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primal.c
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primal.c
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// (C) 2011, Marius Posta ([email protected])
// Check LICENSE.txt for the legal blah-blah.
#include "primal.h"
// Resets tabu search to new best solution
void primal_new_upper_bound (primal_t *primal)
{
int i;
solution_reset(primal->inst, primal->sol, primal->best_x);
for (i = 0; i < primal->inst->n; i++)
if (primal->tabu[i] != INFINITY)
primal->tabu[i] = 0.0;
}
// Resets primal process prior to solving new instance,
// with different costs but same size
//% Algorithm 1 step 0
void primal_reset (primal_t *primal)
{
instance_t *inst = primal->inst;
solution_t *s = primal->sol;
int i;
primal->tabu_length = 10.0; // initial tabu tenure
primal->n_moves_at_last_improvement = 0; // reset counter
primal->n_moves = 0; // reset counter
for (i = 0; i < inst->n; i++) {
primal->guiding_x[i] = 1; // bogus guiding solution
primal->improving_partial_x[i] = -1; // reset improv. part. sol
primal->tabu[i] = 0.0; // nothing is tabu
}
solution_reset(inst, s, primal->best_x); // reset with old best-known solution (chances are, it's not too bad)
primal->best_z = s->total_cost; // reset upper bound
primal->state = primal_state_run; // set state as ready to run
}
// Updates tabu tenure after 1OPT move on location w
void tabu_tenure (primal_t *primal, int w, int improving_move)
{
primal->tabu[w] = primal->tabu_length + ((double) primal->n_moves);
if (improving_move) {
if (primal->tabu_length > 2.0)
--primal->tabu_length;
} else if (primal->tabu_length < 10.0)
++primal->tabu_length;
++primal->n_moves;
}
// Performs one iteration of the primal process
void primal_run (primal_t *primal)
{
instance_t *inst = primal->inst;
solution_t *s = primal->sol;
int i, w, n, aspiration, n_best, n_free, n_diver;
double best_gain;
check_solution(inst, s);
//% Algorithm 1 Step 4 (cont'd)
// Perform moves to conform with the improving partial solution
for (i = 0; i < inst->n; i++)
if (primal->improving_partial_x[i] != -1 && primal->tabu[i] != INFINITY) {
primal->tabu[i] = INFINITY;
if (s->x[i] != primal->improving_partial_x[i]) {
solution_flip(inst, s, i);
check_solution(inst, s);
++primal->n_moves;
if (s->total_cost < primal->best_z) {
primal->n_moves_at_last_improvement = primal->n_moves;
primal->best_z = s->total_cost;
memcpy(primal->best_x, s->x, inst->n * sizeof(int));
}
}
}
// Perturb tabu state using the guiding solution
if (primal->n_moves_at_last_improvement + inst->request_period < primal->n_moves) {
primal->n_moves_at_last_improvement = primal->n_moves;
for (i = 0; i < inst->n; i++)
if (primal->tabu[i] != INFINITY && s->x[i] == primal->guiding_x[i])
primal->tabu[i] = ((double) primal->n_moves) + primal->tabu_length;
}
// Analyze search state
//% Algorithm 1 step 1
for (aspiration = 0, best_gain = -INFINITY, n_best = n_free = n_diver = 0, i = 0; i < inst->n; i++)
if (primal->tabu[i] == INFINITY) {
assert(s->x[i] == primal->improving_partial_x[i]);
} else {
++n_free; // count the number of unfixed locations
if ((primal->n_moves == 0 || (s->total_cost - s->flip_gain[i] <= primal->best_z - bound_eps)) && s->flip_gain[i] != INFINITY)
