void Create2DArray(IloModel model, BoolVarMatrix m){
IloEnv env = model.getEnv();
for(int i = 0; i < m.getSize(); i++){
m[i]=IloBoolVarArray(env);
}
return;
}
DataVarBoolTriMatrix::DataVarBoolTriMatrix(string name, IloEnv env,int n, int m, int K){
this->Matrix = IloArray< IloArray<IloBoolVarArray> > (env,n);
for(int i = 0; i < n; i++){
this->Matrix[i] = IloArray<IloBoolVarArray>(env,m);
for(int j = 0; j < m; j++){
this->Matrix[i][j] = IloBoolVarArray(env,K);
for(int k = 0; k < K; k++){
string var_name = name;
var_name += "(";
var_name += U::to_s(i+1);
var_name += ",";
var_name += U::to_s(j+1);
var_name += ",";
var_name += U::to_s(k);
var_name += ")";
this->Matrix[i][j][k] = IloBoolVar(env,var_name.c_str());
}
}
}
this->n = n;
this->m = m;
this->k = K;
}
/*
* $v_i \in \{0, 1\}$ variables denote whether node i is active.
*/
static IloBoolVarArray createVarArrayVs(IloEnv env, u_int n_nodes)
{
IloBoolVarArray vs = IloBoolVarArray(env, n_nodes);
for (u_int i = 0; i < n_nodes; i++) {
vs[i] = IloBoolVar(env, Tools::indicesToString("v", i).c_str());
}
return vs;
}
void Create3DArray(IloModel model, BoolVar3DMatrix R, int size){
IloEnv env = model.getEnv();
for(int p = 0; p < R.getSize(); p++)
R[p] = BoolVarMatrix(env, E);
for(int p = 0; p < R.getSize(); p++){
for(int e = 0; e < size; e++)
R[p][e]=IloBoolVarArray(env);
}
return;
}
/* $x_{ij} \in \{0, 1\}$ variables denote whether edge (i, j) is active. */
static IloBoolVarArray createVarArrayXs(IloEnv env, vector<Instance::Edge> edges, u_int n_edges)
{
IloBoolVarArray xs = IloBoolVarArray(env, n_edges);
for (u_int k = 0; k < n_edges; k++) {
const u_int i = edges[k].v1;
const u_int j = edges[k].v2;
xs[k] = IloBoolVar(env, Tools::indicesToString("x", i, j).c_str());
}
return xs;
}
DataVarBoolMatrix::DataVarBoolMatrix(string name, IloEnv env,int n, int m){
this->Matrix = IloArray<IloBoolVarArray> (env,n);
for(int i = 0; i < n; i++){
this->Matrix[i] = IloBoolVarArray(env,m);
for(int j = 0; j < m; j++){
string var_name = name;//attribut à nom de la forme x(i,j) à la variable
var_name += "(";
var_name += U::to_s(i+1);
var_name += ",";
var_name += U::to_s(j+1);
var_name += ")";
this->Matrix[i][j] = IloBoolVar(env,var_name.c_str());
}
}
this->name = name;
this->n = n;
this->m = m;
}
void kMST_ILP::addTreeConstraints()
{
edges = IloBoolVarArray(env, instance.n_edges * 2); // edges in one direction and in other
// "to"-edges on lower indices
for (unsigned int i=0; i<instance.n_edges; i++) {
edges[i] = IloBoolVar(env, Tools::indicesToString("edge " , instance.edges[i].v1, instance.edges[i].v2, instance.edges[i].weight).c_str() );
//cerr << "init: edge " << i << " from " << instance.edges[i].v1 << " to " << instance.edges[i].v2 << endl;
}
// edges in other direction
for (unsigned int i=instance.n_edges; i<instance.n_edges*2; i++) {
Instance::Edge edgeInst = instance.edges[ i % instance.n_edges ];
edges[i] = IloBoolVar(env, Tools::indicesToString("edge " , edgeInst.v2, edgeInst.v1, edgeInst.weight).c_str() );
//cerr << "init: edge " << i << " from " << instance.edges[i%instance.n_edges].v2 << " to " << instance.edges[i%instance.n_edges].v1 << endl;
}
// edges in one direction forbid edges in other direction
for (unsigned int i=0; i<instance.n_edges; i++) {
model.add( edges[i] + edges[i + instance.n_edges] <= 1 );
}
// exactly k nodes, so k-1 actual edges plus one to the pseudo node 0
model.add(IloSum(edges) == k);
// no 2 incoming edges per vertex
for (unsigned int i=0; i < instance.n_nodes; i++ ){
IloExpr incomingSum(env);
{
vector<u_int> incomingEdgeIds;
getIncomingEdgeIds(incomingEdgeIds, i);
for (unsigned int i=0; i < incomingEdgeIds.size(); i++ ){
incomingSum += edges[incomingEdgeIds[i]];
}
}
model.add(incomingSum <= 1);
incomingSum.end();
}
// only 1 outgoing node from 0
{
IloExpr outgoingSum(env);
bool hasOutgoing = false;
{
vector<u_int> outgoingEdges;
getOutgoingEdgeIds(outgoingEdges, 0);
for (unsigned int i=0; i<outgoingEdges.size(); i++) {
hasOutgoing = true;
outgoingSum += edges[outgoingEdges[i]];
}
}
if (hasOutgoing) { // only true for special input files
model.add(outgoingSum == 1);
}
outgoingSum.end();
}
// no incoming to 0
{
vector<u_int> incomingEdges;
getIncomingEdgeIds(incomingEdges, 0);
for (unsigned int i=0; i<incomingEdges.size(); i++) {
model.add( edges[incomingEdges[i]] == 0) ;
}
}
}
ILOSTLBEGIN
int main (int argc, char* argv[]) {
//get instance fileName:
const char* fileName;
if(argc>1)//we passed the filename in arg
fileName=argv[1];
else fileName = "instances/instances_eleves/projet_5_8_1.dat";
//DONNEES DE L INSTANCE
