internal static void BuildModelByRow(IModeler model,
Data data,
INumVar[] Buy,
NumVarType type)
{
int nFoods = data.nFoods;
int nNutrs = data.nNutrs;
for (int j = 0; j < nFoods; j++)
{
Buy[j] = model.NumVar(data.foodMin[j], data.foodMax[j], type);
}
model.AddMinimize(model.ScalProd(data.foodCost, Buy));
for (int i = 0; i < nNutrs; i++)
{
model.AddRange(data.nutrMin[i],
model.ScalProd(data.nutrPerFood[i], Buy),
data.nutrMax[i]);
}
}
internal static void BuildModelByRow(IModeler model,
Data data,
INumVar[] Buy,
NumVarType type) {
int nFoods = data.nFoods;
int nNutrs = data.nNutrs;
for (int j = 0; j < nFoods; j++) {
Buy[j] = model.NumVar(data.foodMin[j], data.foodMax[j], type);
}
model.AddMinimize(model.ScalProd(data.foodCost, Buy));
for (int i = 0; i < nNutrs; i++) {
model.AddRange(data.nutrMin[i],
model.ScalProd(data.nutrPerFood[i], Buy),
data.nutrMax[i]);
}
}
// The following method populates the problem with data for the
// following linear program:
//
// Maximize
// x1 + 2 x2 + 3 x3
// Subject To
// - x1 + x2 + x3 <= 20
// x1 - 3 x2 + x3 <= 30
// Bounds
// 0 <= x1 <= 40
// End
//
// using the IModeler API
internal static void PopulateByRow(IModeler model,
INumVar[][] var,
IRange[][] rng)
{
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, System.Double.MaxValue, System.Double.MaxValue };
string[] varname = { "x1", "x2", "x3" };
INumVar[] x = model.NumVarArray(3, lb, ub, varname);
var[0] = x;
double[] objvals = { 1.0, 2.0, 3.0 };
model.AddMaximize(model.ScalProd(x, objvals));
rng[0] = new IRange[2];
rng[0][0] = model.AddLe(model.Sum(model.Prod(-1.0, x[0]),
model.Prod(1.0, x[1]),
model.Prod(1.0, x[2])), 20.0, "c1");
rng[0][1] = model.AddLe(model.Sum(model.Prod(1.0, x[0]),
model.Prod(-3.0, x[1]),
model.Prod(1.0, x[2])), 30.0, "c2");
}
} // END WorkerLP
// This method creates the master ILP (arc variables x and degree constraints).
//
// Modeling variables:
// forall (i,j) in A:
// x(i,j) = 1, if arc (i,j) is selected
// = 0, otherwise
//
// Objective:
// minimize sum((i,j) in A) c(i,j) * x(i,j)
//
// Degree constraints:
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
//
// Binary constraints on arc variables:
// forall (i,j) in A: x(i,j) in {0, 1}
//
internal static void CreateMasterILP(IModeler model,
Data data,
IIntVar[][] x)
{
int i, j;
int numNodes = data.numNodes;
// Create variables x(i,j) for (i,j) in A
// For simplicity, also dummy variables x(i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
for (i = 0; i < numNodes; ++i)
{
x[i] = new IIntVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
x[i][j] = model.BoolVar("x." + i + "." + j);
model.Add(x[i][j]);
}
x[i][i].UB = 0;
}
// Create objective function: minimize sum((i,j) in A ) c(i,j) * x(i,j)
ILinearNumExpr objExpr = model.LinearNumExpr();
for (i = 0; i < numNodes; ++i)
{
objExpr.Add(model.ScalProd(x[i], data.arcCost[i]));
}
model.AddMinimize(objExpr);
// Add the out degree constraints.
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
model.AddEq(expr, 1.0);
}
// Add the in degree constraints.
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
model.AddEq(expr, 1.0);
}
} // END CreateMasterILP
// The following method populates the problem with data for the
// following linear program:
//
// Maximize
// x1 + 2 x2 + 3 x3
// Subject To
// - x1 + x2 + x3 <= 20
// x1 - 3 x2 + x3 <= 30
// Bounds
// 0 <= x1 <= 40
// End
//
// using the IModeler API
internal static void PopulateByRow(IModeler model,
INumVar[][] var,
IRange[][] rng)
{
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
string[] varname = {"x1", "x2", "x3"};
INumVar[] x = model.NumVarArray(3, lb, ub, varname);
var[0] = x;
double[] objvals = {1.0, 2.0, 3.0};
model.AddMaximize(model.ScalProd(x, objvals));
rng[0] = new IRange[2];
rng[0][0] = model.AddLe(model.Sum(model.Prod(-1.0, x[0]),
model.Prod( 1.0, x[1]),
model.Prod( 1.0, x[2])), 20.0, "c1");
rng[0][1] = model.AddLe(model.Sum(model.Prod( 1.0, x[0]),
model.Prod(-3.0, x[1]),
model.Prod( 1.0, x[2])), 30.0, "c2");
}
// This method creates the master ILP (arc variables x and degree constraints).
//
// Modeling variables:
// forall (i,j) in A:
// x(i,j) = 1, if arc (i,j) is selected
// = 0, otherwise
//
// Objective:
// minimize sum((i,j) in A) c(i,j) * x(i,j)
//
// Degree constraints:
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
//
// Binary constraints on arc variables:
// forall (i,j) in A: x(i,j) in {0, 1}
//
internal static void CreateMasterILP(IModeler model,
Data data,
IIntVar[][] x)
{
int i, j;
int numNodes = data.numNodes;
// Create variables x(i,j) for (i,j) in A
// For simplicity, also dummy variables x(i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
for (i = 0; i < numNodes; ++i)
{
x[i] = new IIntVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
x[i][j] = model.BoolVar("x." + i + "." + j);
model.Add(x[i][j]);
}
x[i][i].UB = 0;
}
// Create objective function: minimize sum((i,j) in A ) c(i,j) * x(i,j)
ILinearNumExpr objExpr = model.LinearNumExpr();
for (i = 0; i < numNodes; ++i)
objExpr.Add(model.ScalProd(x[i], data.arcCost[i]));
model.AddMinimize(objExpr);
// Add the out degree constraints.
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j) expr.AddTerm(x[i][j], 1.0);
for (j = i + 1; j < numNodes; ++j) expr.AddTerm(x[i][j], 1.0);
model.AddEq(expr, 1.0);
}
// Add the in degree constraints.
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j) expr.AddTerm(x[j][i], 1.0);
for (j = i + 1; j < numNodes; ++j) expr.AddTerm(x[j][i], 1.0);
model.AddEq(expr, 1.0);
}
}