aspiration = 1; // aspiration criterion is satisfied
if ((double) primal->n_moves > primal->tabu[i] || aspiration) {
++n_diver; // count the number of non-tabu locations
if (s->flip_gain[i] > best_gain + bound_eps && best_gain != INFINITY)
n_best = 1, best_gain = s->flip_gain[i]; // store the best location to perform a move on
else if (fabs(s->flip_gain[i] - best_gain) < 2.0 * bound_eps || (s->flip_gain[i] == INFINITY && best_gain == INFINITY))
++n_best; // count the number of best locations
}
}
// Select the 1OPT move to perform
w = -1;
if (best_gain <= bound_eps) { // if there exist no improving moves
if (n_free == 0) { // if there exist no moves
//% Algorithm 1 step 1(d)
return;
}
if (n_diver == 0) { // if there exist no non-tabu moves
// select one location at random
//% Algorithm 1 step 1(c)
n = RngStream_RandInt(primal->rng, 0, n_free - 1);
for (i = 0; i < inst->n && w == -1; i++)
if (primal->tabu[i] != INFINITY && n-- <= 0)
w = i;
} else { // there exist non-tabu moves
// select one location at random
//% Algorithm 1 step 1(b)
n = RngStream_RandInt(primal->rng, 0, n_diver - 1);
for (i = 0; i < inst->n && w == -1; i++)
if (((double) primal->n_moves > primal->tabu[i] || aspiration) && n-- <= 0)
w = i;
}
} else { // there exists at least one improving move
// select one of the best at random
//% Algorithm 1 step 1(a)
assert(n_best > 0);
n = RngStream_RandInt(primal->rng, 0, n_best - 1);
for (w = -1, i = 0; i < inst->n && w == -1; i++)
if (((double) primal->n_moves > primal->tabu[i] || aspiration)
&& (fabs(s->flip_gain[i] - best_gain) < 2.0 * bound_eps || (s->flip_gain[i] == INFINITY && best_gain == INFINITY))
&& n-- <= 0)
w = i;
}
// check that in all cases we have found something
assert(w >= 0);
assert(w < inst->n);
assert(primal->tabu[w] != INFINITY);
// Update search state
//% Algorithm 1 step 2
tabu_tenure(primal, w, (s->flip_gain[w] > bound_eps));
//% Algorithm 1 step 3(a,b,c)
solution_flip(inst, s, w);
check_solution(inst, s);
//% Algorithm 1 step 3(d)
if (s->total_cost < primal->best_z) {
// Update best known solution
primal->n_moves_at_last_improvement = primal->n_moves;
primal->best_z = s->total_cost;
memcpy(primal->best_x, s->x, inst->n * sizeof(int));
}
}
primal_t *primal_create (instance_t *inst)
{
primal_t *primal = (primal_t*) malloc(sizeof(primal_t));
primal->inst = instance_copy(inst);
primal->state = primal_state_undef;
primal->guiding_x = (int*) calloc(inst->n, sizeof(int));
primal->improving_partial_x = (int*) calloc(inst->n, sizeof(int));
primal->best_x = (int*) calloc(inst->n, sizeof(int));
primal->best_z = INFINITY;
primal->sol = solution_alloc(inst);
primal->tabu = (double*) calloc(inst->n, sizeof(double));
primal->n_moves = 0;
primal->n_moves_at_last_improvement = 0;
primal->rng = RngStream_CreateStream("");
return primal;
}
void primal_destroy (primal_t *primal)
{
instance_destroy(primal->inst);
RngStream_DeleteStream(primal->rng);
free(primal->best_x);
free(primal->improving_partial_x);
free(primal->guiding_x);
free(primal);
}
// ** Location heap operations **
void sift_down(double **c, int j, int *heap, int *heap_inv, int i, int size)
{
int s, t;
while (i * 2 + 1 < size) {
s = i * 2 + 1;
if (s+1 < size && c[heap[s]][j] > c[heap[s+1]][j])
++s;
if (c[heap[i]][j] <= c[heap[s]][j])
