public void BuildRMP(List <Pairing> initialPathSet)
{
//GetCoverMatrix()
INumExpr obj_expr = RMP.NumExpr();
foreach (Pairing path in initialPathSet)
{
if (path.Route.Count <= 2)
{
continue;
}
ColumnPool.Add(path);
//create obj function
INumVar x = RMP.NumVar(0, 1, NumVarType.Float);
DvarSet.Add(x);
obj_expr = RMP.Sum(obj_expr, RMP.Prod(path.Cost_with_penalty, x));
CoverMatrix.Add(path.CoverAaray);
}
RMP.AddObjective(ObjectiveSense.Minimize, obj_expr);
//s.t
for (int i = 0; i < num_task; i++)
{
INumExpr ct = RMP.NumExpr();
for (int j = 0; j < DvarSet.Count; j++)
{
ct = RMP.Sum(ct,
RMP.Prod(CoverMatrix[j][i], DvarSet[j]));
}
constraints[i] = RMP.AddGe(ct, 1);
}
}
void AddColumnsToRMP(List <Pairing> newPaths)
{
foreach (var path in newPaths)
{
if (path.Price > 0 && checkExsitColumn(ColumnPool, path))
{
continue;
}
ColumnPool.Add(path);
INumVar new_col = RMP.NumVar(0, 1, NumVarType.Float);
//renew obj
RMP.GetObjective().Expr = RMP.Sum(RMP.GetObjective().Expr,
RMP.Prod(path.Cost_with_penalty, new_col));
//renew ct
for (int i = 0; i < num_task; i++)
{
constraints[i].Expr = RMP.Sum(constraints[i].Expr,
RMP.Prod(path.CoverAaray[i], new_col));
}
DvarSet.Add(new_col);
}
}
private void initializeNumericVariables(Cplex plex, VariabilityModel vm)
{
foreach (NumericOption numOpt in vm.NumericOptions)
{
// Initialize with the numeric options as numeric variables with a range from min to max
INumVar curr = plex.NumVar(numOpt.Min_value, numOpt.Max_value, NumVarType.Float);
/* plex.IfThen(
* plex.Eq(binOptsToCplexVars[vm.Root], 1),
* plex.Or(new IConstraint[] { plex.Ge(curr, numOpt.Min_value),
* plex.Le(curr, numOpt.Max_value)}
* )
* ); */
numOptsToCplexVars[numOpt] = curr;
List <double> values = numOpt.getAllValues();
IConstraint[] valueSet = new IConstraint[values.Count];
// Limit the values numeric options can have to the precomputed valid values
for (int i = 0; i < values.Count; i++)
{
valueSet[i] = plex.Eq(curr, values.ElementAt(i));
}
plex.Add(plex.Or(valueSet));
}
}
// Step 7
public static void Main(string[] args)
{
if ( args.Length != 1 || args[0].ToCharArray()[0] != '-' ) {
Usage();
return;
}
try {
//Step 3
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
// Step 8
// Step 11
// Step 9
// Step 10
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
}
// Step 7
public static void Main(string[] args)
{
if (args.Length != 1 || args[0].ToCharArray()[0] != '-')
{
Usage();
return;
}
try {
//Step 3
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
// Step 8
// Step 11
// Step 9
// Step 10
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
}
internal static void PopulateByRow (IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
// First define the variables, three continuous and one integer
double[] xlb = {0.0, 0.0, 0.0, 2.0};
double[] xub = {40.0, System.Double.MaxValue,
System.Double.MaxValue, 3.0};
NumVarType[] xt = {NumVarType.Float, NumVarType.Float,
NumVarType.Float, NumVarType.Int};
INumVar[] x = model.NumVarArray(4, xlb, xub, xt);
var[0] = x;
// Objective Function: maximize x0 + 2*x1 + 3*x2 + x3
double[] objvals = {1.0, 2.0, 3.0, 1.0};
model.AddMaximize(model.ScalProd(x, objvals));
// Three constraints
rng[0] = new IRange[3];
// - x0 + x1 + x2 + 10*x3 <= 20
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]),
model.Prod(10.0, x[3])), 20.0);
// x0 - 3*x1 + x2 <= 30
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);
// x1 - 3.5*x3 = 0
rng[0][2] = model.AddEq(model.Sum(model.Prod( 1.0, x[1]),
model.Prod(-3.5, x[3])), 0.0);
}
public static Cplex BuildLPModel(IFTMDP Ida)
{
Cplex model = new Cplex();
INumVar[][] v = new INumVar[Ida.TimeHorizon][]; //V(t,x)
for (int t = 0; t < Ida.TimeHorizon; t++)
{
v[t] = model.NumVarArray(Ida.SS.Count, -double.MaxValue, double.MaxValue);
}
IObjective RevenueUB = model.AddMinimize(model.Prod(1, v[0][Ida.SS.IndexOf(Ida.InitialState)]));
//time->State->Active-> Expression
for (int t = 0; t < Ida.TimeHorizon; t++)
{
foreach (IMDPState s in Ida.SS)
{
foreach (IMDPDecision a in Ida.GenDecisionSpace(s))
{
INumExpr expr = v[t][Ida.SS.IndexOf(s)];
if (t < Ida.TimeHorizon - 1)
{
foreach (IMDPState k in Ida.GenStateSpace(s, a))
{
expr = model.Sum(expr,
model.Prod(-Ida.Prob(t, s, k, a), v[t + 1][Ida.SS.IndexOf(k)]));
}
}
model.AddGe(expr, Ida.Reward(t, s, a));
}
}
}
//model.SetOut(null);
return(model);
}
public static void Main(string[] args) {
try {
Cplex cplex = new Cplex();
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow(cplex, var, rng);
if ( cplex.Solve() ) {
double[] x = cplex.GetValues(var[0]);
double[] slack = cplex.GetSlacks(rng[0]);
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
for (int j = 0; j < x.Length; ++j) {
System.Console.WriteLine("Variable " + j +
": Value = " + x[j]);
}
for (int i = 0; i < slack.Length; ++i) {
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i]);
}
}
cplex.ExportModel("mipex1.lp");
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught '" + e + "' caught");
}
}
private void initializeMinMaxObjective(VariabilityModel vm, Cplex plex, bool minimize,
List <BinaryOption> wanted, List <BinaryOption> unwanted)
{
INumVar[] variables = new INumVar[vm.BinaryOptions.Count];
double[] weights = new double[vm.BinaryOptions.Count];
for (int i = 0; i < vm.BinaryOptions.Count; i++)
{
BinaryOption curr = vm.BinaryOptions.ElementAt(i);
variables[i] = binOptsToCplexVars[curr];
if (wanted != null && wanted.Contains(curr))
{
weights[i] = -100.0;
}
else if (unwanted != null && unwanted.Contains(curr))
{
weights[i] = 1000.0;
}
else
{
weights[i] = minimize ? 100.0 : -100.0;
}
}
ILinearNumExpr weightedVariables = plex.ScalProd(variables, weights);
IObjective objective = plex.Minimize(weightedVariables);
plex.Add(objective);
}
internal static void PopulateByColumn(IMPModeler model,
INumVar[][] var,
IRange[][] rng)
{
IObjective obj = model.AddMaximize();
rng[0] = new IRange[2];
rng[0][0] = model.AddRange(-System.Double.MaxValue, 20.0, "c1");
rng[0][1] = model.AddRange(-System.Double.MaxValue, 30.0, "c2");
IRange r0 = rng[0][0];
IRange r1 = rng[0][1];
var[0] = new INumVar[3];
var[0][0] = model.NumVar(model.Column(obj, 1.0).And(
model.Column(r0, -1.0).And(
model.Column(r1, 1.0))),
0.0, 40.0, "x1");
var[0][1] = model.NumVar(model.Column(obj, 2.0).And(
model.Column(r0, 1.0).And(
model.Column(r1, -3.0))),
0.0, System.Double.MaxValue, "x2");
var[0][2] = model.NumVar(model.Column(obj, 3.0).And(
model.Column(r0, 1.0).And(
model.Column(r1, 1.0))),
0.0, System.Double.MaxValue, "x3");
}
public static void Main(string[] args) {
if ( args.Length != 1 || args[0].ToCharArray()[0] != '-' ) {
Usage();
return;
}
try {
// Create the modeler/solver object
Cplex cplex = new Cplex();
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
// Evaluate command line option and call appropriate populate method.