typedef IloArray<IloNumArray> DataMatrix;
IloEnv env;
instance_Cplex instance ;
getData(fileName,env,instance);
cout << "Données récupérées!\n";
int& n(instance.n);
int& m(instance.m);
try {
IloModel model(env);
BoolVarMatrix x(env,m);
for(int i=0;i<m;i++) x[i]=IloBoolVarArray(env,n);
NumVarMatrix u(env,m);
for(int i=0;i<m;i++) u[i]=IloNumVarArray(env,n);
NumVarMatrix v(env,m);
for(int i=0;i<m;i++) v[i]=IloNumVarArray(env,n);
IloRangeArray constraintSet(env);
IloNumVar y(env);
IloNumVar z(env);
cout << "Variables créées!\n";
setdata(model,env, instance, x,u,v,y,z, constraintSet);
cout << " Modèle et contraintes définies!\n";
IloCplex cplex(model);
cplex.solve();
IloInt solutionUnConnex;
solutionUnConnex=cplex.getObjValue();
DataMatrix xUnconnex(env,m) ; //Solution optimale non connexe
for(int i=0;i<m;i++){
xUnconnex[i]=IloNumArray(env,n);
cplex.getValues(xUnconnex[i], x[i]);
}
std::string Method ="MinimizeEdges"; //connexityTree";
if(Method=="connexityTree"){
//We solve a first time the model without the connexity constraints, to get a good max bound of the height max : the value of the solution/2, then we add the connexity constraints :
IloInt hMax;
if(argc>2){ // we gave the hmax in argument/
istringstream (argv[2])>>hMax;
if(hMax==0) hMax=solutionUnConnex/2+1;
} //else we use our upper bound
else hMax=solutionUnConnex/2+1;//(n*m/2+n/2);
bool useCallBack=false;
if(argc>3 && *argv[3]=='1') useCallBack= true;
solveTreeConnexityConstraints(cplex,model,env,instance,x,u,v,y,z,useCallBack,hMax);
}
Variables *kMST_ILP::modelMCF()
{
MCFVariables *v = new MCFVariables();
/***** generic part ***/
const vector<Instance::Edge> edges = directed_edges(instance.edges);
const u_int n_edges = edges.size();
/* $x_{ij} \in \{0, 1\}$ variables denote whether edge (i, j) is active. */
v->xs = createVarArrayXs(env, edges, n_edges);
/* $v_i \in \{0, 1\}$ variables denote whether node i is active. */
v->vs = createVarArrayVs(env, instance.n_nodes);
/* add objective function */
addObjectiveFunction(env, model, v->xs, edges, n_edges);
/* There are exactly k - 1 edges not counting edges from the artificial root node 0. */
addConstraint_k_minus_one_active_edges(env,model,v->xs,edges,n_edges,this->k);
/* Exactly one node is chosen as the tree root. */
addConstraint_one_active_outgoing_arc_for_node_zero(env,model,v->xs,edges,n_edges);
/* No edge leads back to the artificial root node 0. */
addConstraint_no_active_incoming_arc_for_node_zero(env,model,v->xs,edges,n_edges);
IloExprArray e_in_degree = createExprArray_in_degree(env, edges, n_edges, v->xs, instance);
IloExprArray e_out_degree = createExprArray_out_degree(env, edges, n_edges, v->xs, instance);
/* Inactive nodes have no outgoing active edges, active ones at most k - 1. TODO: A tighter bound is to take the sum of incoming goods - 1.*/
addConstraint_bound_on_outgoing_arcs(model,v->vs,e_out_degree,instance,this->k);
/* Active nodes have at least one active arc.*/
addConstraint_active_node_at_least_one_active_arc(model,v->vs,e_in_degree, e_out_degree,instance);
/* Exactly one incoming edge for an active node and none for an inactive node (omitting artificial root). */
addConstraint_in_degree_one_for_active_node_zero_for_inactive(model,v->vs,e_in_degree,instance);
//note: position matters. Tried worse positions than this one
/* $\sum_{i > 0} v_i = k$. Ensure that exactly k nodes are active. */
addConstraint_k_nodes_active(env, model, v->vs, instance, this->k);
e_in_degree.endElements();
e_out_degree.endElements();
/***** MCF specific part ***/
/* $f^k_{ij} \in \{0, 1\}$ variables denote the flow on edge (i, j) for commodity k. */
for (u_int i = 0; i < instance.n_nodes; i++) {
v->fss.push_back(IloBoolVarArray(env, n_edges));
}
for (u_int k = 0; k < n_edges; k++) {
const u_int i = edges[k].v1;
const u_int j = edges[k].v2;
for (u_int l = 0; l < (u_int) instance.n_nodes; l++) {
v->fss[l][k] = IloBoolVar(env, Tools::indicesToString("f", l, i, j).c_str());
}
}
/*
* Each commodity l is generated once by the artificial root node if node l is active, not at all otherwise:
* $\forall l \in \{1, \ldots, n\}: \sum_{j:j>0,(0,j) \in A} f^l_{0j} == v_l$
*/
for (u_int c = 1; c < instance.n_nodes; c++){
IloExpr e_one_commodity(env);
for (u_int m = 0; m < n_edges; m++) {
const u_int i = edges[m].v1;
const u_int j = edges[m].v2;
if (i == 0 && j > 0){
e_one_commodity += v->fss[c][m];
}
}
model.add(e_one_commodity == v->vs[c]);
e_one_commodity.end();
}
/*
* The artifical root generates k commodities:
* $\forall l \in \{0,\ldots,n\}\sum_{j:j>0,(0,j) \in A} f^l_{0j} = k$.