return;
heap_inv[heap[s]] = i;
heap_inv[heap[i]] = s;
t = heap[i];
heap[i] = heap[s];
heap[s] = t;
i = s;
}
}
void sift_up(double **c, int j, int *heap, int *heap_inv, int i)
{
int p, t;
while (i > 0) {
p = (i - 1) / 2;
if (c[heap[p]][j] <= c[heap[i]][j])
return;
heap_inv[heap[p]] = i;
heap_inv[heap[i]] = p;
t = heap[p];
heap[p] = heap[i];
heap[i] = t;
i = p;
}
}
solution_t *solution_alloc (instance_t *inst)
{
solution_t *s = (solution_t*) malloc(sizeof(solution_t));
int j;
s->x = (int*) calloc(inst->n, sizeof(int));
s->flip_gain = (double*) calloc(inst->n, sizeof(double));
s->heap = (int**) calloc(inst->m, sizeof(int*));
s->heap_inv = (int**) calloc(inst->m, sizeof(int*));
s->besti1 = (int*) calloc(inst->m, sizeof(int));
s->besti2 = (int*) calloc(inst->m, sizeof(int));
for (j = 0; j < inst->m; j++) {
// allocate j-th heap
s->heap[j] = (int*) calloc(inst->n, sizeof(int));
s->heap_inv[j] = (int*) calloc(inst->n, sizeof(int));
}
return s;
}
// Performs 1OPT move on location w in O(m log n) time
void solution_flip(instance_t *inst, solution_t *s, int w)
{
int i, j, w2, i2;
// Update costs
s->total_cost -= s->flip_gain[w];
s->flip_gain[w] *= -1.0;
// Deal with special case where the solution was 'all locations closed'
if (s->heap_size == 0) {
s->x[w] = 1;
for (j = 0; j < inst->m; j++) {
// the cheapest location in each heap is the only open location
s->heap[j][0] = w;
s->heap_inv[j][w] = 0;
s->besti1[j] = w;
}
for (i = 0; i < inst->n; i++)
if (i != w) {
// recompute cost differences for all remaining closed locations
s->flip_gain[i] = -inst->f[i];
for (j = 0; j < inst->m; j++) {
if (inst->c[i][j] < inst->c[w][j])
s->flip_gain[i] += inst->c[w][j] - inst->c[i][j];
}
}
s->heap_size = 1;
return;
}
// Deal with the special case where we close the only remaining open solution
if (s->heap_size == 1 && s->x[w]) {
s->x[w] = 0;
for (j = 0; j < inst->m; j++)
s->besti1[j] = s->heap_inv[j][w] = s->heap[j][0] = -1; //remove w from the heap
for (i = 0; i < inst->n; i++)
if (i != w) {
// compute fictional cost differences
s->flip_gain[i] = inst->ub - inst->f[i];
for (j = 0; j < inst->m; j++)
s->flip_gain[i] -= inst->c[i][j];
}
s->heap_size = 0;
return;
}
// Deal with the general cases
if (s->x[w]) { // case where we close location w
s->x[w] = 0;
--s->heap_size;
for (j = 0; j < inst->m; j++) {
// carefully remove it from each heap
i = s->heap_inv[j][w];
assert(i != -1);
assert(s->heap[j][i] == w);
w2 = s->heap[j][s->heap_size];
assert(s->heap_inv[j][w2] == s->heap_size);
s->heap_inv[j][w] = -1;
if (w != w2) {
s->heap_inv[j][w2] = i;
s->heap[j][i] = w2;
sift_up(inst->c, j, s->heap[j], s->heap_inv[j], i);
sift_down(inst->c, j, s->heap[j], s->heap_inv[j], s->heap_inv[j][w2], s->heap_size);
}
}
} else { // case where we open location w
s->x[w] = 1;
for (j = 0; j < inst->m; j++) {
// add it to each heap
s->heap[j][s->heap_size] = w;
s->heap_inv[j][w] = s->heap_size;
sift_up(inst->c, j, s->heap[j], s->heap_inv[j], s->heap_size);
}
++s->heap_size;
}
// Update move costs of all closed locations
for (j = 0; j < inst->m; j++) {
if (inst->c[s->heap[j][0]][j] <= inst->c[s->besti1[j]][j]) {
// the client j can use a cheaper location than previously
for (i = 0; i < inst->n; i++)
if (i != w && !s->x[i]) {