// The created ranges and variables are returned as element 0 of arrays
// var and rng.
switch ( args[0].ToCharArray()[1] ) {
case 'r': PopulateByRow(cplex, var, rng);
break;
case 'c': PopulateByColumn(cplex, var, rng);
break;
case 'n': PopulateByNonzero(cplex, var, rng);
break;
default: Usage();
return;
}
// write model to file
cplex.ExportModel("lpex1.lp");
// solve the model and display the solution if one was found
if ( cplex.Solve() ) {
double[] x = cplex.GetValues(var[0]);
double[] dj = cplex.GetReducedCosts(var[0]);
double[] pi = cplex.GetDuals(rng[0]);
double[] slack = cplex.GetSlacks(rng[0]);
cplex.Output().WriteLine("Solution status = " + cplex.GetStatus());
cplex.Output().WriteLine("Solution value = " + cplex.ObjValue);
int nvars = x.Length;
for (int j = 0; j < nvars; ++j) {
cplex.Output().WriteLine("Variable " + j +
": Value = " + x[j] +
" Reduced cost = " + dj[j]);
}
int ncons = slack.Length;
for (int i = 0; i < ncons; ++i) {
cplex.Output().WriteLine("Constraint " + i +
": Slack = " + slack[i] +
" Pi = " + pi[i]);
}
}
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
}
private void AddCplexLEqual(Cplex model, dc_FGPair fg, INumVar slack)
{
INumExpr fi = fg.f.AddExpression(model);
INumExpr gi = fg.g.Minorize(model);
model.AddLe(fi, model.Sum(gi, slack));
}
protected void AddCol(int t, IALPDecision a)//Add a column into RMP model
{
if (var[t].ContainsKey(a))
{
return;
}
//目标函数
Column col = RMPModel.Column(cost, Data.Rt(t, a));
//第一类约束
foreach (IALPResource re in Data.RS)
{
for (int k = t + 1; k < Data.TimeHorizon; k++)
{
col = col.And(RMPModel.Column(constraint1[k][Data.RS.IndexOf(re)], Data.Qti(t, re, a)));
}
if (a.UseResource(re))
{
col = col.And(RMPModel.Column(constraint1[t][Data.RS.IndexOf(re)], 1));
}
}
//第二类约束
col = col.And(RMPModel.Column(constraint2[t], 1));
INumVar v = RMPModel.NumVar(col, 0, 1, NumVarType.Float);
var[t].Add(a, v);
}
static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, Double.MaxValue, Double.MaxValue };
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
INumVar y = model.IntVar(model.Column(lp), 0, 3);
// - x0 + x1 + x2 + 10*y <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = { -Double.MaxValue, -Double.MaxValue };
double[] rhs = { 20.0, 30.0 };
double[][] val = { new double[] { -1.0, 1.0, 1.0, 10.0 },
new double[] { 1.0, -3.0, 1.0 } };
int[][] ind = { new int[] { 0, 1, 2, 3 },
new int[] { 0, 1, 2 } };
lp.AddRows(lhs, rhs, ind, val);
// x1 + 3.5*y = 0
lp.AddRow(model.Eq(model.Diff(x[1], model.Prod(3.5, y)), 0.0));
// Q = 0.5 ( 33*x0*x0 + 22*x1*x1 + 11*x2*x2 - 12*x0*x1 - 23*x1*x2 )
INumExpr x00 = model.Prod(33.0, model.Square(x[0]));
INumExpr x11 = model.Prod(22.0, model.Square(x[1]));
INumExpr x22 = model.Prod(11.0, model.Square(x[2]));
INumExpr x01 = model.Prod(-12.0, model.Prod(x[0], x[1]));
INumExpr x12 = model.Prod(-23.0, model.Prod(x[1], x[2]));
INumExpr Q = model.Prod(0.5, model.Sum(x00, x11, x22, x01, x12));
// maximize x0 + 2*x1 + 3*x2 + Q
double[] objvals = { 1.0, 2.0, 3.0 };
model.Add(model.Maximize(model.Diff(model.ScalProd(x, objvals), Q)));
return(lp);
}
//void RecordFeasibleSolution(TreeNode node, ref List<int> best_feasible_solution)
//{
// best_feasible_solution.Clear(); //找到更好的可行解了，不需要之前的了
// ///方式2
// //已分支的变量固定为 1，直接添加
// foreach (var v in node.fixing_vars)
// {
// best_feasible_solution.Add(v);
// }
// //TODO:回溯剪枝掉的var也得判断其值
// //未分支的变量，判断其是否为 1（为不失一般性，写的函数功能是判断是否为整数）
// foreach (var var_value in node.not_fixed_var_value_pairs)
// {
// if (Convert.ToInt32(var_value.Value) > 0 && ISInteger(var_value.Value))
// {
// best_feasible_solution.Add(var_value.Key);
// }
// }
//}
#endregion//
#region 列生成
/// <summary>在树节点"tree_node"章进行列生成
/// 求得当前树节点的最优目标值
/// </summary>
/// <param name="tree_node"></param>
public void CG(ref TreeNode tree_node)
{
//固定分支变量的值（==1）等于是另外加上变量的取值范围约束
FixVars(tree_node.fixing_vars);
double cur_reducedCost = 0;
//迭代生成列
for (;;)
{
this.OBJVALUE = SolveRMP();
//求解子问题，判断 检验数 < -1e-8 ?
if (IsLPOpt(cur_reducedCost))
{
break;
}
Console.WriteLine("检验数 = {0}", R_C_SPP.Reduced_Cost);
cur_reducedCost = R_C_SPP.Reduced_Cost;
double col_coef = 0;
int[] aj;
//ColumnPool = DeleteColumn(ColumnPool);
foreach (Pairing column in R_C_SPP.New_Columns)
{
ColumnPool.Add(column);
col_coef = column.ObjCoef;
aj = column.CoverMatrix;
INumVar column_var = masterModel.NumVar(0, 1, NumVarType.Float); //每加一列都要对模型进行修改，因为决策变量多了
// function
Obj.Expr = masterModel.Sum(Obj.Expr, masterModel.Prod(col_coef, column_var));
// constrains
for (int i = 0; i < realistic_trip_num; i++)
{
Constraint[i].Expr = masterModel.Sum(Constraint[i].Expr,
masterModel.Prod(aj[i], column_var));
} //TODO 20191006
DvarSet.Add(column_var);
A_Matrix.Add(aj);
ObjCoefSet.Add(col_coef);
}
}
//传递信息给tree_node
tree_node.obj_value = this.OBJVALUE;
tree_node.not_fixed_var_value_pairs.Clear();
for (int i = 0; i < DvarSet.Count; i++)
{
//将未分支的变量添加到待分支变量集合中
//!被回溯“扔掉”的变量不能再添加到fixed_vars中,须加上 && tree_node.fixed_vars.Contains(i) == false
if (tree_node.fixing_vars.Contains(i) == false && tree_node.fixed_vars.Contains(i) == false)
{
tree_node.not_fixed_var_value_pairs.Add(i, masterModel.GetValue(DvarSet[i]));
}
}
}
public static void Main( string[] args )
{
try {
string filename = "../../../../examples/data/facility.dat";
if (args.Length > 0)
filename = args[0];
ReadData(filename);
Cplex cplex = new Cplex();
INumVar[] open = cplex.BoolVarArray(_nbLocations);
INumVar[][] supply = new INumVar[_nbClients][];
for(int i = 0; i < _nbClients; i++)
supply[i] = cplex.BoolVarArray(_nbLocations);
for(int i = 0; i < _nbClients; i++)
cplex.AddEq(cplex.Sum(supply[i]), 1);
for(int j = 0; j < _nbLocations; j++) {
ILinearNumExpr v = cplex.LinearNumExpr();
for(int i = 0; i < _nbClients; i++)
v.AddTerm(1.0, supply[i][j]);
cplex.AddLe(v, cplex.Prod(_capacity[j], open[j]));
}
ILinearNumExpr obj = cplex.ScalProd(_fixedCost, open);
for(int i = 0; i < _nbClients; i++)
obj.Add(cplex.ScalProd(_cost[i], supply[i]));
cplex.AddMinimize(obj);
if (cplex.Solve()) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
double tolerance = cplex.GetParam(Cplex.Param.MIP.Tolerances.Integrality);
System.Console.WriteLine("Optimal value: " + cplex.ObjValue);
for(int j = 0; j < _nbLocations; j++) {
if (cplex.GetValue(open[j]) >= 1 - tolerance) {
System.Console.Write("Facility " + j +" is open, it serves clients ");
for(int i = 0; i < _nbClients; i++)
if (cplex.GetValue(supply[i][j]) >= 1 - tolerance)
System.Console.Write(" " + i);
System.Console.WriteLine();
}
}
}
cplex.End();
}
catch(ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
catch (System.IO.IOException exc) {
System.Console.WriteLine("Error reading file " + args[0] + ": " + exc);
}
catch (InputDataReader.InputDataReaderException exc) {
System.Console.WriteLine(exc);
}
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow(cplex, var, rng);
Cplex.BasisStatus[] cstat =
{
Cplex.BasisStatus.AtUpper,
Cplex.BasisStatus.Basic,
Cplex.BasisStatus.Basic
};
Cplex.BasisStatus[] rstat =
{
Cplex.BasisStatus.AtLower,
Cplex.BasisStatus.AtLower
};
cplex.SetBasisStatuses(var[0], cstat, rng[0], rstat);
if (cplex.Solve())
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