*/
IloExpr e_root_generates_k(env);
for (u_int c = 0; c < instance.n_nodes; c++){
for (u_int m = 0; m < n_edges; m++) {
const u_int i = edges[m].v1;
const u_int j = edges[m].v2;
if (i == 0 && j > 0){
e_root_generates_k += v->fss[c][m];
}
}
}
model.add(e_root_generates_k == this->k);
e_root_generates_k.end();
/*
* No commodity is generated for the artificial root:
* $\forall i, j: f^0_{ij} = 0$.
*/
for (u_int m = 0; m < n_edges; m++) {
model.add(v->fss[0][m] == 0);
}
/*
* Transmitted commodities end up at the target node:
* $\forall l>0: \sum_i f^l_{il} = \sum_j f^l_{0j}$. (here: = v_l)
*/
for (u_int c = 1; c < (u_int) instance.n_nodes; c++){
IloExpr e_commodity_reaches_target(env);
for (u_int m = 0; m < n_edges; m++) {
const u_int i = edges[m].v1;
const u_int j = edges[m].v2;
if (i != c && j == c){
e_commodity_reaches_target += v->fss[c][m];
}
}
model.add(e_commodity_reaches_target == v->vs[c]);
e_commodity_reaches_target.end();
}
/*
* Once reached, the commodity never leaves the target node:
* $\forall l>0: \sum_j f^l_{lj} = 0$.
*/
for (u_int c = 1; c < (u_int) instance.n_nodes; c++){
IloExpr e_commodity_stays_at_target(env);
for (u_int m = 0; m < n_edges; m++) {
const u_int i = edges[m].v1;
const u_int j = edges[m].v2;
if (i == c && j != c){
e_commodity_stays_at_target += v->fss[c][m];
}
}
model.add(e_commodity_stays_at_target == 0);
e_commodity_stays_at_target.end();
}
/*
* Flow is conserved when not at target node.
* $\forall j, l s.t. j \neq l: \sum_i f^l_{ij} = \sum_i f^l_{ji}$.
*/
for (u_int c = 0; c < (u_int) instance.n_nodes; c++){
IloExprArray e_in_flow(env, instance.n_nodes);
IloExprArray e_out_flow(env, instance.n_nodes);
for (u_int m = 0; m < instance.n_nodes; m++){
e_in_flow[m] = IloExpr(env);
e_out_flow[m] = IloExpr(env);
}
for (u_int m = 0; m < n_edges; m++) {
const u_int i = edges[m].v1;
const u_int j = edges[m].v2;
e_out_flow[i] += v->fss[c][m];
e_in_flow[j] += v->fss[c][m];
}
for (u_int m = 1; m < instance.n_nodes; m++){
if (m != c) {
model.add(e_in_flow[m] == e_out_flow[m]);
}
}
e_in_flow.endElements();
e_out_flow.endElements();
}
/*
* Commodities may only be transmitted on active edges:
* $\forall l, i, j: f^l_{ij} \leq x_{ij}$.
*/
for (u_int c = 0; c < (u_int) instance.n_nodes; c++){
for (u_int m = 0; m < n_edges; m++) {
model.add(v->fss[c][m] <= v->xs[m]);
}
}
/*
* For each commodity l , the total flow is <= k if node l is active, 0 otherwise
* (works well for all before g05, k=n/2 which is a bit slower with this)
*/
for (u_int c = 1; c < (u_int) instance.n_nodes; c++){
IloExpr e_total_flow(env);
for (u_int m = 0; m < n_edges; m++) {
e_total_flow += v->fss[c][m];
}
model.add(e_total_flow <= this->k * v->vs[c]);
e_total_flow.end();
}
return v;
}
