked.\n");
double opt_val = 0.0;
for (int i = 0; i < data.graph->edge_count; i++)
{
struct Edge *e = &data.graph->edges[i];
opt_val += OPTIMAL_X[i + input_node_count] * e->weight;
}
log_info(" opt = %.2lf\n", opt_val);
}
log_info("Initializing LP...\n");
rval = BNC_init_lp(&bnc);
abort_if(rval, "BNC_init_lp failed");
@@ -684,8 +930,9 @@ int GTSP_main(int argc, char **argv)
log_info("Optimal integral solution:\n");
log_info(" obj value = %.2lf **\n", bnc.best_obj_val);
rval = GTSP_write_solution(&data, "gtsp.out", bnc.best_x);
abort_if(rval, "GTSP_write_solution failed");
log_info("Branch-and-bound nodes: %d\n", BNC_NODE_COUNT);
log_info("Max-flow computations: %d\n", FLOW_MAX_FLOW_COUNT);
CLEANUP:
GTSP_free(&data);

12
src/util.h
View File

@@ -11,18 +11,18 @@
#define LOG_LEVEL LOG_LEVEL_INFO
#if LOG_LEVEL < LOG_LEVEL_DEBUG
#define log_debug(...)
#else
#define log_debug(...) time_printf( __VA_ARGS__)
#endif
#if LOG_LEVEL < LOG_LEVEL_VERBOSE
#define log_verbose(...)
#else
#define log_verbose(...) time_printf( __VA_ARGS__)
#endif
#if LOG_LEVEL < LOG_LEVEL_DEBUG
#define log_debug(...)
#else
#define log_debug(...) time_printf( __VA_ARGS__)
#endif
#if LOG_LEVEL < LOG_LEVEL_INFO
#define log_info(...)
#else