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");
}
}
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[] fused = cplex.BoolVarArray(_nbMachines);
INumVar[] x = cplex.NumVarArray(_nbMachines, 0.0, System.Double.MaxValue);
// Objective: minimize the sum of fixed and variable costs
cplex.AddMinimize(cplex.Sum(cplex.ScalProd(_cost, x),
cplex.ScalProd(fused, _fixedCost)));
for (int i = 0; i < _nbMachines; i++) {
// Constraint: respect capacity constraint on machine 'i'
cplex.AddLe(x[i], _capacity[i]);
// Constraint: only produce product on machine 'i' if it is 'used'
// (to capture fixed cost of using machine 'i')
cplex.AddLe(x[i], cplex.Prod(10000, fused[i]));
}
// Constraint: meet demand
cplex.AddEq(cplex.Sum(x), _demand);
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("Obj " + cplex.ObjValue);
double eps = cplex.GetParam(Cplex.Param.MIP.Tolerances.Integrality);
for(int i = 0; i < _nbMachines; i++)
if (cplex.GetValue(fused[i]) > eps)
System.Console.WriteLine("E" + i + " is used for " +
cplex.GetValue(x[i]));
System.Console.WriteLine();
System.Console.WriteLine("----------------------------------------");
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
int nbWhouses = 4;
int nbLoads = 31;
INumVar[] capVars =
cplex.NumVarArray(nbWhouses, 0, 10,
NumVarType.Int); // Used capacities
double[] capLbs = { 2.0, 3.0, 5.0, 7.0 }; // Minimum usage level
double[] costs = { 1.0, 2.0, 4.0, 6.0 }; // Cost per warehouse
// These variables represent the assigninment of a
// load to a warehouse.
INumVar[][] assignVars = new INumVar[nbWhouses][];
for (int w = 0; w < nbWhouses; w++)
{
assignVars[w] = cplex.NumVarArray(nbLoads, 0, 1,
NumVarType.Int);
// Links the number of loads assigned to a warehouse with
// the capacity variable of the warehouse.
cplex.AddEq(cplex.Sum(assignVars[w]), capVars[w]);
}
// Each load must be assigned to just one warehouse.
for (int l = 0; l < nbLoads; l++)
{
INumVar[] aux = new INumVar[nbWhouses];
for (int w = 0; w < nbWhouses; w++)
{
aux[w] = assignVars[w][l];
}
cplex.AddEq(cplex.Sum(aux), 1);
}
cplex.AddMinimize(cplex.ScalProd(costs, capVars));
cplex.SetParam(Cplex.Param.MIP.Strategy.Search, Cplex.MIPSearch.Traditional);
if (cplex.Solve(new SemiContGoal(capVars, capLbs)))
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("--------------------------------------------");
System.Console.WriteLine();
System.Console.WriteLine("Solution found:");
System.Console.WriteLine(" Objective value = " + cplex.ObjValue);
System.Console.WriteLine();
for (int w = 0; w < nbWhouses; w++)
{
System.Console.WriteLine("Warehouse " + w + ": stored "
+ cplex.GetValue(capVars[w]) + " loads");
for (int l = 0; l < nbLoads; l++)
{
if (cplex.GetValue(assignVars[w][l]) > 1e-5)
{
System.Console.Write("Load " + l + " | ");
}
}
System.Console.WriteLine(); System.Console.WriteLine();
}
System.Console.WriteLine("--------------------------------------------");
}
else
{
System.Console.WriteLine(" No solution found ");
}
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
/// <summary>
/// The example's main function.
/// </summary>
public static void Main(string[] args)
{
int retval = 0;
Cplex cplex = null;
try
{
cplex = new Cplex();
/* ***************************************************************** *
* *
* S E T U P P R O B L E M *
* *
* We create the following problem: *
* Minimize *
* obj: 3x1 - x2 + 3x3 + 2x4 + x5 + 2x6 + 4x7 *
* Subject To *
* c1: x1 + x2 = 4 *
* c2: x1 + x3 >= 3 *
* c3: x6 + x7 <= 5 *
* c4: -x1 + x7 >= -2 *
* q1: [ -x1^2 + x2^2 ] <= 0 *
* q2: [ 4.25x3^2 -2x3*x4 + 4.25x4^2 - 2x4*x5 + 4x5^2 ] + 2 x1 <= 9.0
* q3: [ x6^2 - x7^2 ] >= 4 *
* Bounds *
* 0 <= x1 <= 3 *
* x2 Free *
* 0 <= x3 <= 0.5 *
* x4 Free *
* x5 Free *
* x7 Free *
* End *
* *
* ***************************************************************** */
INumVar[] x = new INumVar[7];
x[0] = cplex.NumVar(0, 3, "x1");
x[1] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x2");
x[2] = cplex.NumVar(0, 0.5, "x3");
x[3] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x4");
x[4] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x5");
x[5] = cplex.NumVar(0, System.Double.PositiveInfinity, "x6");
x[6] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x7");
IRange[] linear = new IRange[4];
linear[0] = cplex.AddEq(cplex.Sum(x[0], x[1]), 4.0, "c1");
linear[1] = cplex.AddGe(cplex.Sum(x[0], x[2]), 3.0, "c2");
linear[2] = cplex.AddLe(cplex.Sum(x[5], x[6]), 5.0, "c3");
linear[3] = cplex.AddGe(cplex.Diff(x[6], x[0]), -2.0, "c4");
IRange[] quad = new IRange[3];
quad[0] = cplex.AddLe(cplex.Sum(cplex.Prod(-1, x[0], x[0]),
cplex.Prod(x[1], x[1])), 0.0, "q1");
quad[1] = cplex.AddLe(cplex.Sum(cplex.Prod(4.25, x[2], x[2]),
cplex.Prod(-2,x[2],x[3]),
cplex.Prod(4.25,x[3],x[3]),
cplex.Prod(-2,x[3],x[4]),
cplex.Prod(4,x[4],x[4]),
cplex.Prod(2,x[0])), 9.0, "q2");
quad[2] = cplex.AddGe(cplex.Sum(cplex.Prod(x[5], x[5]),
cplex.Prod(-1, x[6], x[6])), 4.0, "q3");
cplex.AddMinimize(cplex.Sum(cplex.Prod(3.0, x[0]),
cplex.Prod(-1.0, x[1]),
cplex.Prod(3.0, x[2]),
cplex.Prod(2.0, x[3]),
cplex.Prod(1.0, x[4]),
cplex.Prod(2.0, x[5]),
cplex.Prod(4.0, x[6])), "obj");
/* ***************************************************************** *
* *
* O P T I M I Z E P R O B L E M *
* *
* ***************************************************************** */
cplex.SetParam(Cplex.Param.Barrier.QCPConvergeTol, 1e-10);
cplex.Solve();
/* ***************************************************************** *
* *
* Q U E R Y S O L U T I O N *
* *
* ***************************************************************** */
double[] xval = cplex.GetValues(x);
double[] slack = cplex.GetSlacks(linear);
double[] qslack = cplex.GetSlacks(quad);
double[] cpi = cplex.GetReducedCosts(x);
double[] rpi = cplex.GetDuals(linear);
double[] qpi = getqconstrmultipliers(cplex, xval, ZEROTOL, x, quad);
// Also store solution in a dictionary so that we can look up
// values by variable and not only by index.