if (inst->c[i][j] < inst->c[s->heap[j][0]][j])
s->flip_gain[i] -= inst->c[s->besti1[j]][j] - inst->c[s->heap[j][0]][j];
else if (inst->c[i][j] < inst->c[s->besti1[j]][j])
s->flip_gain[i] -= inst->c[s->besti1[j]][j] - inst->c[i][j];
}
} else {
for (i = 0; i < inst->n; i++)
if (i != w && !s->x[i]) {
if (inst->c[i][j] < inst->c[s->besti1[j]][j])
s->flip_gain[i] += inst->c[s->heap[j][0]][j] - inst->c[s->besti1[j]][j] ;
else if (inst->c[i][j] < inst->c[s->heap[j][0]][j])
s->flip_gain[i] += inst->c[s->heap[j][0]][j] - inst->c[i][j];
}
}
}
if (s->heap_size == 1) { // Special case where one location is open
// This special case only occurs when we close one of two open locations
// Recompute all move costs and two cheapest locations from scratch
i = s->heap[0][0];
assert(s->x[i]);
s->flip_gain[i] = -inst->ub + inst->f[i];
for (j = 0; j < inst->m; j++) {
s->flip_gain[i] += inst->c[i][j];
s->besti2[j] = -1;
s->besti1[j] = s->heap[j][0];
}
} else if (s->heap_size == 2 && s->x[w]) { // Special case where two locations are open
// This special case only occurs when only one location was open an we open another
// Recompute all move costs and two cheapest locations from scratch
i = (s->heap[0][0] == w) ? s->heap[0][1] : s->heap[0][0];
assert(s->x[i]);
assert(i != w);
s->flip_gain[i] = inst->f[i];
for (j = 0; j < inst->m; j++) {
assert(s->besti2[j] == -1);
if (s->heap[j][0] == i)
s->flip_gain[i] += inst->c[i][j] - inst->c[s->heap[j][1]][j];
s->besti2[j] = s->heap[j][1];
s->besti1[j] = s->heap[j][0];
}
} else {
// Update all move costs and the two cheapest locations
for (j = 0; j < inst->m; j++) {
i2 = (s->heap_size == 2 || inst->c[s->heap[j][1]][j] <= inst->c[s->heap[j][2]][j]) ? 1 : 2;
if (s->heap[j][0] != s->besti1[j] || inst->c[s->heap[j][i2]][j] != inst->c[s->besti2[j]][j]) {
i = s->besti1[j];
if (i != w && s->x[i])
s->flip_gain[i] += inst->c[s->besti2[j]][j] - inst->c[i][j];
i = s->heap[j][0];
if (i != w && s->x[i])
s->flip_gain[i] -= inst->c[s->heap[j][i2]][j] - inst->c[i][j];
}
s->besti2[j] = s->heap[j][i2];
s->besti1[j] = s->heap[j][0];
}
}
}
void check_solution(instance_t *inst, solution_t *s)
{
int i, j;
double g, t;
return; // Delete this line if assert checks are needed
// check heaps
assert(s->heap_size >= 0);
assert(s->heap_size <= inst->n);
for (j = 0; j < inst->m; j++) {
for (i = 0; i < inst->n; i++)
if (s->heap_inv[j][i] == -1) {
assert(!s->x[i]);
} else {
assert(s->heap_inv[j][i] >= 0);
assert(s->heap_inv[j][i] < s->heap_size);
assert(s->heap[j][s->heap_inv[j][i]] == i);
}
for (i = 0; i < s->heap_size; i++) {
assert(s->x[s->heap[j][i]]);
if (i * 2 + 1 < s->heap_size)
assert(inst->c[s->heap[j][i]][j] <= inst->c[s->heap[j][i*2+1]][j]);
if (i * 2 + 2 < s->heap_size)
assert(inst->c[s->heap[j][i]][j] <= inst->c[s->heap[j][i*2+2]][j]);
}
assert(s->besti1[j] == -1 || s->besti1[j] == s->heap[j][0]);
if (s->heap_size == 0) {
assert(s->besti1[j] == s->besti2[j] && s->besti1[j] == -1);
} else if (s->heap_size == 1) {
assert(s->besti2[j] == -1);
} else if (s->heap_size == 2) {
assert(s->besti2[j] == s->heap[j][1]);
} else {
assert(s->besti2[j] == s->heap[j][1] || s->besti2[j] == s->heap[j][2]);
if (s->besti2[j] == s->heap[j][2])
assert(inst->c[s->heap[j][2]][j] <= inst->c[s->heap[j][1]][j]);
else