System.Console.WriteLine("Iteration count = " + cplex.Niterations);
double[] x = cplex.GetValues(var[0]);
double[] dj = cplex.GetReducedCosts(var[0]);
double[] pi = cplex.GetDuals(rng[0]);
double[] slack = cplex.GetSlacks(rng[0]);
int nvars = x.Length;
for (int j = 0; j < nvars; ++j)
{
System.Console.WriteLine("Variable " + j +
": Value = " + x[j] +
" Reduced cost = " + dj[j]);
}
int ncons = slack.Length;
for (int i = 0; i < ncons; ++i)
{
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i] +
" Pi = " + pi[i]);
}
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
private INumVar[] populateArray(INumVar current, List <ConfigurationOption> others)
{
INumVar[] alternativeGroup = new INumVar[1 + others.Count];
alternativeGroup[0] = current;
for (int i = 1; i <= others.Count; i++)
{
alternativeGroup[i] = binOptsToCplexVars[(BinaryOption)others.ElementAt(i - 1)];
}
return(alternativeGroup);
}
static void Main(string[] args)
{
Console.WriteLine("hi justin");
Cplex cpl = new Cplex();
INumVar x = cpl.NumVar(0, 1);
Console.WriteLine("upper bound: " + Convert.ToString(x.UB));
Console.ReadKey();
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
INumVar[] inside = cplex.NumVarArray(_nbProds, 10.0, Double.MaxValue);
INumVar[] outside = cplex.NumVarArray(_nbProds, 0.0, Double.MaxValue);
INumVar costVar = cplex.NumVar(0.0, Double.MaxValue);
cplex.AddEq(costVar, cplex.Sum(cplex.ScalProd(inside, _insideCost),
cplex.ScalProd(outside, _outsideCost)));
IObjective obj = cplex.AddMinimize(costVar);
// Must meet demand for each product
for (int p = 0; p < _nbProds; p++)
{
cplex.AddEq(cplex.Sum(inside[p], outside[p]), _demand[p]);
}
// Must respect capacity constraint for each resource
for (int r = 0; r < _nbResources; r++)
{
cplex.AddLe(cplex.ScalProd(_consumption[r], inside), _capacity[r]);
}
cplex.Solve();
if (cplex.GetStatus() != Cplex.Status.Optimal)
{
System.Console.WriteLine("No optimal solution found");
return;
}
// New constraint: cost must be no more than 10% over minimum
double cost = cplex.ObjValue;
costVar.UB = 1.1 * cost;
// New objective: minimize outside production
obj.Expr = cplex.Sum(outside);
cplex.Solve();
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
DisplayResults(cplex, costVar, inside, outside);
System.Console.WriteLine("----------------------------------------");
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
internal static void DisplayResults(Cplex cplex,
INumVar[] inside,
INumVar[] outside) {
System.Console.WriteLine("cost: " + cplex.ObjValue);
for(int p = 0; p < _nbProds; p++) {
System.Console.WriteLine("P" + p);
System.Console.WriteLine("inside: " + cplex.GetValue(inside[p]));
System.Console.WriteLine("outside: " + cplex.GetValue(outside[p]));
}
}
public static void Main(string[] args)
{
try {
// create CPLEX optimizer/modeler and turn off presolve to make
// the output more interesting
Cplex cplex = new Cplex();
cplex.SetParam(Cplex.Param.Preprocessing.Presolve, false);
// build model
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow(cplex, var, rng);
// setup branch priorities
INumVar[] ordvar = { var[0][1], var[0][3] };
int[] ordpri = { 8, 7 };
cplex.SetPriorities(ordvar, ordpri);
// setup branch directions
cplex.SetDirection(ordvar[0], Cplex.BranchDirection.Up);
cplex.SetDirection(ordvar[1], Cplex.BranchDirection.Down);
// write priority order to file
cplex.WriteOrder("mipex3.ord");
// optimize and output solution information
if (cplex.Solve())
{
double[] x = cplex.GetValues(var[0]);
double[] slack = cplex.GetSlacks(rng[0]);
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
for (int j = 0; j < x.Length; ++j)
{
System.Console.WriteLine("Variable " + j +
": Value = " + x[j]);
}
for (int i = 0; i < slack.Length; ++i)
{
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i]);
}
}
cplex.ExportModel("mipex3.lp");
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
internal static void Report2(Cplex patSolver, INumVar[] Use) {
System.Console.WriteLine();
System.Console.WriteLine("Reduced cost is " + patSolver.ObjValue);
System.Console.WriteLine();
if (patSolver.ObjValue <= -RC_EPS) {
for (int i = 0; i < Use.Length; i++)
System.Console.WriteLine(" Use" + i + " = "
+ patSolver.GetValue(Use[i]));
System.Console.WriteLine();
}
}
private void countConstraint(Cplex plex, List <BinaryOption> options, double count)
{
INumVar[] blacklistedVars = new INumVar[options.Count];
for (int i = 0; i < options.Count; i++)
{
blacklistedVars[i] = binOptsToCplexVars[options.ElementAt(i)];
}
plex.Add(plex.Eq(
plex.Constant(count),
plex.Sum(blacklistedVars)
));
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow(cplex, var, rng);
Cplex.BasisStatus[] cstat = {
Cplex.BasisStatus.AtUpper,
Cplex.BasisStatus.Basic,
Cplex.BasisStatus.Basic
};
Cplex.BasisStatus[] rstat = {
Cplex.BasisStatus.AtLower,
Cplex.BasisStatus.AtLower
};
cplex.SetBasisStatuses(var[0], cstat, rng[0], rstat);
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
System.Console.WriteLine("Iteration count = " + cplex.Niterations);
double[] x = cplex.GetValues(var[0]);
double[] dj = cplex.GetReducedCosts(var[0]);
double[] pi = cplex.GetDuals(rng[0]);
double[] slack = cplex.GetSlacks(rng[0]);
int nvars = x.Length;
for (int j = 0; j < nvars; ++j) {
System.Console.WriteLine("Variable " + j +
": Value = " + x[j] +
" Reduced cost = " + dj[j]);
}
int ncons = slack.Length;
for (int i = 0; i < ncons; ++i) {
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i] +
" Pi = " + pi[i]);
}
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
/// <summary>建立最初的RMP
/// 依据初始解
/// </summary>
/// <param name="IS"></param>
public void Build_RMP(InitialSolution IS)
{
initialPath_num = IS.PathSet.Count;
trip_num = TripList.Count;
realistic_trip_num = NetWork.num_Physical_trip;
DvarSet = new List <INumVar>();
CoefSet = new List <double>();
A_Matrix = new List <int[]>();
PathSet = new List <Pairing>();
//virtualVarSet = new List<INumVar>();
//for (int virtual_x = 0; virtual_x < realistic_trip_num; virtual_x++) {
// virtualVarSet.Add(masterModel.NumVar(0, 1, NumVarType.Float));
//}
CoefSet = IS.Coefs;
A_Matrix = IS.A_Matrix;
PathSet = IS.PathSet;
foreach (var p in PathSet)
{
ColumnPool.Add(p);
}
int i, j;
Obj = masterModel.AddMinimize();
Constraint = new IRange[realistic_trip_num];
/**按行建模**/
//vars and obj function
for (j = 0; j < initialPath_num; j++)
{
INumVar var = masterModel.NumVar(0, 1, NumVarType.Float);
DvarSet.Add(var);
Obj.Expr = masterModel.Sum(Obj.Expr, masterModel.Prod(CoefSet[j], DvarSet[j]));
}
//constraints
for (i = 0; i < realistic_trip_num; i++)
{
INumExpr expr = masterModel.NumExpr();
for (j = 0; j < initialPath_num; j++)
{
expr = masterModel.Sum(expr,
masterModel.Prod(A_Matrix[j][i], DvarSet[j]));//在从初始解传值给A_Matrix，已经针对网络复制作了处理
}
Constraint[i] = masterModel.AddGe(expr, 1);
}
}
// This function creates the following model:
// Minimize
// obj: x1 + x2 + x3 + x4 + x5 + x6
// Subject To
// c1: x1 + x2 + x5 = 8
// c2: x3 + x5 + x6 = 10
// q1: [ -x1^2 + x2^2 + x3^2 ] <= 0
// q2: [ -x4^2 + x5^2 ] <= 0
// Bounds
// x2 Free
// x3 Free
// x5 Free
// End
// which is a second order cone program in standard form.