IDictionary<INumVar, System.Double> xmap = new Dictionary<INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
xmap.Add(x[j], xval[j]);
}
/* ***************************************************************** *
* *
* C H E C K K K T C O N D I T I O N S *
* *
* Here we verify that the optimal solution computed by CPLEX *
* (and the qpi[] values computed above) satisfy the KKT *
* conditions. *
* *
* ***************************************************************** */
// Primal feasibility: This example is about duals so we skip this test.
// Dual feasibility: We must verify
// - for <= constraints (linear or quadratic) the dual
// multiplier is non-positive.
// - for >= constraints (linear or quadratic) the dual
// multiplier is non-negative.
for (int i = 0; i < linear.Length; ++i)
{
if (linear[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (rpi[i] > ZEROTOL)
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
else if (linear[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (rpi[i] < -ZEROTOL)
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
else
{
// nothing to do for equality constraints
}
}
for (int i = 0; i < quad.Length; ++i)
{
if (quad[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (qpi[i] > ZEROTOL)
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
else if (quad[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (qpi[i] < -ZEROTOL)
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
else
{
// nothing to do for equality constraints
}
}
// Complementary slackness.
// For any constraint the product of primal slack and dual multiplier
// must be 0.
for (int i = 0; i < linear.Length; ++i)
{
if (System.Math.Abs(linear[i].UB - linear[i].LB) > ZEROTOL &&
System.Math.Abs(slack[i] * rpi[i]) > ZEROTOL)
throw new System.SystemException("Complementary slackness test failed for row " + linear[i]
+ ": " + System.Math.Abs(slack[i] * rpi[i]));
}
for (int i = 0; i < quad.Length; ++i)
{
if (System.Math.Abs(quad[i].UB - quad[i].LB) > ZEROTOL &&
System.Math.Abs(qslack[i] * qpi[i]) > ZEROTOL)
throw new System.SystemException("Complementary slackness test failed for quad " + quad[i]
+ ": " + System.Math.Abs(qslack[i] * qpi[i]));
}
for (int j = 0; j < x.Length; ++j)
{
if (x[j].UB < System.Double.PositiveInfinity)
{
double slk = x[j].UB - xval[j];
double dual = cpi[j] < -ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
if (x[j].LB > System.Double.NegativeInfinity)
{
double slk = xval[j] - x[j].LB;
double dual = cpi[j] > ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
}
// Stationarity.
// The difference between objective function and gradient at optimal
// solution multiplied by dual multipliers must be 0, i.E., for the
// optimal solution x
// 0 == c
// - sum(r in rows) r'(x)*rpi[r]
// - sum(q in quads) q'(x)*qpi[q]
// - sum(c in cols) b'(x)*cpi[c]
// where r' and q' are the derivatives of a row or quadratic constraint,
// x is the optimal solution and rpi[r] and qpi[q] are the dual
// multipliers for row r and quadratic constraint q.
// b' is the derivative of a bound constraint and cpi[c] the dual bound
// multiplier for column c.
IDictionary<INumVar, System.Double> kktsum = new Dictionary<INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
kktsum.Add(x[j], 0.0);
}
// Objective function.
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)cplex.GetObjective().Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = it.Value;
}
// Linear constraints.
// The derivative of a linear constraint ax - b (<)= 0 is just a.
for (int i = 0; i < linear.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)linear[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - rpi[i] * it.Value;
}
}
// Quadratic constraints.
// The derivative of a constraint xQx + ax - b <= 0 is
// Qx + Q'x + a.
for (int i = 0; i < quad.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)quad[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - qpi[i] * it.Value;
}
for (IQuadNumExprEnumerator it = ((IQuadNumExpr)quad[i].Expr).GetQuadEnumerator();
it.MoveNext(); /* nothing */)
{
INumVar v1 = it.NumVar1;
INumVar v2 = it.NumVar2;
kktsum[v1] = kktsum[v1] - qpi[i] * xmap[v2] * it.Value;
kktsum[v2] = kktsum[v2] - qpi[i] * xmap[v1] * it.Value;
}
}
// Bounds.
// The derivative for lower bounds is -1 and that for upper bounds
// is 1.
