public double solve(Instance ins, Solution sol, int timeout) throws IloException {
IloCplex solver = new IloCplex();
BiIndexedIntVarMap y = new BiIndexedIntVarMap(solver, 0, 1, "y"); // (k,v) (cluster,node)
IndexedNumVarMap d =
new IndexedNumVarMap(solver, 0, Double.MAX_VALUE, "dp"); // (k) (cluster)
TriIndexedNumVarMap f =
new TriIndexedNumVarMap(solver, 0, Double.MAX_VALUE, "f"); // (k,i,j) (cluster,tail,head)
BiIndexedIntVarMap r = new BiIndexedIntVarMap(solver, 0, 1, "r"); // (k,i) (cluster,node
BiIndexedNumVarMap w = new BiIndexedNumVarMap(solver, 0, 1, "w"); // (i,j) (node1<node2)
int superRoot = ins.getNumNodes();
// compute the weights of the objective function
double w1 = ins.getW1() / ins.getNumNodes();
double w2 = ins.getW2() / (ins.getLambda() * ins.getMaxClusterNumber());
double w3 =
2
* ins.getW3()
/ (ins.getNumNodes() * (ins.getNumNodes() - 1) * (ins.getDMax() - ins.getDMin()));
Set<OrderedPair> fp = new TreeSet<OrderedPair>(ins.getP());
if (isActiveExtension(Extension.PFILTER)) {
fp = ins.filterP();
System.out.println("PFILTER: " + (ins.getP().size() - fp.size()) + " pairs filtered");
}
// compute the objective function expression
IloNumExpr expr = solver.numExpr();
// O1
IloNumExpr exprO1 = solver.numExpr();
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.numExpr();
expr = solver.sum(expr, 1);
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) expr = solver.diff(expr, y.get(k, i));
exprO1 = solver.sum(exprO1, solver.prod(w1, expr));
}
// O2
IloNumExpr exprO2 = solver.numExpr();
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
exprO2 = solver.sum(exprO2, solver.prod(w2, d.get(k)));
}
// O3
IloNumExpr exprO3 = solver.numExpr();
for (OrderedPair p : fp) {
double dmax = ins.getDMax();
double dist = ins.getD(p.i, p.j);
IloNumVar wvar = w.get(p.i, p.j);
exprO3 = solver.sum(exprO3, solver.prod(w3 * (dmax - dist), wvar));
}
expr = solver.sum(exprO1, solver.sum(exprO2, exprO3));
solver.add(solver.objective(IloObjectiveSense.Minimize, expr));
// packing constraints
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.numExpr();
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) expr = solver.sum(expr, y.get(k, i));
solver.addLe(expr, 1);
}
// root uniqueness constraints
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
expr = solver.numExpr();
for (int i = 0; i < ins.getNumNodes(); ++i) expr = solver.sum(expr, r.get(k, i));
solver.addLe(expr, 1);
}
// f,y linking constraints
// OUT
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.numExpr();
for (Integer j : ins.getOutcut(i)) {
expr = solver.sum(expr, f.get(k, i, j));
}
expr = solver.diff(expr, solver.prod(ins.getMaxClusterSize() - 2, y.get(k, i)));
solver.addLe(expr, 0);
}
}
// f,r linking constraints
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (int i = 0; i < ins.getNumNodes(); ++i) {
solver.addLe(f.get(k, superRoot, i), solver.prod(ins.getMaxClusterSize(), r.get(k, i)));
}
}
// //flow generation constraints
// for(int k=0;k<ins.getMaxClusterNumber();++k){
// expr=solver.numExpr();
// for(int i=0;i<ins.getNumNodes();++i){
// expr=solver.sum(expr,f.get(k,superRoot,i));
// expr=solver.diff(expr, y.get(k, i));
// }
// solver.addEq(expr, 0);
// }
// flow conservation constraints
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.numExpr();
for (Integer j : ins.getOutcut(i)) {
expr = solver.diff(expr, f.get(k, i, j));
expr = solver.sum(expr, f.get(k, j, i));
}
// i can receive flow also from the super root
expr = solver.sum(expr, f.get(k, superRoot, i));
solver.addEq(expr, y.get(k, i));
}
}
// delta definition constraints
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
expr = solver.numExpr();
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.sum(expr, y.get(k, i));
}
solver.addLe(solver.diff(expr, ins.getLambda()), d.get(k));
solver.addGe(solver.diff(expr, ins.getLambda()), solver.prod(-1, d.get(k)));
}
// w var definition constraints
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (OrderedPair p : fp) {
expr = solver.numExpr();
expr = solver.sum(expr, w.get(p.i, p.j));
expr = solver.diff(expr, y.get(k, p.i));
expr = solver.diff(expr, y.get(k, p.j));
expr = solver.sum(expr, 1);
solver.addGe(expr, 0);
}
}
if (isActiveExtension(Extension.ROOT_MINIMIZATION_CONSTRAINTS)) {
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (OrderedPair p : fp) {
expr = solver.sum(y.get(k, p.i), r.get(k, p.j));
solver.addLe(expr, 1);
}
}
}
if (isActiveExtension(Extension.POLYNOMIAL_ORBITOPE)) {
// first family
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
expr = solver.numExpr();
for (int v = 0; v <= k - 1; ++v) {
expr = solver.sum(expr, y.get(k, v));
}
solver.addEq(expr, 0);
}
// second family
for (int k = 1; k < ins.getMaxClusterNumber(); ++k) {
for (int v = k; v < ins.getNumNodes(); ++v) {
expr = solver.numExpr();
expr = solver.sum(expr, y.get(k, v));
for (int u = k - 1; u <= v - 1; ++u) {
expr = solver.diff(expr, y.get(k - 1, u));
}
solver.addLe(expr, 0);
}
}
}
if (isActiveExtension(Extension.EXPONENTIAL_ORBITOPE)) {
System.err.println("Extension " + Extension.EXPONENTIAL_ORBITOPE + " not implemented yet");
throw new IllegalArgumentException();
}
if (isActiveExtension(Extension.FLOW_LB)) {
// f,x lower bound
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (int i = 0; i < ins.getNumNodes(); ++i) {
expr = solver.numExpr();
for (Integer j : ins.getOutcut(i)) {
expr = solver.sum(expr, f.get(k, j, i));
}
expr = solver.sum(expr, f.get(k, superRoot, i));
solver.addGe(expr, y.get(k, i));
solver.addLe(r.get(k, i), f.get(k, superRoot, i));
}
}
}
solver.setParam(IloCplex.DoubleParam.TiLim, timeout);
if (isActiveExtension(Extension.ROOT_BRANCHING_PRIORITY)) {
// Add branching priorities to the root variables
for (int k = 0; k < ins.getMaxClusterNumber(); ++k)
for (int i = 0; i < ins.getNumNodes(); ++i) solver.setPriority(r.get(k, i), 100);
}
solver.setParam(IloCplex.IntParam.ParallelMode, 1);
solver.solve();
System.out.println("STATE=" + solver.getStatus());
System.out.println("NN=" + solver.getNnodes());
System.out.println("LB=" + solver.getBestObjValue());
// If we have a feasible solution we save it
if (solver.getStatus() == IloCplex.Status.Feasible
|| solver.getStatus() == IloCplex.Status.Optimal) {
for (int k = 0; k < ins.getMaxClusterNumber(); ++k) {
for (int v = 0; v < ins.getNumNodes(); ++v) {
if (FloatUtils.eq(solver.getValue(y.get(k, v)), 1.0)) {
sol.insert(k, v);
}
}
}
}
return solver.getObjValue();
}