private static IObjective Createmodel(Cplex cplex,
ICollection <INumVar> vars,
ICollection <IRange> rngs,
IDictionary <INumVar, IRange> cone)
{
System.Double pinf = System.Double.PositiveInfinity;
System.Double ninf = System.Double.NegativeInfinity;
INumVar x1 = cplex.NumVar(0, pinf, "x1");
INumVar x2 = cplex.NumVar(ninf, pinf, "x2");
INumVar x3 = cplex.NumVar(ninf, pinf, "x3");
INumVar x4 = cplex.NumVar(0, pinf, "x4");
INumVar x5 = cplex.NumVar(ninf, pinf, "x5");
INumVar x6 = cplex.NumVar(0, pinf, "x6");
IObjective obj = cplex.AddMinimize(cplex.Sum(cplex.Sum(cplex.Sum(x1, x2),
cplex.Sum(x3, x4)),
cplex.Sum(x5, x6)),
"obj");
IRange c1 = cplex.AddEq(cplex.Sum(x1, cplex.Sum(x2, x5)), 8, "c1");
IRange c2 = cplex.AddEq(cplex.Sum(x3, cplex.Sum(x5, x6)), 10, "c2");
IRange q1 = cplex.AddLe(cplex.Sum(cplex.Prod(-1, cplex.Prod(x1, x1)),
cplex.Sum(cplex.Prod(x2, x2),
cplex.Prod(x3, x3))), 0, "q1");
cone[x1] = q1;
cone[x2] = NOT_CONE_HEAD;
cone[x3] = NOT_CONE_HEAD;
IRange q2 = cplex.AddLe(cplex.Sum(cplex.Prod(-1, cplex.Prod(x4, x4)),
cplex.Prod(x5, x5)), 0, "q2");
cone[x4] = q2;
cone[x5] = NOT_CONE_HEAD;
cone[x6] = NOT_IN_CONE;
vars.Add(x1);
vars.Add(x2);
vars.Add(x3);
vars.Add(x4);
vars.Add(x5);
vars.Add(x6);
rngs.Add(c1);
rngs.Add(c2);
rngs.Add(q1);
rngs.Add(q2);
return(obj);
}
public static void Main(string[] args)
{
try
{
// setup files to transfer model to server
string mfile = "Model.dat";
string sfile = "Solution.dat";
// build model
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
CplexModeler model = new CplexModeler();
PopulateByRow(model, var, rng);
FileStream mstream = new FileStream(mfile, FileMode.Create);
BinaryFormatter formatter = new BinaryFormatter();
formatter.Serialize(mstream, new ModelData(model, var[0]));
mstream.Close();
// start server
Server server = new Server(mfile, sfile);
SolutionData sol = null;
FileStream sstream = new FileStream(sfile, FileMode.Open);
sol = (SolutionData)formatter.Deserialize(sstream);
sstream.Close();
System.Console.WriteLine("Solution status = " + sol.status);
if (sol.status.Equals(Cplex.CplexStatus.Optimal))
{
System.Console.WriteLine("Solution value = " + sol.obj);
int ncols = var[0].Length;
for (int j = 0; j < ncols; ++j)
{
System.Console.WriteLine("Variable " + j + ": Value = " + sol.vals[j]);
}
}
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
catch (System.Exception t)
{
System.Console.WriteLine("terminating due to exception " + t);
}
}
public static void Main(string[] args)
{
try {
// create CPLEX optimizer/modeler and turn off presolve to make
// the output more interesting
Cplex cplex = new Cplex();
cplex.SetParam(Cplex.Param.Preprocessing.Presolve, false);
// build model
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow (cplex, var, rng);
// setup branch priorities
INumVar[] ordvar = {var[0][1], var[0][3]};
int[] ordpri = {8, 7};
cplex.SetPriorities (ordvar, ordpri);
// setup branch directions
cplex.SetDirection(ordvar[0], Cplex.BranchDirection.Up);
cplex.SetDirection(ordvar[1], Cplex.BranchDirection.Down);
// write priority order to file
cplex.WriteOrder("mipex3.ord");
// optimize and output solution information
if ( cplex.Solve() ) {
double[] x = cplex.GetValues(var[0]);
double[] slack = cplex.GetSlacks(rng[0]);
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
for (int j = 0; j < x.Length; ++j) {
System.Console.WriteLine("Variable " + j +
": Value = " + x[j]);
}
for (int i = 0; i < slack.Length; ++i) {
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i]);
}
}
cplex.ExportModel("mipex3.lp");
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
public static Cplex Build_CD3_Model(IALPFTMDP aff)
{
Cplex model = new Cplex();
IObjective cost = model.AddMaximize();
INumVar[][] var = new INumVar[aff.TimeHorizon][];
#region //////////////生成约束//////////////
IRange[][] constraint1 = new IRange[aff.TimeHorizon][];
IRange[] constraint2 = new IRange[aff.TimeHorizon];
for (int i = 0; i < aff.TimeHorizon; i++)
{
var[i] = new INumVar[aff.DS.Count];
constraint1[i] = new IRange[aff.RS.Count];
foreach (IALPResource re in aff.RS)
{
constraint1[i][aff.RS.IndexOf(re)] = model.AddRange(double.MinValue, (aff.InitialState as IALPState)[re]);
}
constraint2[i] = model.AddRange(1, 1);
}
#endregion
#region //////////////生成变量//////////////
for (int t = 0; t < aff.TimeHorizon; t++)
{
foreach (IALPDecision a in aff.DS)
{
//目标函数
Column col = model.Column(cost, aff.Rt(t, a));
//第一类约束
foreach (IALPResource re in aff.RS)
{
for (int k = t + 1; k < aff.TimeHorizon; k++)
{
col = col.And(model.Column(constraint1[k][aff.RS.IndexOf(re)], aff.Qti(t, re, a)));
}
if (a.UseResource(re))
{
col = col.And(model.Column(constraint1[t][aff.RS.IndexOf(re)], 1));
}
}
//第二类约束
col = col.And(model.Column(constraint2[t], 1));
var[t][aff.DS.IndexOf(a)] = model.NumVar(col, 0, double.MaxValue, NumVarType.Float);
}
}
#endregion
return(model);
}
public static void Main(string[] args)
{
try {
string filename = "../../../../examples/data/rates.dat";
if (args.Length > 0)
{
filename = args[0];
}
ReadData(filename);
Cplex cplex = new Cplex();
INumVar[] production = new INumVar[_generators];
for (int j = 0; j < _generators; ++j)
{
production[j] = cplex.SemiContVar(_minArray[j], _maxArray[j],
NumVarType.Float);
}
cplex.AddMinimize(cplex.ScalProd(_cost, production));
cplex.AddGe(cplex.Sum(production), _demand);
cplex.ExportModel("rates.lp");
if (cplex.Solve())
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
for (int j = 0; j < _generators; ++j)
{
System.Console.WriteLine(" generator " + j + ": " +
cplex.GetValue(production[j]));
}
System.Console.WriteLine("Total cost = " + cplex.ObjValue);
}
else
{
System.Console.WriteLine("No solution");
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
catch (System.IO.IOException exc) {
System.Console.WriteLine("Error reading file " + args[0] + ": " + exc);
}
catch (InputDataReader.InputDataReaderException exc) {
System.Console.WriteLine(exc);
}
}
static void DisplayResults(Cplex cplex,
INumVar costVar,
INumVar[] inside,
INumVar[] outside)
{
System.Console.WriteLine("cost: " + cplex.GetValue(costVar));
for (int p = 0; p < _nbProds; p++)
{
System.Console.WriteLine("P" + p);
System.Console.WriteLine("inside: " + cplex.GetValue(inside[p]));
System.Console.WriteLine("outside: " + cplex.GetValue(outside[p]));
}
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
INumVar[] inside = new INumVar[_nbProds];
INumVar[] outside = new INumVar[_nbProds];
IObjective obj = cplex.AddMinimize();
// Must meet demand for each product
for (int p = 0; p < _nbProds; p++)
{
IRange demRange = cplex.AddRange(_demand[p], _demand[p]);
inside[p] = cplex.NumVar(cplex.Column(obj, _insideCost[p]).And(
cplex.Column(demRange, 1.0)),
0.0, System.Double.MaxValue);
outside[p] = cplex.NumVar(cplex.Column(obj, _outsideCost[p]).And(
cplex.Column(demRange, 1.0)),
0.0, System.Double.MaxValue);
}
// Must respect capacity constraint for each resource
for (int r = 0; r < _nbResources; r++)
{
cplex.AddLe(cplex.ScalProd(_consumption[r], inside), _capacity[r]);
}
cplex.Solve();
if (!cplex.GetStatus().Equals(Cplex.Status.Optimal))
{
System.Console.WriteLine("No optimal solution found");
return;
}
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
DisplayResults(cplex, inside, outside);
System.Console.WriteLine("----------------------------------------");
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
private void initializeImpliedOptions(Cplex cplex, INumVar currentOption, BinaryOption currentBinOpt)
{