// CPLEX already returns dj with the appropriate sign so there is
// no need to distinguish between different bound types here.
for (int j = 0; j < x.Length; ++j)
{
kktsum[x[j]] = kktsum[x[j]] - cpi[j];
}
foreach (INumVar v in x)
{
if (System.Math.Abs(kktsum[v]) > ZEROTOL)
throw new System.SystemException("Stationarity test failed at " + v
+ ": " + System.Math.Abs(kktsum[v]));
}
// KKT conditions satisfied. Dump out the optimal solutions and
// the dual values.
System.Console.WriteLine("Optimal solution satisfies KKT conditions.");
System.Console.WriteLine(" x[] = " + arrayToString(xval));
System.Console.WriteLine(" cpi[] = " + arrayToString(cpi));
System.Console.WriteLine(" rpi[] = " + arrayToString(rpi));
System.Console.WriteLine(" qpi[] = " + arrayToString(qpi));
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("IloException: " + e.Message);
System.Console.WriteLine(e.StackTrace);
retval = -1;
}
finally
{
if (cplex != null)
cplex.End();
}
System.Environment.Exit(retval);
}
public void Build_RMP_YY(InitialSolution IS)//主问题的建模
{
initialPath_num = IS.PathSet.Count;
trip_num = TripList.Count;
realistic_trip_num = NetWork.num_Physical_trip;
A_Matrix = IS.A_Matrix;
DvarSet = new List <INumVar>(); //x
CoefSet = new List <double>(); //cij
ObjCoefSet = new List <double>();
PathSet = new List <Pairing>(); //列池
CoefSet = IS.Coefs; //IS初始解
PathSet = IS.PathSet;
ObjCoefSet = IS.ObjCoefs;
foreach (var p in PathSet)
{
ColumnPool.Add(p);
}
masterModel = new Cplex();
Obj = masterModel.AddMinimize();
//Constraint = new IRange[realistic_trip_num];
Ct_cover = new IRange[NUMBER_CREW];
Ct_crewNum = new IRange[5][]; //默认每条交路为5天
ct_nb = new List <IRange>();
/**按行建模**/
//vars and obj function
int i, j;
for (j = 0; j < initialPath_num; j++) //定义决策变量和目标函数
{
INumVar dvar = masterModel.NumVar(0, 1, NumVarType.Float); //INumVar-cplex里面的，定义决策变量。后面括号中的意思是定义var是0-1之间的浮点值
dvar.Name = "crew_" + PathSet[j].Arcs.First().D_Point.CrewID + "_" + j;
DvarSet.Add(dvar);
Obj.Expr = masterModel.Sum(Obj.Expr, masterModel.Prod(CoefSet[j], DvarSet[j]));//后面的小括号里面是一个cij*xj，大括号里面的是累计，包括之前的expr
}
/*constraints*/
//ct:每条交路每条担当的人数满足要求
#region //该条约束不需要，因为输入已经决定了，只要有可行解，该条约束必然满足
/*for (i = 0; i < 5; i++)//对每一天
* {
* INumExpr expr = masterModel.NumExpr();
* Dictionary<int, List<int>> route_paths_map = new Dictionary<int, List<int>>();
* for (j = 0; j < initialPath_num; j++) //对每天的工作链分类
* {
* if (A_Matrix[j][i] == 0) {
* continue;
* }
* if (!route_paths_map.ContainsKey(A_Matrix[j][i])) {
* route_paths_map.Add(A_Matrix[j][i], new List<int>());
* }
* route_paths_map[A_Matrix[j][i]].Add(j);
* }
*
* Ct_crewNum[i] = new IRange[route_paths_map.Count];
* foreach (var routePathsPair in route_paths_map) { //对第i天的每条交路
* foreach (var xj in routePathsPair.Value)
* {
* expr = masterModel.Sum(expr, DvarSet[xj]);
* }
*
* Ct_crewNum[i][routePathsPair.Key-1] = masterModel.AddGe(expr, 1); //20191004 一条交路1个人 TODO
* string name = "day_" + i + "_route_" + routePathsPair.Key;
* Ct_crewNum[i][routePathsPair.Key-1].Name = name;
*
* ct_nb.Add(Ct_crewNum[i][routePathsPair.Key - 1]);
* }
* }
*/
#endregion
// ct:每个乘务员只能有一条工作链
Dictionary <int, List <int> > crewID_paths_map = new Dictionary <int, List <int> >();
for (j = 0; j < initialPath_num; j++)
{
Pairing path = PathSet[j];
int crew_id = path.crewID;
if (!crewID_paths_map.ContainsKey(crew_id))
{
crewID_paths_map.Add(crew_id, new List <int>());
}
crewID_paths_map[crew_id].Add(j);
}
if (crewID_paths_map.Count != NUMBER_CREW)
{
throw new System.Exception("乘务员数量有误");
}
foreach (var crewID_paths_pair in crewID_paths_map)
{
INumExpr expr = masterModel.NumExpr();
foreach (var xj in crewID_paths_pair.Value)
{
expr = masterModel.Sum(expr, DvarSet[xj]);
}
Ct_cover[crewID_paths_pair.Key - 1] = masterModel.AddEq(expr, 1);
}
}
/// <summary>
/// Blend Optimizasyon Çözüm Modeli
/// </summary>
/// <param name="data"></param>
/// <returns>BlendResultModel</returns>
private BlendResultModel Model(BlendDataModel data)
{
#region Veriler
//parametrelerin local değişkenlere aktarılması.