assert(inst->c[s->heap[j][1]][j] <= inst->c[s->heap[j][2]][j]);
}
}
// check flip costs
if (s->heap_size == 0) {
for (i = 0; i < inst->n; i++) {
assert(!s->x[i]);
for (g = inst->ub - inst->f[i], j = 0; j < inst->m; j++)
g -= inst->c[i][j];
assert(fabs(g - s->flip_gain[i]) < bound_eps);
}
} else {
for (i = 0; i < inst->n; i++)
if (s->x[i] && s->heap_size == 1) {
for (g = -inst->ub + inst->f[i], j = 0; j < inst->m; j++)
g += inst->c[i][j];
assert(fabs(g - s->flip_gain[i]) < bound_eps);
} else if (s->x[i]) {
assert(s->heap_size >= 2);
for (g = inst->f[i], j = 0; j < inst->m; j++)
if (s->besti1[j] == i)
g -= inst->c[s->besti2[j]][j] - inst->c[i][j];
assert(fabs(g - s->flip_gain[i]) < bound_eps);
} else {
assert(s->x[i] == 0 && s->heap_size >= 1);
for (g = -inst->f[i], j = 0; j < inst->m; j++)
if (inst->c[s->besti1[j]][j] > inst->c[i][j])
g += inst->c[s->besti1[j]][j] - inst->c[i][j];
assert(fabs(g - s->flip_gain[i]) < bound_eps);
}
}
// check solution cost
if (s->heap_size == 0) {
assert(fabs(s->total_cost - inst->ub) < bound_eps);
} else {
t = 0.0;
for (i = 0; i < inst->n; i++)
if (s->x[i])
t += inst->f[i];
for (j = 0; j < inst->m; j++) {
for (g = 1e50, i = 0; i < inst->n; i++)
if (s->x[i] && inst->c[i][j] < g)
g = inst->c[i][j];
t += g;
}
assert(fabs(t - s->total_cost) < bound_eps);
}
}
// Rebuild the solution_t data structure using 'x'
void solution_reset (instance_t *inst, solution_t *s, int *x)
{
int i, j, k, l;
// Empty all heaps
for (j = 0; j < inst->m; j++) {
s->besti1[j] = s->besti2[j] = -1;
for (i = 0; i < inst->n; i++)
s->heap[j][i] = s->heap_inv[j][i] = -1;
}
// Compute total opening costs and heap size
s->heap_size = 0;
s->total_cost = 0.0;
if (NULL != x) {
for (s->heap_size = i = 0; i < inst->n; i++) {
s->x[i] = x[i];
if (x[i] == 1) {
++s->heap_size;
s->total_cost += inst->f[i];
}
}
}
// Populate heaps, compute move costs and total solution cost
if (NULL == x || s->heap_size == 0) { // Special case where all locations are closed
s->total_cost = inst->ub;
for (i = 0; i < inst->n; i++) {
s->x[i] = 0;
s->flip_gain[i] = s->total_cost - inst->f[i];
for (j = 0; j < inst->m; j++)
s->flip_gain[i] -= inst->c[i][j];
}
} else { // General case
// Populate heaps by simply adding all open locations in increasing service costs,
// as this verifies the heap property.
for (j = 0; j < inst->m; j++) {
for (i = k = l = 0; k < inst->n && l < s->heap_size; k++) {
i = inst->inc[j][k];
if (x[i] == 1) {
s->heap[j][l] = i;
s->heap_inv[j][i] = l;
if (l == 0) {
s->besti1[j] = i;
s->total_cost += inst->c[i][j];
} else if (l == 1)
s->besti2[j] = i;
++l;
}
}
assert(l == s->heap_size);
}
// Compute move costs
for (i = 0; i < inst->n; i++) {
if (s->x[i] && s->heap_size == 1) {
for (s->flip_gain[i] = - inst->ub + inst->f[i], j = 0; j < inst->m; j++)
s->flip_gain[i] += inst->c[i][j];
} else if (s->x[i]) {
assert(s->heap_size >= 2);
for (s->flip_gain[i] = inst->f[i], j = 0; j < inst->m; j++)
if (s->besti1[j] == i)
s->flip_gain[i] -= inst->c[s->besti2[j]][j] - inst->c[i][j];
} else {
assert(s->x[i] == 0 && s->heap_size >= 1);
for (s->flip_gain[i] = -inst->f[i], j = 0; j < inst->m; j++)
if (inst->c[s->besti1[j]][j] > inst->c[i][j])
s->flip_gain[i] += inst->c[s->besti1[j]][j] - inst->c[i][j];
}
}
}
check_solution(inst, s);
}