List <List <ConfigurationOption> > impliedOptions = currentBinOpt.Implied_Options;
foreach (List <ConfigurationOption> impliedGroup in impliedOptions)
{
INumVar[] implVars = populateArray(currentOption, impliedGroup);
// For implication groups the sum of the options has to be the number of implied options
// if the current options is selected
cplex.Add(cplex.IfThen(
cplex.Eq(one, currentOption),
cplex.Eq(cplex.Sum(implVars), cplex.Constant(implVars.Count()))
));
}
}
public static void Main(string[] args)
{
try {
// setup files to transfer model to server
string mfile = "Model.dat";
string sfile = "Solution.dat";
// build model
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
CplexModeler model = new CplexModeler();
PopulateByRow(model, var, rng);
FileStream mstream = new FileStream(mfile, FileMode.Create);
BinaryFormatter formatter = new BinaryFormatter ();
formatter.Serialize(mstream, new ModelData(model, var[0]));
mstream.Close();
// start server
Server server = new Server(mfile, sfile);
SolutionData sol = null;
FileStream sstream = new FileStream(sfile, FileMode.Open);
sol = (SolutionData) formatter.Deserialize(sstream);
sstream.Close();
System.Console.WriteLine("Solution status = " + sol.status);
if ( sol.status.Equals(Cplex.CplexStatus.Optimal) ) {
System.Console.WriteLine("Solution value = " + sol.obj);
int ncols = var[0].Length;
for (int j = 0; j < ncols; ++j)
System.Console.WriteLine("Variable " + j + ": Value = " + sol.vals[j]);
}
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
catch (System.Exception t) {
System.Console.WriteLine("terminating due to exception " + t);
}
}
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 PopulateByRow(IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
var[0] = model.NumVarArray(3, lb, ub);
double[] objvals = {1.0, 2.0, 3.0};
model.AddMaximize(model.ScalProd(var[0], objvals));
rng[0] = new IRange[2];
rng[0][0] = model.AddLe(model.Sum(model.Prod(-1.0, var[0][0]),
model.Prod( 1.0, var[0][1]),
model.Prod( 1.0, var[0][2])), 20.0);
rng[0][1] = model.AddLe(model.Sum(model.Prod( 1.0, var[0][0]),
model.Prod(-3.0, var[0][1]),
model.Prod( 1.0, var[0][2])), 30.0);
}
public static void Main( string[] args )
{
try {
Cplex cplex = new Cplex();
INumVar[] inside = new INumVar[_nbProds];
INumVar[] outside = new INumVar[_nbProds];
IObjective obj = cplex.AddMinimize();
// Must meet demand for each product
for(int p = 0; p < _nbProds; p++) {
IRange demRange = cplex.AddRange(_demand[p], _demand[p]);
inside[p] = cplex.NumVar(cplex.Column(obj, _insideCost[p]).And(
cplex.Column(demRange, 1.0)),
0.0, System.Double.MaxValue);
outside[p] = cplex.NumVar(cplex.Column(obj, _outsideCost[p]).And(
cplex.Column(demRange, 1.0)),
0.0, System.Double.MaxValue);
}
// Must respect capacity constraint for each resource
for(int r = 0; r < _nbResources; r++)
cplex.AddLe(cplex.ScalProd(_consumption[r], inside), _capacity[r]);
cplex.Solve();
if ( !cplex.GetStatus().Equals(Cplex.Status.Optimal) ) {
System.Console.WriteLine("No optimal solution found");
return;
}
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
DisplayResults(cplex, inside, outside);
System.Console.WriteLine("----------------------------------------");
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
public static void Main( string[] args )
{
try {
string filename = "../../../../examples/data/rates.dat";
if (args.Length > 0)
filename = args[0];
ReadData(filename);
Cplex cplex = new Cplex();
INumVar[] production = new INumVar[_generators];
for (int j = 0; j < _generators; ++j) {
production[j] = cplex.SemiContVar(_minArray[j], _maxArray[j],
NumVarType.Float);
}
cplex.AddMinimize(cplex.ScalProd(_cost, production));
cplex.AddGe(cplex.Sum(production), _demand);
cplex.ExportModel("rates.lp");
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
for (int j = 0; j < _generators; ++j) {
System.Console.WriteLine(" generator " + j + ": " +
cplex.GetValue(production[j]));
}
System.Console.WriteLine("Total cost = " + cplex.ObjValue);
}
else
System.Console.WriteLine("No solution");
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
catch (System.IO.IOException exc) {
System.Console.WriteLine("Error reading file " + args[0] + ": " + exc);
}
catch (InputDataReader.InputDataReaderException exc) {
System.Console.WriteLine(exc);
}
}
private bool AddCol(int t, IALPState s, IMDPDecision a)//Add a column into RMP model
{
Column col = RMPModel.Column(cost, Data.Rt(t, a));
foreach (IALPResource re in Data.RS)
{
col = col.And(RMPModel.Column(constraint1[t][Data.RS.IndexOf(re)], (s as IALPState)[re]));
if (t < Data.TimeHorizon - 1)
{
col = col.And(RMPModel.Column(constraint1[t + 1][Data.RS.IndexOf(re)], (Data.Qti(t, re, a)) - (s as IALPState)[re]));
}
}
col = col.And(RMPModel.Column(constraint2[t], 1));
INumVar var = RMPModel.NumVar(col, 0, double.MaxValue, NumVarType.Float);
sas.Add(new StateActive()
{
S = s, D = a, Var = var
});
return(true);
}
internal static void PopulateByRow(IMPModeler model,
INumVar[][] var,
IRange[][] rng)
{
// Define the variables one-by-one
INumVar[] x = new INumVar[4];
x[0] = model.NumVar(0.0, 40.0, "x0");
x[1] = model.IntVar(0, System.Int32.MaxValue, "x1");
x[2] = model.IntVar(0, System.Int32.MaxValue, "x2");
x[3] = model.IntVar(2, 3, "x3");
var[0] = x;
// Objective Function
model.AddMaximize(model.Sum(model.Prod(1.0, x[0]),
model.Prod(2.0, x[1]),
model.Prod(3.0, x[2]),
model.Prod(1.0, x[3])));
// Define three constraints one-by-one
rng[0] = new IRange[3];
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]),
model.Prod(10.0, x[3])),
20.0, "rng0");
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, "rng1");
rng[0][2] = model.AddEq(model.Sum(model.Prod(1.0, x[1]),
model.Prod(-3.5, x[3])),
0, "rng2");
// add special ordered set of type 1
INumVar[] sosvars = { x[2], x[3] };
double[] sosweights = { 25.0, 18.0 };
model.AddSOS1(sosvars, sosweights);
}
internal static void PopulateByRow (IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
// Define the variables one-by-one
INumVar[] x = new INumVar[4];
x[0] = model.NumVar(0.0, 40.0, "x0");
x[1] = model.IntVar(0, System.Int32.MaxValue, "x1");
x[2] = model.IntVar(0, System.Int32.MaxValue, "x2");
x[3] = model.IntVar(2, 3, "x3");
var[0] = x;
// Objective Function
model.AddMaximize(model.Sum(model.Prod( 1.0, x[0]),
model.Prod( 2.0, x[1]),
model.Prod( 3.0, x[2]),
model.Prod( 1.0, x[3])));
// Define three constraints one-by-one
rng[0] = new IRange[3];
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]),
model.Prod(10.0, x[3])),
20.0, "rng0");
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, "rng1");
rng[0][2] = model.AddEq(model.Sum(model.Prod( 1.0, x[1]),
model.Prod(-3.5, x[3])),
0, "rng2");
// add special ordered set of type 1
INumVar[] sosvars = {x[2], x[3]};
double[] sosweights = {25.0, 18.0};
model.AddSOS1(sosvars, sosweights);
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
INumVar[][] var = new INumVar[1][];
IRange[][] rng = new IRange[1][];
PopulateByRow(cplex, var, rng);
if (cplex.Solve())
{
double[] x = cplex.GetValues(var[0]);
double[] slack = cplex.GetSlacks(rng[0]);
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Solution value = " + cplex.ObjValue);
for (int j = 0; j < x.Length; ++j)
{
System.Console.WriteLine("Variable " + j +
": Value = " + x[j]);
}
for (int i = 0; i < slack.Length; ++i)
{
System.Console.WriteLine("Constraint " + i +
": Slack = " + slack[i]);
}
}
cplex.ExportModel("mipex1.lp");
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught '" + e + "' caught");
}
}
// Print out the objective function.