_modelAdi = "Blend";
_dataModel = data;
cplex = new Cplex();
#endregion
#region Karar Değişkenleri
//Karar Değişkenleri
m = cplex.NumVarArray(_dataModel.NbElements, 0.0, Double.MaxValue);
r = cplex.NumVarArray(_dataModel.NbRaw, 0.0, Double.MaxValue);
s = cplex.NumVarArray(_dataModel.NbScrap, 0.0, Double.MaxValue);
i = cplex.NumVarArray(_dataModel.NbIngot, 0.0, Double.MaxValue);
le = new INumVar[_dataModel.NbElements];
#endregion
#region Amaç Fonksiyonu
// Objective Function: Minimize Cost
cplex.AddMinimize(cplex.Sum(cplex.ScalProd(_dataModel.Cm, m),
cplex.ScalProd(_dataModel.Cr, r),
cplex.ScalProd(_dataModel.Cs, s),
cplex.ScalProd(_dataModel.Ci, i)));
#endregion
#region Kısıtlar
// Min and max quantity of each element in alloy
for (int j = 0; j < _dataModel.NbElements; j++)
{
le[j] = cplex.NumVar(_dataModel._p[j] * _dataModel.Alloy, _dataModel._P[j] * _dataModel.Alloy);
}
// Constraint: produce requested quantity of alloy
cplex.AddEq(cplex.Sum(le), _dataModel.Alloy);
// Constraints: Satisfy element quantity requirements for alloy
for (int j = 0; j < _dataModel.NbElements; j++)
{
cplex.AddEq(le[j],
cplex.Sum(m[j],
cplex.ScalProd(_dataModel.PRaw[j], r),
cplex.ScalProd(_dataModel.PScrap[j], s),
cplex.ScalProd(_dataModel.PIngot[j], i)));
}
#endregion
#region Çözümün işlenmesi
try
{
if (cplex.Solve())
{
if (cplex.GetStatus().Equals(Cplex.Status.Infeasible))
{
throw new ILOG.Concert.Exception("No feasible solution found!");
}
#region Sonuçların Alınması
Results = new BlendResultModel()
{
Satatus = cplex.GetStatus().ToString(),
ObjectiveValue = cplex.GetObjValue(),
ResultMessage = "Çözüm başarılı.",
BlendResults = new BlendResult()
{
MVals = cplex.GetValues(m),
RVals = cplex.GetValues(r),
SVals = cplex.GetValues(s),
IVals = cplex.GetValues(i),
EVals = cplex.GetValues(le)
}
};
#endregion
}
cplex.End();
return(Results);
}
catch (ILOG.Concert.Exception exc)
{
//exc.GetBaseException();
Console.WriteLine("Concert exception '" + exc + "' caught");
Console.ReadKey();
}
return(Results);
#endregion
}
//Building initial model
public static INumVar[] BuildModel(Cplex cplex, Instance instance, int nEdges)
{
//Init the model's variables
INumVar[] x = new INumVar[(instance.NNodes - 1) * instance.NNodes / 2];
/*
* expr will hold all the expressions that needs to be added to the model
* initially it will be the optimality's functions
* later it will be Ax's rows
*/
ILinearNumExpr expr = cplex.LinearNumExpr();
//Populating objective function
for (int i = 0; i < instance.NNodes; i++)
{
if (nEdges >= 0)
{
List <int>[] listArray = BuildSL(instance);
//Only links (i,i) with i < i are correct
for (int j = i + 1; j < instance.NNodes; j++)
{
//xPos return the correct position where to store the variable corresponding to the actual link (i,i)
int position = xPos(i, j, instance.NNodes);
if ((listArray[i]).IndexOf(j) < nEdges)
{
x[position] = cplex.NumVar(0, 1, NumVarType.Bool, "x(" + (i + 1) + "," + (j + 1) + ")");
}
else
{
x[position] = cplex.NumVar(0, 0, NumVarType.Bool, "x(" + (i + 1) + "," + (j + 1) + ")");
}
expr.AddTerm(x[position], Point.Distance(instance.Coord[i], instance.Coord[j], instance.EdgeType));
}
}
else
{
//Only links (i,i) with i < i are correct
for (int j = i + 1; j < instance.NNodes; j++)
{
//xPos return the correct position where to store the variable corresponding to the actual link (i,i)
int position = xPos(i, j, instance.NNodes);
x[position] = cplex.NumVar(0, 1, NumVarType.Bool, "x(" + (i + 1) + "," + (j + 1) + ")");
expr.AddTerm(x[position], Point.Distance(instance.Coord[i], instance.Coord[j], instance.EdgeType));
}
}
}
//Setting the optimality's function
cplex.AddMinimize(expr);
//Starting to elaborate Ax
for (int i = 0; i < instance.NNodes; i++)
{
//Resetting expr
expr = cplex.LinearNumExpr();
for (int j = 0; j < instance.NNodes; j++)
{
//For each row i only the links (i,i) or (i,i) have coefficent 1
//xPos return the correct position where link is stored inside the vector x
if (i != j)//No loops wioth only one node
{
expr.AddTerm(x[xPos(i, j, instance.NNodes)], 1);
}
}
//Adding to Ax the current equation with known term 2 and name degree(<current i node>)
cplex.AddEq(expr, 2, "degree(" + (i + 1) + ")");
}
//Printing the complete model inside the file <name_file.tsp.lp>
if (Program.VERBOSE >= -1)
{
cplex.ExportModel(instance.InputFile + ".lp");
}
return(x);
}
private double one_tsp(int dim, int [][] matrix, int [] path)
{
int[] lo = new int[dim];
for (int i = 0; i < dim; i++)
{
lo[i] = 1;
}
Cplex cplex = new Cplex();
NumVarType varType = NumVarType.Bool;
INumVar[][] x = new INumVar[dim][];
for (int i = 0; i < dim; i++)
{
x[i] = cplex.NumVarArray(dim, 0, 1);
}
