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();
}
public boolean solve(
double[] Pmax,
double[] PregMax,
double[] Emin,
double[] Emax,
int quartersLeftInFirstBid,
int[] bids,
int bidSize,
ArrayList<FlexGraph> flexGraphs) {
double[] Pmin = new double[Pmax.length];
// Pre-process data
if ((Pmin.length - quartersLeftInFirstBid) % 4 != 0) {
int extraQuarters = 4 - ((Pmin.length - quartersLeftInFirstBid) % 4);
Pmin = concat(Pmin, new double[extraQuarters]);
Pmax = concat(Pmax, new double[extraQuarters]);
PregMax = concat(PregMax, new double[extraQuarters]);
double[] endE = new double[extraQuarters];
for (int i = 0; i < endE.length; i++) {
endE[i] = Emin[Emin.length - 1];
}
Emin = concat(Emin, endE);
Emax = concat(Emax, endE);
}
this.quartersLeftInFirstBid = quartersLeftInFirstBid;
// Solve optimization problem
try {
IloCplex cplex = new IloCplex();
// for all evs
ArrayList<IloNumVar[]> flexpowers = new ArrayList<IloNumVar[]>();
ArrayList<IloNumVar[]> flexenergies = new ArrayList<IloNumVar[]>();
for (int i = 0; i < flexGraphs.size(); i++) {
FlexGraph flexGraph = flexGraphs.get(i);
double[] energyMin = convertToDoubles(flexGraph.getEnergyMin());
double[] energyMax = convertToDoubles(flexGraph.getEnergyMax());
double[] powerMax = convertToDoubles(flexGraph.getPowerMax());
// charging power
IloNumVar[] p = cplex.numVarArray(powerMax.length, new double[powerMax.length], powerMax);
// path
IloNumVar[] e = cplex.numVarArray(energyMin.length, energyMin, energyMax);
for (int j = 0; j < p.length; j++) {
cplex.addEq(cplex.diff(e[j + 1], e[j]), cplex.prod(1.0 / 4, p[j]));
}
flexpowers.add(p);
flexenergies.add(e);
}
// total charging power
IloNumVar[] p = cplex.numVarArray(Pmin.length, Pmin, Pmax);
// individual bin constraints
for (int t = 0; t < p.length; t++) {
ArrayList<IloNumVar> tempVars = new ArrayList<IloNumVar>();
for (IloNumVar[] var : flexpowers) {
if (var.length >= t + 1) {
tempVars.add(var[t]);
}
}
IloNumVar[] tempVars_array = new IloNumVar[tempVars.size()];
tempVars.toArray(tempVars_array);
cplex.addEq(p[t], cplex.sum(tempVars_array));
}
// path
IloNumVar[] e = cplex.numVarArray(Emin.length, Emin, Emax);
for (int i = 0; i < p.length; i++) {
cplex.addEq(cplex.diff(e[i + 1], e[i]), cplex.prod(1.0 / 4, p[i]));
}
// Emin < path < Emax
for (int i = 0; i < e.length; i++) {
cplex.addGe(e[i], Emin[i]);
cplex.addLe(e[i], Emax[i]);
}
// regulation power in each optimziation interval
IloNumVar[] regPowerQ = cplex.numVarArray(Pmin.length, Pmin, PregMax);
// calculate regulation power in each optimization interval
for (int i = 0; i < regPowerQ.length; i++) {
cplex.addEq(regPowerQ[i], cplex.diff(PregMax[i], p[i]));
}
// regulation bids in each hour
// 1. max nr of bids per houd
int hours =
(int) Math.ceil(quartersLeftInFirstBid / 4.0)
+ (int) Math.ceil((regPowerQ.length - quartersLeftInFirstBid) / 4.0);
int[] maxNrOfBidsPerHour = new int[hours];
// init with max nr of bids per hour
for (int i = 0; i < maxNrOfBidsPerHour.length; i++) {
maxNrOfBidsPerHour[i] = Integer.MAX_VALUE;
}
if (quartersLeftInFirstBid > 0) {
maxNrOfBidsPerHour[0] = bids[0];
try {
maxNrOfBidsPerHour[1] = bids[1];
} catch (IndexOutOfBoundsException ew) {
System.out.print("Emin = ");
printArray(Emin);
System.out.print("Emax = ");
printArray(Emax);
System.out.print("Pmax = ");
printArray(Pmax);
System.out.println("FirstBidQuarter = " + quartersLeftInFirstBid);
System.out.print("Bids = ");
printArray(bids);
System.out.println("Bidsize = " + bidSize);
}
} else {
maxNrOfBidsPerHour[0] = bids[1];
}
// 2. bids per hour
IloIntVar[] bidsH = cplex.intVarArray(hours, new int[hours], maxNrOfBidsPerHour);
// limit bids by provided regulation power
for (int i = 0; i < regPowerQ.length; i++) {
// convert Q to H
int h = (int) Math.ceil(((i + 1) - quartersLeftInFirstBid) / 4.0);
if (quartersLeftInFirstBid == 0) {
h--;
}
// bidsH*bidSize <= regPowerQ[i]
if (i > 0) {
// reserve some extra regulation power
cplex.addLe(cplex.prod(bidsH[h], bidSize), cplex.prod(0.95, regPowerQ[i]));