// Note that the quadratic expression in the objective
// is normalized: i.E., for all i != j, terms
// c(i,j)*x[i]*x[j] + c(j,i)*x[j]*x[i] is normalized as
// (c(i,j) + c(j,i)) * x[i]*x[j], or
// (c(i,j) + c(j,i)) * x[j]*x[i].
internal static void PrintObjective(IObjective obj)
{
System.Console.WriteLine("obj: " + obj);
// Count the number of linear terms
// in the objective function.
int nlinterms = 0;
ILinearNumExprEnumerator len = ((ILQNumExpr)obj.Expr).GetLinearEnumerator();
while (len.MoveNext())
{
++nlinterms;
}
// Count the number of quadratic terms
// in the objective function.
int nquadterms = 0;
int nquaddiag = 0;
IQuadNumExprEnumerator qen = ((ILQNumExpr)obj.Expr).GetQuadEnumerator();
while (qen.MoveNext())
{
++nquadterms;
INumVar var1 = qen.GetNumVar1();
INumVar var2 = qen.GetNumVar2();
if (var1.Equals(var2))
{
++nquaddiag;
}
}
System.Console.WriteLine("number of linear terms in the objective : " + nlinterms);
System.Console.WriteLine("number of quadratic terms in the objective : " + nquadterms);
System.Console.WriteLine("number of diagonal quadratic terms in the objective : " + nquaddiag);
System.Console.WriteLine();
}
internal static void BuildModelByColumn(IMPModeler model,
Data data,
INumVar[] Buy,
NumVarType type)
{
int nFoods = data.nFoods;
int nNutrs = data.nNutrs;
IObjective cost = model.AddMinimize();
IRange[] constraint = new IRange[nNutrs];
for (int i = 0; i < nNutrs; i++) {
constraint[i] = model.AddRange(data.nutrMin[i], data.nutrMax[i]);
}
for (int j = 0; j < nFoods; j++) {
Column col = model.Column(cost, data.foodCost[j]);
for (int i = 0; i < nNutrs; i++) {
col = col.And(model.Column(constraint[i], data.nutrPerFood[i][j]));
}
Buy[j] = model.NumVar(col, data.foodMin[j], data.foodMax[j], type);
}
}
internal Solve(INumVar[] vars, double[] x) { _vars = vars; _x = x; }
internal MyBranchGoal(INumVar[] vars)
{
_vars = vars;
}
// 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");
}
internal ModelData(IModel m, INumVar[] v)
{
model = m;
vars = v;
}
public INumExpr Prod(double coef, INumVar var)
{
INumExpr result = new INumExpr();
result.expr += coef * var.var;
return result;
}
internal static void PopulateByNonzero(IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
INumVar[] x = model.NumVarArray(3, lb, ub);
var[0] = x;
double[] objvals = {1.0, 2.0, 3.0};
model.Add(model.Maximize(model.ScalProd(x, objvals)));
rng[0] = new IRange[2];
rng[0][0] = model.AddRange(-System.Double.MaxValue, 20.0);
rng[0][1] = model.AddRange(-System.Double.MaxValue, 30.0);
rng[0][0].Expr = model.Sum(model.Prod(-1.0, x[0]),
model.Prod( 1.0, x[1]),
model.Prod( 1.0, x[2]));
rng[0][1].Expr = model.Sum(model.Prod( 1.0, x[0]),
model.Prod(-3.0, x[1]),
model.Prod( 1.0, x[2]));
x[0].Name = "x1";
x[1].Name = "x2";
x[2].Name = "x3";
rng[0][0].Name = "c1";
rng[0][0].Name = "c2";
}
public static void Main(string[] args)
{
try {
string filename = "../../../../examples/data/steel.dat";
if ( args.Length > 0 )
filename = args[0];
ReadData(filename);
Cplex cplex = new Cplex();
// VARIABLES
INumVar[][] Make = new INumVar[_nProd][];
for (int p = 0; p < _nProd; p++) {
Make[p] = cplex.NumVarArray(_nTime, 0.0, System.Double.MaxValue);
}
INumVar[][] Inv = new INumVar[_nProd][];
for (int p = 0; p < _nProd; p++) {
Inv[p] = cplex.NumVarArray(_nTime, 0.0, System.Double.MaxValue);
}
INumVar[][] Sell = new INumVar[_nProd][];
for (int p = 0; p < _nProd; p++) {
Sell[p] = new INumVar[_nTime];
for (int t = 0; t < _nTime; t++) {
Sell[p][t] = cplex.NumVar(0.0, _market[p][t]);
}
}
// OBJECTIVE
ILinearNumExpr TotalRevenue = cplex.LinearNumExpr();
ILinearNumExpr TotalProdCost = cplex.LinearNumExpr();
ILinearNumExpr TotalInvCost = cplex.LinearNumExpr();
for (int p = 0; p < _nProd; p++) {
for (int t = 1; t < _nTime; t++) {
TotalRevenue.AddTerm (_revenue[p][t], Sell[p][t]);
TotalProdCost.AddTerm(_prodCost[p], Make[p][t]);
TotalInvCost.AddTerm (_invCost[p], Inv[p][t]);
}
}
cplex.AddMaximize(cplex.Diff(TotalRevenue,
cplex.Sum(TotalProdCost, TotalInvCost)));
// TIME AVAILABILITY CONSTRAINTS
for (int t = 0; t < _nTime; t++) {
ILinearNumExpr availExpr = cplex.LinearNumExpr();
for (int p = 0; p < _nProd; p++) {
availExpr.AddTerm(1.0/_rate[p], Make[p][t]);
}
cplex.AddLe(availExpr, _avail[t]);
}
// MATERIAL BALANCE CONSTRAINTS
for (int p = 0; p < _nProd; p++) {
cplex.AddEq(cplex.Sum(Make[p][0], _inv0[p]),
cplex.Sum(Sell[p][0], Inv[p][0]));
for (int t = 1; t < _nTime; t++) {
cplex.AddEq(cplex.Sum(Make[p][t], Inv[p][t-1]),
cplex.Sum(Sell[p][t], Inv[p][t]));
}
}
cplex.ExportModel("steel.lp");
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine();
System.Console.WriteLine("Total Profit = " + cplex.ObjValue);
System.Console.WriteLine();
System.Console.WriteLine("\tp\tt\tMake\tInv\tSell");
for (int p = 0; p < _nProd; p++) {
for (int t = 0; t < _nTime; t++) {
System.Console.WriteLine("\t" + p +"\t" + t +"\t" + cplex.GetValue(Make[p][t]) +
"\t" + cplex.GetValue(Inv[p][t]) +"\t" + cplex.GetValue(Sell[p][t]));
}
}