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
x[i][j] = cplex.BoolVar();
}
}
for (int j = 0; j < dim; j++)
{
INumExpr xcolSum = cplex.NumExpr();
for (int i = 0; i < dim; i++)
{
xcolSum = cplex.Sum(xcolSum, x[i][j]);
}
cplex.AddEq(lo[j], xcolSum);
}
varType = NumVarType.Float;
INumVar[] u = new INumVar[dim];
for (int j = 0; j < dim; j++)
{
u[j] = cplex.NumVar(0, 100000);
}
for (int j = 1; j < dim; j++)
{
cplex.AddGe(u[j], 0);
}
for (int i = 1; i < dim; i++)
{
for (int j = 1; j < dim; j++)
{
if (i != j)
{
cplex.AddLe(cplex.Sum(cplex.Diff(u[i], u[j]), cplex.Prod(dim, x[i][j])), dim - 1);
}
}
}
for (int i = 0; i < dim; i++)
{
INumExpr xrowSum = cplex.NumExpr();
for (int j = 0; j < dim; j++)
{
xrowSum = cplex.Sum(xrowSum, x[i][j]);
}
cplex.AddEq(lo[i], xrowSum);
}
INumExpr costSum = cplex.NumExpr();
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
costSum = cplex.Sum(costSum, cplex.Prod(x[i][j], matrix[i][j]));
}
}
cplex.AddMinimize(costSum);
try
{
if (cplex.Solve())
{
//MessageBox.Show("Solution status = " + cplex.GetStatus());
//MessageBox.Show("cost = " + cplex.ObjValue);
int ipath = 0;
int depo = -1;
for (int i = dim - 1; i >= 0; i--)
{
for (int j = 0; j < dim; j++)
{
if (Convert.ToInt16(cplex.GetValue(x[i][j])) == 1)
{
depo = i;
}
}
}
path[ipath] = depo;
ipath++;
while (depo > -1)
{
for (int j = 0; j < dim; j++)
{
if (Convert.ToInt16(cplex.GetValue(x[path[ipath - 1]][j])) == 1)
{
path[ipath] = j;
ipath++;
if (j == depo)
{
depo = -1;
}
break;
}
}
}
return(cplex.ObjValue);
}
cplex.End();
}
catch (ILOG.Concert.Exception ex)
{
System.Console.WriteLine("Concert Error: " + ex);
}
return(-1);
}
static void Main()
{
try
{
string resultFilename = "./ResultFiles/MTSP_MTZ.csv";
string filename = "./DataFiles/Data.dat";
Data data = new Data(filename);
double timeFactor = 0;
double distanceFactor = 1;
double step = 0.1;
int routeCounter = 0;
File.WriteAllText(resultFilename, "");
do
{
using (Cplex cplex = new Cplex())
{
#region [Decision Variables]
IIntVar[][] x = new IIntVar[data.n][];
IIntVar[] u = cplex.IntVarArray(data.n, 0, (data.n - 1));
cplex.Add(u);
for (int i = 0; i < data.n; i++)
{
x[i] = cplex.BoolVarArray(data.n);
cplex.Add(x[i]);
}
#endregion
#region [Objective Function]
INumExpr obj = cplex.NumExpr();
for (int i = 0; i < data.n; i++)
{
for (int j = 0; j < data.n; j++)
{
if (i != j)
{
obj = cplex.Sum(obj,
cplex.Prod(
(
(timeFactor * data.timeNormalized[i][j]) +
(distanceFactor * data.distanceNormalized[i][j])
), x[i][j]));
}
}
}
cplex.AddMinimize(obj);
#endregion
#region [Restrictions]
for (int j = 0; j < data.n; j++)
{
ILinearNumExpr sumj = cplex.LinearNumExpr();
for (int i = 0; i < data.n; i++)
{
if (i != j)
{
sumj.AddTerm(1, x[i][j]);
}
}
cplex.AddEq(sumj, 1);
}
for (int i = 0; i < data.n; i++)
{
ILinearNumExpr sumi = cplex.LinearNumExpr();
for (int j = 0; j < data.n; j++)
{
if (i != j)
{
sumi.AddTerm(1, x[i][j]);
}
}
cplex.AddEq(sumi, 1);
}
for (int i = 0; i < data.n; i++)
{
for (int j = 0; j < data.n; j++)
{
if (i >= 1 && i != j && j < data.n)
{
cplex.AddLe(
cplex.Sum(cplex.Diff(u[i], u[j]),
cplex.Prod(data.n, x[i][j])),
(data.n - 1));
}
}
}
#endregion
cplex.SetParam(Cplex.DoubleParam.WorkMem, 4000.0);
cplex.SetParam(Cplex.Param.MIP.Strategy.File, 2);
cplex.SetParam(Cplex.DoubleParam.EpGap, 0.1);
cplex.SetParam(Cplex.BooleanParam.MemoryEmphasis, true);
cplex.SetParam(Cplex.IntParam.VarSel, 4);
Stopwatch stopWatch = new Stopwatch();
stopWatch.Start();
if (cplex.Solve())
{
stopWatch.Stop();
double[][] sol_x = new double[data.n][];
for (int i = 0; i < data.n; i++)
{
sol_x[i] = cplex.GetValues(x[i]);
}
double[] sol_u = new double[data.n];
sol_u = cplex.GetValues(u);
double timeTotal = 0;
double distanceTotal = 0;
for (int i = 0; i < data.n; i++)
{
for (int j = 0; j < data.n; j++)
{
timeTotal += data.time[i][j] * sol_x[i][j];
distanceTotal += data.distance[i][j] * sol_x[i][j];
}
}
StreamWriter file = new StreamWriter(resultFilename, true);
file.WriteLine($"{timeFactor},{distanceFactor},{stopWatch.Elapsed.TotalSeconds},{cplex.ObjValue},{timeTotal},{distanceTotal}");
file.Close();
StreamWriter fileRouteResult = new StreamWriter($"./ResultFiles/Route-{routeCounter}.txt");
for (int i = 0; i < data.n; i++)
{
for (int j = 0; j < data.n; j++)
{
if (sol_x[i][j] == 1)
{
fileRouteResult.WriteLine($"From city {i} to city {j} - u[i] = {sol_u[i]} and u[j] = {sol_u[j]}");
}
}
}
fileRouteResult.Close();
}
cplex.End();
}
timeFactor += step;
distanceFactor -= step;
routeCounter++;
} while (timeFactor <= 1);
}
catch (ILOG.Concert.Exception ex)
{
StreamWriter errorfile = new StreamWriter("./ErrorLog.txt");
errorfile.WriteLine("Exception Kind: ILOG.Concert.Exception (Concert Error)");
errorfile.WriteLine("Message: " + ex.Message);