} else {
cplex.addLe(cplex.prod(bidsH[h], bidSize), cplex.prod(1, regPowerQ[i]));
}
// System.out.println("h = " + h + ", i=" + i);
}
// create model and solve it
// cplex.addMaximize(cplex.scalProd(p,prices));
double[] rewards = new double[bidsH.length];
// init to rewards = 1 for all, but two first hours
for (int i = 0; i < rewards.length; i++) {
rewards[i] = 1;
}
rewards[0] = 100;
if (rewards.length > 1) {
rewards[1] = 100;
}
IloLinearNumExpr maximization = cplex.scalProd(bidsH, rewards);
IloObjective maxObjective = cplex.addMaximize(maximization);
cplex.setOut(null);
cplex.solve();
// if(cplex.solve()) {
// cplex.output().println("Solution status = " + cplex.getStatus());
// cplex.output().println("Solution value = " + cplex.getObjValue());
//
// System.out.print("Emin = ");
// printArray(Emin);
//
// System.out.print("Emax = ");
// printArray(Emax);
//
// System.out.print("Pmax = ");
// printArray(Pmax);
//
// powerPath = cplex.getValues(p);
// System.out.print("Power = ");
// printArray(powerPath);
//
// energyPath = cplex.getValues(e);
// System.out.print("Energy = ");
// printArray(energyPath);
//
// regPower = cplex.getValues(regPowerQ);
// System.out.print("RegPower = ");
// printArray(regPower);
//
// bidsN = new int[bidsH.length];
// for(int i = 0; i < bidsN.length; i++) {
// bidsN[i] = (int) Math.round(cplex.getValue(bidsH[i]));
// }
// shift bids right if no quarter left in current bid slot -- hack-ish
if (quartersLeftInFirstBid == 0) {
bidsN = concat(new int[1], bidsN);
}
//
// System.out.print("Bids = ");
// printArray(bidsN);
//
// this.bidSize = bidSize;
// }
// stage two
// System.out.println((int) );
// System.out.println("sum = " + cplex.getValue(cplex.sum(bidsH)));
// System.out.println(bidsH[0].getUB());;
// System.out.println((int) Math.round(cplex.getValue(bidsH[0])));
// bidsH[0].setMin((int) Math.round(cplex.getValue(bidsH[0])));
// .setUB(cplex.getValue(bidsH[0]));
// cplex.addEq(bidsH[1], (int) Math.round(cplex.getValue(bidsH[1])));
// cplex.addGe(bidsH[1], (int) Math.round(cplex.getValue(bidsH[1])));
double bid1 = cplex.getValue(bidsH[0]);
double bid2 = 0;
if (bidsH.length > 1) {
bid2 = cplex.getValue(bidsH[1]);
}
int totalBids = 0;
for (int i = 0; i < bidsH.length; i++) {
totalBids = totalBids + (int) Math.round(cplex.getValue(bidsH[i]));
}
cplex.addGe(cplex.sum(bidsH), totalBids);
cplex.addLe(bid1, bidsH[0]);
// cplex.getValue(bidsH[1]);
if (bidsH.length > 1) {
cplex.addLe(bid2, bidsH[1]);
}
cplex.remove(maxObjective);
IloQuadNumExpr minimization = cplex.quadNumExpr();
double[] coeff = new double[p.length];
for (int i = 0; i < p.length; i++) {
coeff[i] = 1;
}
minimization.addTerms(coeff, p, p);
cplex.addMinimize(minimization);
cplex.setOut(null);
if (cplex.solve()) {
// cplex.output().println("Solution status = " + cplex.getStatus());
// cplex.output().println("Solution value = " + cplex.getObjValue());
//
// System.out.print("Emin = ");
// printArray(Emin);
//
// System.out.print("Emax = ");
// printArray(Emax);
//
// System.out.print("Pmax = ");
// printArray(Pmax);
//
powerPath = cplex.getValues(p);
System.out.print("Power = ");
printArray(powerPath);
energyPath = cplex.getValues(e);
// System.out.print("Energy = ");
// printArray(energyPath);
regPower = cplex.getValues(regPowerQ);
System.out.print("RegPower = ");
printArray(regPower);
bidsN = new int[bidsH.length];
for (int i = 0; i < bidsN.length; i++) {
bidsN[i] = (int) Math.round(cplex.getValue(bidsH[i]));
}
// shift bids right if no quarter left in current bid slot -- hack-ish
if (quartersLeftInFirstBid == 0) {
bidsN = concat(new int[1], bidsN);
}
System.out.print("Bids = ");
printArray(bidsN);
this.bidSize = bidSize;
}
for (int i = 0; i < flexpowers.size(); i++) {
flexGraphs.get(i).setSolutionPath(cplex.getValues(flexenergies.get(i)));
}
return true;
} catch (IloException e) {
System.err.println("Concert exception caught: " + e);
e.printStackTrace();
return false;
}
}