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
catch (System.IO.IOException exc) {
System.Console.WriteLine("Error reading file " + args[0] + ": " + exc);
}
catch (InputDataReader.InputDataReaderException exc) {
System.Console.WriteLine(exc);
}
}
public INumExpr ScalProd(INumVar[] vars, double[] coefs)
{
return ScalProd(coefs, vars);
}
internal LogCallback(INumVar[] var, int lastLog, double lastIncumbent) {
_var = var;
_lastLog = lastLog;
_lastIncumbent = lastIncumbent;
}
public INumExpr Prod(INumVar var, double coef)
{
return Prod(coef, var);
}
public static void Main(string[] args)
{
try {
string filename = "../../../../examples/data/diet.dat";
bool byColumn = false;
NumVarType varType = NumVarType.Float;
for (int i = 0; i < args.Length; i++) {
if ( args[i].ToCharArray()[0] == '-') {
switch (args[i].ToCharArray()[1]) {
case 'c':
byColumn = true;
break;
case 'i':
varType = NumVarType.Int;
break;
default:
Usage();
return;
}
}
else {
filename = args[i];
break;
}
}
Data data = new Data(filename);
int nFoods = data.nFoods;
int nNutrs = data.nNutrs;
// Build model
Cplex cplex = new Cplex();
INumVar[] Buy = new INumVar[nFoods];
if ( byColumn ) BuildModelByColumn(cplex, data, Buy, varType);
else BuildModelByRow (cplex, data, Buy, varType);
// Solve model
if ( cplex.Solve() ) {
System.Console.WriteLine();
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine();
System.Console.WriteLine(" cost = " + cplex.ObjValue);
for (int i = 0; i < nFoods; i++) {
System.Console.WriteLine(" Buy" + i + " = " + cplex.GetValue(Buy[i]));
}
System.Console.WriteLine();
}
cplex.End();
}
catch (ILOG.Concert.Exception ex) {
System.Console.WriteLine("Concert Error: " + ex);
}
catch (InputDataReader.InputDataReaderException ex) {
System.Console.WriteLine("Data Error: " + ex);
}
catch (System.IO.IOException ex) {
System.Console.WriteLine("IO Error: " + ex);
}
}
public static void Main( string[] args ) {
try {
Cplex cplex = new Cplex();
INumVar[] m = cplex.NumVarArray(_nbElements, 0.0, System.Double.MaxValue);
INumVar[] r = cplex.NumVarArray(_nbRaw, 0.0, System.Double.MaxValue);
INumVar[] s = cplex.NumVarArray(_nbScrap, 0.0, System.Double.MaxValue);
INumVar[] i = cplex.IntVarArray(_nbIngot, 0, System.Int32.MaxValue);
INumVar[] e = new INumVar[_nbElements];
// Objective Function: Minimize Cost
cplex.AddMinimize(cplex.Sum(cplex.ScalProd(_cm, m),
cplex.ScalProd(_cr, r),
cplex.ScalProd(_cs, s),
cplex.ScalProd(_ci, i)));
// Min and max quantity of each element in alloy
for (int j = 0; j < _nbElements; j++) {
e[j] = cplex.NumVar(_p[j] * _alloy, _P[j] * _alloy);
}
// Constraint: produce requested quantity of alloy
cplex.AddEq(cplex.Sum(e), _alloy);
// Constraints: Satisfy element quantity requirements for alloy
for (int j = 0; j < _nbElements; j++) {
cplex.AddEq(e[j],
cplex.Sum(m[j],
cplex.ScalProd(_PRaw[j], r),
cplex.ScalProd(_PScrap[j], s),
cplex.ScalProd(_PIngot[j], i)));
}
if ( cplex.Solve() ) {
if ( cplex.GetStatus().Equals(Cplex.Status.Infeasible) ) {
System.Console.WriteLine("No feasible solution found");
return;
}
double[] mVals = cplex.GetValues(m);
double[] rVals = cplex.GetValues(r);
double[] sVals = cplex.GetValues(s);
double[] iVals = cplex.GetValues(i);
double[] eVals = cplex.GetValues(e);
// Print results
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Cost:" + cplex.ObjValue);
System.Console.WriteLine("Pure metal:");
for(int j = 0; j < _nbElements; j++)
System.Console.WriteLine("(" + j + ") " + mVals[j]);
System.Console.WriteLine("Raw material:");
for(int j = 0; j < _nbRaw; j++)
System.Console.WriteLine("(" + j + ") " + rVals[j]);
System.Console.WriteLine("Scrap:");
for(int j = 0; j < _nbScrap; j++)
System.Console.WriteLine("(" + j + ") " + sVals[j]);
System.Console.WriteLine("Ingots : ");
for(int j = 0; j < _nbIngot; j++)
System.Console.WriteLine("(" + j + ") " + iVals[j]);
System.Console.WriteLine("Elements:");
for(int j = 0; j < _nbElements; j++)
System.Console.WriteLine("(" + j + ") " + eVals[j]);
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
// The constructor sets up the Cplex instance to solve the worker LP,
// and creates the worker LP (i.e., the dual of flow constraints and
// capacity constraints of the flow MILP)
//
// Modeling variables:
// forall k in V0, i in V:
// u(k,i) = dual variable associated with flow constraint (k,i)
//
// forall k in V0, forall (i,j) in A:
// v(k,i,j) = dual variable associated with capacity constraint (k,i,j)
//
// Objective:
// minimize sum(k in V0) sum((i,j) in A) x(i,j) * v(k,i,j)
// - sum(k in V0) u(k,0) + sum(k in V0) u(k,k)
//
// Constraints:
// forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j)
//
// Nonnegativity on variables v(k,i,j)
// forall k in V0, forall (i,j) in A: v(k,i,j) >= 0
//
internal WorkerLP(int numNodes)
{
this.numNodes = numNodes;
int i, j, k;
// Set up Cplex instance to solve the worker LP
cplex = new Cplex();
cplex.SetOut(null);
// Turn off the presolve reductions and set the CPLEX optimizer
// to solve the worker LP with primal simplex method.