errorfile.WriteLine("StackTrace: " + ex.StackTrace);
errorfile.Close();
}
catch (InputDataReader.InputDataReaderException ex)
{
StreamWriter errorfile = new StreamWriter("./ErrorLog.txt");
errorfile.WriteLine("Exception Kind: InputDataReader.InputDataReaderException (Data Error)");
errorfile.WriteLine("Message: " + ex.Message);
errorfile.WriteLine("StackTrace: " + ex.StackTrace);
errorfile.Close();
}
catch (System.IO.IOException ex)
{
StreamWriter errorfile = new StreamWriter("./ErrorLog.txt");
errorfile.WriteLine("Exception Kind: System.IO.IOException (IO Error)");
errorfile.WriteLine("Message: " + ex.Message);
errorfile.WriteLine("StackTrace: " + ex.StackTrace);
errorfile.Close();
}
}
public static void Main(string[] args)
{
int nMonths = cost.Length;
int nProducts = cost[0].Length;
try {
Cplex cplex = new Cplex();
INumVar[] produce = cplex.NumVarArray(nMonths, 0, System.Double.MaxValue);
INumVar[][] use = new INumVar[nMonths][];
INumVar[][] buy = new INumVar[nMonths][];
INumVar[][] store = new INumVar[nMonths][];
for (int i = 0; i < nMonths; i++)
{
use[i] = cplex.NumVarArray(nProducts, 0.0, System.Double.MaxValue);
buy[i] = cplex.NumVarArray(nProducts, 0.0, System.Double.MaxValue);
store[i] = cplex.NumVarArray(nProducts, 0.0, 1000.0);
}
for (int p = 0; p < nProducts; p++)
{
store[nMonths - 1][p].LB = 500.0;
store[nMonths - 1][p].UB = 500.0;
}
INumExpr profit = cplex.NumExpr();
for (int i = 0; i < nMonths; i++)
{
// Not more than 200 tons of vegetable oil can be refined
cplex.AddLe(cplex.Sum(use[i][v1], use[i][v2]), 200.0);
// Not more than 250 tons of non-vegetable oil can be refined
cplex.AddLe(cplex.Sum(use[i][o1], use[i][o2], use[i][o3]), 250.0);
// Constraints on food composition
cplex.AddLe(cplex.Prod(3.0, produce[i]),
cplex.Sum(cplex.Prod(8.8, use[i][v1]),
cplex.Prod(6.1, use[i][v2]),
cplex.Prod(2.0, use[i][o1]),
cplex.Prod(4.2, use[i][o2]),
cplex.Prod(5.0, use[i][o3])));
cplex.AddGe(cplex.Prod(6.0, produce[i]),
cplex.Sum(cplex.Prod(8.8, use[i][v1]),
cplex.Prod(6.1, use[i][v2]),
cplex.Prod(2.0, use[i][o1]),
cplex.Prod(4.2, use[i][o2]),
cplex.Prod(5.0, use[i][o3])));
cplex.AddEq(produce[i], cplex.Sum(use[i]));
// Raw oil can be stored for later use
if (i == 0)
{
for (int p = 0; p < nProducts; p++)
{
cplex.AddEq(cplex.Sum(500.0, buy[i][p]),
cplex.Sum(use[i][p], store[i][p]));
}
}
else
{
for (int p = 0; p < nProducts; p++)
{
cplex.AddEq(cplex.Sum(store[i - 1][p], buy[i][p]),
cplex.Sum(use[i][p], store[i][p]));
}
}
// Logical constraints:
// The food cannot use more than 3 oils
// (or at least two oils must not be used)
cplex.AddGe(cplex.Sum(cplex.Eq(use[i][v1], 0),
cplex.Eq(use[i][v2], 0),
cplex.Eq(use[i][o1], 0),
cplex.Eq(use[i][o2], 0),
cplex.Eq(use[i][o3], 0)), 2);
// When an oil is used, the quantity must be at least 20 tons
for (int p = 0; p < nProducts; p++)
{
cplex.Add(cplex.Or(cplex.Eq(use[i][p], 0),
cplex.Ge(use[i][p], 20)));
}
// If products v1 or v2 are used, then product o3 is also used
cplex.Add(cplex.IfThen(cplex.Or(cplex.Ge(use[i][v1], 20),
cplex.Ge(use[i][v2], 20)),
cplex.Ge(use[i][o3], 20)));
// Objective function
profit = cplex.Sum(profit, cplex.Prod(150, produce[i]));
profit = cplex.Diff(profit, cplex.ScalProd(cost[i], buy[i]));
profit = cplex.Diff(profit, cplex.Prod(5, cplex.Sum(store[i])));
}
cplex.AddMaximize(profit);
if (cplex.Solve())
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine(" Maximum profit = " + cplex.ObjValue);
for (int i = 0; i < nMonths; i++)
{
System.Console.WriteLine(" Month {0}", i);
System.Console.Write(" . buy ");
for (int p = 0; p < nProducts; p++)
{
System.Console.Write("{0,8:F2} ", cplex.GetValue(buy[i][p]));
}
System.Console.WriteLine();
System.Console.Write(" . use ");
for (int p = 0; p < nProducts; p++)
{
System.Console.Write("{0,8:F2} ", cplex.GetValue(use[i][p]));
}
System.Console.WriteLine();
System.Console.Write(" . store ");
for (int p = 0; p < nProducts; p++)
{
System.Console.Write("{0,8:F2} ", cplex.GetValue(store[i][p]));
}
System.Console.WriteLine();
}
}
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
static void Main(string[] args)
{
// Portfolio asset daily price data:
var assets = new[] { "A", "B", "C" };
var prices = new double[][] {
new double[] { .02, .03, .02, .05 },
new double[] { .01, .01, .05, .01 },
new double[] { .1, .05, .04, .02 },
};
// Pre-process data
var covmat = CovarianceMatrix(prices);
DisplayCovariance(covmat);
var expReturns = AssetReturns(prices);
DisplayReturns(assets, expReturns);
var rho = 0.05;
// Create LP model
try
{
Cplex cplex = new Cplex();
// Weights bounded 0 <= weight <= 1.0
var weights = cplex.NumVarArray(assets.Length, 0, 1.0);
// x = weights.
