public TrafficNetworkModel
(int numberOfNodes,
int source_idx,
int sink_idx,
int[] arc_i,
int[] arc_j,
double[] arcSensitivity,
double[] arcCapacity,
double[] arcBaseTravelTime,
double T) :
base("Traffic Network")
{
bool finished = false;
try
{
int n = numberOfNodes;
int narcs = arc_j.Length;
double[] n_ones = new double[narcs]; for (int i = 0; i < narcs; ++i)
{
n_ones[i] = 1.0;
}
Set NxN = new NDSet(new int[] { 0, 0 },
new int[] { n, n });
Matrix sens =
Matrix.Sparse(n, n, arc_i, arc_j, arcSensitivity);
Matrix cap =
Matrix.Sparse(n, n, arc_i, arc_j, arcCapacity);
Matrix basetime =
Matrix.Sparse(n, n, arc_i, arc_j, arcBaseTravelTime);
Matrix e =
Matrix.Sparse(n, n, arc_i, arc_j, n_ones);
Matrix e_e =
Matrix.Sparse(n, n,
new int[] { sink_idx }, new int[] { source_idx },
new double[] { 1.0 });
double[] cs_inv = new double[narcs];
double[] s_inv = new double[narcs];
for (int i = 0; i < narcs; ++i)
{
cs_inv[i] = 1.0 / (arcSensitivity[i] * arcCapacity[i]);
}
for (int i = 0; i < narcs; ++i)
{
s_inv[i] = 1.0 / arcSensitivity[i];
}
Matrix cs_inv_matrix = Matrix.Sparse(n, n, arc_i, arc_j, cs_inv);
Matrix s_inv_matrix = Matrix.Sparse(n, n, arc_i, arc_j, s_inv);
flow = Variable("traffic_flow", NxN, Domain.GreaterThan(0.0));
Variable x = flow;
Variable t = Variable("travel_time", NxN, Domain.GreaterThan(0.0));
Variable d = Variable("d", NxN, Domain.GreaterThan(0.0));
Variable z = Variable("z", NxN, Domain.GreaterThan(0.0));
// Set the objective:
Objective(ObjectiveSense.Minimize,
Expr.Mul(1.0 / T, Expr.Add(Expr.Dot(basetime, x), Expr.Dot(e, d))));
// Set up constraints
// Constraint (1a)
{
Variable[][] v = new Variable[narcs][];
for (int i = 0; i < narcs; ++i)
{
v[i] = new Variable[3] {
d.Index(arc_i[i], arc_j[i]),
z.Index(arc_i[i], arc_j[i]),
x.Index(arc_i[i], arc_j[i])
};
}
Constraint(mosek.fusion.Variable.Stack(v), Domain.InRotatedQCone(narcs, 3));
}
// Constraint (1b)
Constraint(Expr.Sub(Expr.Add(z, Expr.MulElm(x, cs_inv_matrix)), s_inv_matrix),
Domain.EqualsTo(0.0));
// Constraint (2)
Constraint(Expr.Sub(Expr.Add(Expr.MulDiag(x, e.Transpose()),
Expr.MulDiag(x, e_e.Transpose())),
Expr.Add(Expr.MulDiag(x.Transpose(), e),
Expr.MulDiag(x.Transpose(), e_e))),
Domain.EqualsTo(0.0));
// Constraint (3)
Constraint(x.Index(sink_idx, source_idx), Domain.EqualsTo(T));
finished = true;
}
finally
{
if (!finished)
{
Dispose();
}
}
}
public TrafficNetworkModel
( int numberOfNodes,
int source_idx,
int sink_idx,
int[] arc_i,
int[] arc_j,
double[] arcSensitivity,
double[] arcCapacity,
double[] arcBaseTravelTime,
double T) :
base("Traffic Network")
{
bool finished = false;
try
{
int n = numberOfNodes;
int narcs = arc_j.Length;
double[] n_ones = new double[narcs]; for (int i = 0; i < narcs; ++i) n_ones[i] = 1.0;
Set NxN = new NDSet(new int[] { 0, 0 },
new int[] { n, n});
Matrix sens =
Matrix.Sparse(n, n, arc_i, arc_j, arcSensitivity);
Matrix cap =
Matrix.Sparse(n, n, arc_i, arc_j, arcCapacity);
Matrix basetime =
Matrix.Sparse(n, n, arc_i, arc_j, arcBaseTravelTime);
Matrix e =
Matrix.Sparse(n, n, arc_i, arc_j, n_ones);
Matrix e_e =
Matrix.Sparse(n,n,
new int[] { sink_idx}, new int[] { source_idx},
new double[] { 1.0 });
double[] cs_inv = new double[narcs];
double[] s_inv = new double[narcs];
for (int i = 0; i < narcs; ++i) cs_inv[i] = 1.0 / (arcSensitivity[i] * arcCapacity[i]);
for (int i = 0; i < narcs; ++i) s_inv[i] = 1.0 / arcSensitivity[i];
Matrix cs_inv_matrix = Matrix.Sparse(n, n, arc_i, arc_j, cs_inv);
Matrix s_inv_matrix = Matrix.Sparse(n, n, arc_i, arc_j, s_inv);
flow = Variable("traffic_flow", NxN, Domain.GreaterThan(0.0));
Variable x = flow;
Variable t = Variable("travel_time", NxN, Domain.GreaterThan(0.0));
Variable d = Variable("d", NxN, Domain.GreaterThan(0.0));
Variable z = Variable("z", NxN, Domain.GreaterThan(0.0));
// Set the objective:
Objective(ObjectiveSense.Minimize,
Expr.Mul(1.0/T, Expr.Add(Expr.Dot(basetime,x), Expr.Dot(e,d))));
// Set up constraints
// Constraint (1a)
{
Variable[][] v = new Variable[narcs][];
for (int i = 0; i < narcs; ++i)
{
v[i] = new Variable[3] { d.Index(arc_i[i],arc_j[i]),
z.Index(arc_i[i],arc_j[i]),
x.Index(arc_i[i],arc_j[i]) };
}
Constraint(mosek.fusion.Variable.Stack(v),Domain.InRotatedQCone(narcs,3));
}
// Constraint (1b)
Constraint(Expr.Sub(Expr.Add(z,Expr.MulElm(x,cs_inv_matrix)),s_inv_matrix),
Domain.EqualsTo(0.0));
// Constraint (2)
Constraint(Expr.Sub(Expr.Add(Expr.MulDiag(x, e.Transpose()),
Expr.MulDiag(x, e_e.Transpose())),
Expr.Add(Expr.MulDiag(x.Transpose(), e),
Expr.MulDiag(x.Transpose(), e_e))),
Domain.EqualsTo(0.0));
// Constraint (3)
Constraint(x.Index(sink_idx, source_idx), Domain.EqualsTo(T));
finished = true;
}
finally
{
if (!finished)
Dispose();
}
}