cplex.SetParam(Cplex.Param.Preprocessing.Reduce, 0);
cplex.SetParam(Cplex.Param.RootAlgorithm, Cplex.Algorithm.Primal);
// Create variables v(k,i,j) forall k in V0, (i,j) in A
// For simplicity, also dummy variables v(k,i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
v = new INumVar[numNodes-1][][];
for (k = 1; k < numNodes; ++k)
{
v[k-1] = new INumVar[numNodes][];
for (i = 0; i < numNodes; ++i)
{
v[k-1][i] = new INumVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
v[k-1][i][j] = cplex.NumVar(0.0, System.Double.MaxValue, "v." + k + "." + i + "." + j);
cplex.Add(v[k-1][i][j]);
}
v[k-1][i][i].UB = 0.0;
}
}
// Create variables u(k,i) forall k in V0, i in V
u = new INumVar[numNodes-1][];
for (k = 1; k < numNodes; ++k)
{
u[k-1] = new INumVar[numNodes];
for (i = 0; i < numNodes; ++i)
{
u[k-1][i] = cplex.NumVar(-System.Double.MaxValue, System.Double.MaxValue, "u." + k + "." + i);
cplex.Add(u[k-1][i]);
}
}
// Initial objective function is empty
cplex.AddMinimize();
// Add constraints:
// forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j)
for (k = 1; k < numNodes; ++k)
{
for (i = 0; i < numNodes; ++i)
{
for (j = 0; j < numNodes; ++j)
{
if ( i != j )
{
ILinearNumExpr expr = cplex.LinearNumExpr();
expr.AddTerm(v[k-1][i][j], -1.0);
expr.AddTerm(u[k-1][i], 1.0);
expr.AddTerm(u[k-1][j], -1.0);
cplex.AddLe(expr, 0.0);
}
}
}
}
}
internal static IRange[] MakeCuts(IModeler m, ILPMatrix lp)
{
INumVar x11 = null, x12 = null, x13 = null, x14 = null, x15 = null;
INumVar x21 = null, x22 = null, x23 = null, x24 = null, x25 = null;
INumVar x31 = null, x32 = null, x33 = null, x34 = null, x35 = null;
INumVar x41 = null, x42 = null, x43 = null, x44 = null, x45 = null;
INumVar x51 = null, x52 = null, x53 = null, x54 = null, x55 = null;
INumVar w11 = null, w12 = null, w13 = null, w14 = null, w15 = null;
INumVar w21 = null, w22 = null, w23 = null, w24 = null, w25 = null;
INumVar w31 = null, w32 = null, w33 = null, w34 = null, w35 = null;
INumVar w41 = null, w42 = null, w43 = null, w44 = null, w45 = null;
INumVar w51 = null, w52 = null, w53 = null, w54 = null, w55 = null;
INumVar[] vars = lp.NumVars;
int num = vars.Length;
for (int i = 0; i < num; ++i)
{
if (vars[i].Name.Equals("X11"))
{
x11 = vars[i];
}
else if (vars[i].Name.Equals("X12"))
{
x12 = vars[i];
}
else if (vars[i].Name.Equals("X13"))
{
x13 = vars[i];
}
else if (vars[i].Name.Equals("X14"))
{
x14 = vars[i];
}
else if (vars[i].Name.Equals("X15"))
{
x15 = vars[i];
}
else if (vars[i].Name.Equals("X21"))
{
x21 = vars[i];
}
else if (vars[i].Name.Equals("X22"))
{
x22 = vars[i];
}
else if (vars[i].Name.Equals("X23"))
{
x23 = vars[i];
}
else if (vars[i].Name.Equals("X24"))
{
x24 = vars[i];
}
else if (vars[i].Name.Equals("X25"))
{
x25 = vars[i];
}
else if (vars[i].Name.Equals("X31"))
{
x31 = vars[i];
}
else if (vars[i].Name.Equals("X32"))
{
x32 = vars[i];
}
else if (vars[i].Name.Equals("X33"))
{
x33 = vars[i];
}
else if (vars[i].Name.Equals("X34"))
{
x34 = vars[i];
}
else if (vars[i].Name.Equals("X35"))
{
x35 = vars[i];
}
else if (vars[i].Name.Equals("X41"))
{
x41 = vars[i];
}
else if (vars[i].Name.Equals("X42"))
{
x42 = vars[i];
}
else if (vars[i].Name.Equals("X43"))
{
x43 = vars[i];
}
else if (vars[i].Name.Equals("X44"))
{
x44 = vars[i];
}
else if (vars[i].Name.Equals("X45"))
{
x45 = vars[i];
}
else if (vars[i].Name.Equals("X51"))
{
x51 = vars[i];
}
else if (vars[i].Name.Equals("X52"))
{
x52 = vars[i];
}
else if (vars[i].Name.Equals("X53"))
{
x53 = vars[i];
}
else if (vars[i].Name.Equals("X54"))
{
x54 = vars[i];
}
else if (vars[i].Name.Equals("X55"))
{
x55 = vars[i];
}
else if (vars[i].Name.Equals("W11"))
{
w11 = vars[i];
}
else if (vars[i].Name.Equals("W12"))
{
w12 = vars[i];
}
else if (vars[i].Name.Equals("W13"))
{
w13 = vars[i];
}
else if (vars[i].Name.Equals("W14"))
{
w14 = vars[i];
}
else if (vars[i].Name.Equals("W15"))
{
w15 = vars[i];
}
else if (vars[i].Name.Equals("W21"))
{
w21 = vars[i];
}
else if (vars[i].Name.Equals("W22"))
{
w22 = vars[i];
}
else if (vars[i].Name.Equals("W23"))
{
w23 = vars[i];
}
else if (vars[i].Name.Equals("W24"))
{
w24 = vars[i];
}
else if (vars[i].Name.Equals("W25"))
{
w25 = vars[i];
}
else if (vars[i].Name.Equals("W31"))
{
w31 = vars[i];
}
else if (vars[i].Name.Equals("W32"))
{
w32 = vars[i];
}
else if (vars[i].Name.Equals("W33"))
{
w33 = vars[i];
}
else if (vars[i].Name.Equals("W34"))
{
w34 = vars[i];
}
else if (vars[i].Name.Equals("W35"))
{
w35 = vars[i];
}
else if (vars[i].Name.Equals("W41"))
{
w41 = vars[i];
}
else if (vars[i].Name.Equals("W42"))
{
w42 = vars[i];
}
else if (vars[i].Name.Equals("W43"))
{
w43 = vars[i];
}
else if (vars[i].Name.Equals("W44"))
{
w44 = vars[i];
}
else if (vars[i].Name.Equals("W45"))
{
w45 = vars[i];
}
else if (vars[i].Name.Equals("W51"))
{
w51 = vars[i];
}
else if (vars[i].Name.Equals("W52"))
{
w52 = vars[i];
}
else if (vars[i].Name.Equals("W53"))
{
w53 = vars[i];
}
else if (vars[i].Name.Equals("W54"))
{
w54 = vars[i];
}
else if (vars[i].Name.Equals("W55"))
{
w55 = vars[i];
}
}
IRange[] cut = new IRange[8];
cut[0] = m.Le(m.Diff(x21, x22), 0.0);
cut[1] = m.Le(m.Diff(x22, x23), 0.0);
cut[2] = m.Le(m.Diff(x23, x24), 0.0);
cut[3] = m.Le(m.Sum(m.Sum(m.Prod(2.08, x11),
m.Prod(2.98, x21),
m.Prod(3.47, x31),
m.Prod(2.24, x41),
m.Prod(2.08, x51)),
m.Sum(m.Prod(0.25, w11),
m.Prod(0.25, w21),
m.Prod(0.25, w31),
m.Prod(0.25, w41),
m.Prod(0.25, w51))), 20.25);
cut[4] = m.Le(m.Sum(m.Sum(m.Prod(2.08, x12),
m.Prod(2.98, x22),
m.Prod(3.47, x32),
m.Prod(2.24, x42),
m.Prod(2.08, x52)),
m.Sum(m.Prod(0.25, w12),
m.Prod(0.25, w22),
m.Prod(0.25, w32),
m.Prod(0.25, w42),
m.Prod(0.25, w52))), 20.25);
cut[5] = m.Le(m.Sum(m.Sum(m.Prod(2.08, x13),
m.Prod(2.98, x23),
m.Prod(3.47, x33),
m.Prod(2.24, x43),
m.Prod(2.08, x53)),
m.Sum(m.Prod(0.25, w13),
m.Prod(0.25, w23),
m.Prod(0.25, w33),
m.Prod(0.25, w43),
m.Prod(0.25, w53))), 20.25);
cut[6] = m.Le(m.Sum(m.Sum(m.Prod(2.08, x14),
m.Prod(2.98, x24),
m.Prod(3.47, x34),
m.Prod(2.24, x44),
m.Prod(2.08, x54)),
m.Sum(m.Prod(0.25, w14),
m.Prod(0.25, w24),
m.Prod(0.25, w34),
m.Prod(0.25, w44),
m.Prod(0.25, w54))), 20.25);
cut[7] = m.Le(m.Sum(m.Sum(m.Prod(2.08, x15),
m.Prod(2.98, x25),
m.Prod(3.47, x35),
m.Prod(2.24, x45),
m.Prod(2.08, x55)),
m.Sum(m.Prod(0.25, w15),
m.Prod(0.25, w25),
m.Prod(0.25, w35),
m.Prod(0.25, w45),
m.Prod(0.25, w55))), 16.25);
return(cut);
}
internal static void PopulateByColumn(IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
IObjective obj = model.AddMaximize();
rng[0] = new IRange[2];
rng[0][0] = model.AddRange(-System.Double.MaxValue, 20.0, "c1");
rng[0][1] = model.AddRange(-System.Double.MaxValue, 30.0, "c2");
IRange r0 = rng[0][0];
IRange r1 = rng[0][1];
var[0] = new INumVar[3];
var[0][0] = model.NumVar(model.Column(obj, 1.0).And(
model.Column(r0, -1.0).And(
model.Column(r1, 1.0))),
0.0, 40.0, "x1");
var[0][1] = model.NumVar(model.Column(obj, 2.0).And(
model.Column(r0, 1.0).And(
model.Column(r1, -3.0))),
0.0, System.Double.MaxValue, "x2");
var[0][2] = model.NumVar(model.Column(obj, 3.0).And(
model.Column(r0, 1.0).And(
model.Column(r1, 1.0))),
0.0, System.Double.MaxValue, "x3");
}