// Expected (mean) return of portfolio: ∑ᵢ x[i]*assetReturn[i]
var expRet = cplex.ScalProd(expReturns, weights);
// Portfolio variance : xᵀ∑x (matrix form of bi-linear: ∑ᵢ∑ⱼ x[i]*x[j]*cov(i,j)
// where ∑ is the covariance matrix m*m of m assets.
var pvar = cplex.QuadNumExpr();
for (int i = 0; i < assets.Length; ++i)
{
for (int j = 0; j < assets.Length; ++j)
{
pvar.AddTerm(covmat[i][j], weights[i], weights[j]);
}
}
// Objective (maximize): portfolio return - (Rho/2) * portfolio variance.
// Where 0 <= Rho <= 1 is the desired risk tolerance.
var obj = cplex.Diff(expRet, cplex.Prod(rho / 2, pvar));
cplex.AddMaximize(obj);
// Subject to:
// Sum of weights <= 1.0
cplex.AddEq(cplex.Sum(weights), 1.0);
// Exports model definition to readable LP format
cplex.ExportModel(@"c:\users\mike\cplexfin.lp");
// Solve and print results
if (cplex.Solve())
{
var w = new double[weights.Length];
Console.WriteLine("\nResulting Weights:");
for (int i = 0; i < weights.Length; i++)
{
Console.WriteLine($"{i + 1} : {cplex.GetValue(weights[i]) * 100:0.0}%");
w[i] = cplex.GetValue(weights[i]);
}
var totReturn = WeightedReturn(w, expReturns);
var totVariance = PortfolioVariance(w, covmat);
Console.WriteLine($"Total Return: {totReturn:0.00}, Total Variance: {totVariance:0.0000}");
}
cplex.End();
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception caught: " + e);
}
Console.WriteLine("Press any key to quit.");
Console.ReadKey();
}
private void Calculate()
{
try
{
btnCalc.Enabled = false;
int ret;
for (int i = 0; i > dgvTransport.ColumnCount; i++)
{
for (int j = 0; j > dgvTransport.RowCount; j++)
{
if ((int.TryParse(dgvTransport[i, j].Value.ToString(), out ret) == false || dgvTransport[i, j].Value.ToString() != "T") && i != dgvTransport.ColumnCount - 1 && j != dgvTransport.RowCount - 1)
{
throw new ILOG.Concert.Exception("A beviteli mezők értékének vagy egész számnak, vagy T-nek kell lennie!");
}
}
}
Cplex cplex = new Cplex();
int Supply = (int)nudSourceNum.Value;
int Drain = (int)nudDrainNum.Value;
int[] temp;
int SumSources = 0;
int SumDrains = 0;
int sumValue;
sumValue = 0;
for (int i = 0; i < dgvTransport.RowCount - 1; i++)
{
int.TryParse(dgvTransport[dgvTransport.ColumnCount - 1, i].Value.ToString(), out sumValue);
SumSources += sumValue;
}
sumValue = 0;
for (int i = 0; i < dgvTransport.ColumnCount - 1; i++)
{
int.TryParse(dgvTransport[i, dgvTransport.RowCount - 1].Value.ToString(), out sumValue);
SumDrains += sumValue;
}
if (SumSources != SumDrains)
{
//Nyílt szállítási feladat
if (SumSources < SumDrains)
{
DataGridViewRow r = new DataGridViewRow();
r.HeaderCell.Value = "FIKTÍV";
for (int i = 0; i < dgvTransport.ColumnCount - 1; i++)
{
DataGridViewCell c = new DataGridViewTextBoxCell();
c.Value = 0;
r.Cells.Add(c);
}
DataGridViewTextBoxCell cSupply = new DataGridViewTextBoxCell();
cSupply.Value = SumDrains - SumSources;
r.Cells.Add(cSupply);
dgvTransport.Rows.Insert(dgvTransport.RowCount - 1, r);
Supply++;
}
//egyenlő itt nem lehet, mert csak akkor lép be, ha nem egyenlő a két érték
else
{
DataGridViewTextBoxColumn col = new DataGridViewTextBoxColumn();
col.HeaderText = "FIKTÍV";
dgvTransport.Columns.Insert(dgvTransport.ColumnCount - 1, col);
for (int i = 0; i < dgvTransport.RowCount - 1; i++)
{
dgvTransport[dgvTransport.ColumnCount - 2, i].Value = 0;
}
dgvTransport[dgvTransport.ColumnCount - 2, dgvTransport.RowCount - 1].Value = SumSources - SumDrains;
Drain++;
}
}
int[][] Cmatrix = new int[Supply][];
int[] sources = new int[Supply];
int[] drains = new int[Drain];
INumVar[][] x = new INumVar[Supply][];
INumVar[][] y = new INumVar[Supply][];
for (int i = 0; i < Supply; i++)
{
x[i] = cplex.NumVarArray(Drain, 0.0, int.MaxValue);
y[i] = cplex.NumVarArray(Drain, 0.0, int.MaxValue);
}
//források
for (int i = 0; i < dgvTransport.RowCount - 1; i++)
{
int.TryParse(dgvTransport[dgvTransport.ColumnCount - 1, i].Value.ToString(), out sources[i]);
}
//nyelők
for (int i = 0; i < dgvTransport.ColumnCount - 1; i++)
{
int.TryParse(dgvTransport[i, dgvTransport.RowCount - 1].Value.ToString(), out drains[i]);
}
//Coef Matrix
for (int i = 0; i < dgvTransport.RowCount - 1; i++)
{
temp = new int[Drain];
for (int j = 0; j < dgvTransport.ColumnCount - 1; j++)
{
if (dgvTransport[j, i].Value.ToString() != "T")
{
int.TryParse(dgvTransport[j, i].Value.ToString(), out temp[j]);
}
else
{
temp[j] = int.MaxValue;
}
}
Cmatrix[i] = temp;
}
for (int i = 0; i < Supply; i++) // supply must meet demand
{
cplex.AddEq(cplex.Sum(x[i]), sources[i]);
}
for (int j = 0; j < Drain; j++)
{ // demand must meet supply
ILinearNumExpr v = cplex.LinearNumExpr();
for (int i = 0; i < Supply; i++)
{
v.AddTerm(1.0, x[i][j]);
}
cplex.AddEq(v, drains[j]);
}
ILinearNumExpr expr = cplex.LinearNumExpr();
for (int i = 0; i < Supply; ++i)
{
for (int j = 0; j < Drain; ++j)
{
expr.AddTerm(x[i][j], Cmatrix[i][j]);
}
}
cplex.AddMinimize(expr);
cplex.Solve();
MessageBox.Show("A megoldás: " + cplex.GetStatus().ToString());
lblSolutionType.Text = "A megoldás: " + cplex.GetStatus().ToString();
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine(" - Solution: ");
dgvSolution.RowCount = Supply;
dgvSolution.ColumnCount = Drain;
for (int i = 0; i < Supply; ++i)
{
System.Console.Write(" " + i + ": ");
for (int j = 0; j < Drain; ++j)
{
System.Console.Write("" + cplex.GetValue(x[i][j]) + "\t");
dgvSolution[j, i].Value = cplex.GetValue(x[i][j]);
}
System.Console.WriteLine();
}
System.Console.WriteLine(" Cost = " + cplex.ObjValue);
lblZValue.Text = "A célfüggvény értéke: " + cplex.ObjValue;
cplex.End();
}
catch (ILOG.Concert.Exception icex) { MessageBox.Show(icex.Message); }
}
// GED formulation from the paper
// https://ieeexplore.ieee.org/document/1642656
public override void BLPjusticehero()
{
int nbNode1 = graph1.ListNodes.Count;
int nbNode2 = graph2.ListNodes.Count;
int N = nbNode1 + nbNode2; // nombre de noeuds du graphe d'édition
// #region
//création matrices de placement standard A0 et A1
Graph gridg1 = new Graph();
Graph gridg2 = new Graph();
Type typeNodeLabel = graph1.ListNodes[0].Label.GetType();
object objNode = Activator.CreateInstance(typeNodeLabel);
Graphs.Label nodeepslabel = (Graphs.Label)objNode;
nodeepslabel.Id = ConstantsAC.EPS_ID;
Type typeEdgeLabel = null;
object objEdge = null;
Graphs.Label edgeepslabel = null;
if (graph1.ListEdges.Count > 0)
{
typeEdgeLabel = graph1.ListEdges[0].Label.GetType();
objEdge = Activator.CreateInstance(typeEdgeLabel);
edgeepslabel = (Graphs.Label)objEdge;
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
if (graph2.ListEdges.Count > 0)
{
typeEdgeLabel = graph2.ListEdges[0].Label.GetType();
objEdge = Activator.CreateInstance(typeEdgeLabel);
edgeepslabel = (Graphs.Label)objEdge;
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
if (graph1.ListEdges.Count == 0 && graph2.ListEdges.Count == 0)
{
Console.Out.WriteLine("error no edges random edge label alkane");
edgeepslabel = (Graphs.Label) new LabelEdgeAlkane();
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
//else
//{
//edgeepslabel = (Graphs.Label)new LabelEdgeAlkane();
//edgeepslabel.Id = ConstantsAC.EPS_ID;
//}
for (int i = 0; i < nbNode1; i++)
{
gridg1.addNode(graph1.ListNodes[i]);
}
for (int i = 0; i < graph1.ListEdges.Count; i++)
{
gridg1.addEdge(graph1.ListEdges[i]);
}
// ajout des noeuds "virtuels" au graphe g1, pour que g1 corresponde au placement standard dans le graphe d'édition (A0)
for (int i = nbNode1; i < N; i++)
{
Node n = new Node((i + 2).ToString());
gridg1.addNode(n);
n.Label = nodeepslabel;
n.Label.Id = ConstantsAC.EPS_ID;
// LabelEdgeLetter
//n.Label = new Graphs.GenericLabel();
//n.Label.Id = n.Id;
}
MatrixLibrary.Matrix A0 = gridg1.calculateAdjacencyMatrix(); // création matrice d'adajcence de g1
// idem pour g2 (A1)
for (int i = 0; i < nbNode2; i++)
{
gridg2.addNode(graph2.ListNodes[i]);
}
for (int i = 0; i < graph2.ListEdges.Count; i++)
{
gridg2.addEdge(graph2.ListEdges[i]);
}
for (int i = nbNode2; i < N; i++)
{
Node n = new Node((i + 2).ToString());
gridg2.addNode(n);
n.Label = nodeepslabel;//new LabelNodeMutagen();
n.Label.Id = ConstantsAC.EPS_ID;
//n.Label = new Graphs.GenericLabel();
//n.Label.Id = n.Id;
}
MatrixLibrary.Matrix A1 = gridg2.calculateAdjacencyMatrix(); // création matrice d'adajcence de g2
// les graphes vont être étiquetés avec un label LabelNodeMolecule (pour les noeuds) et LabelEdgeMolecule (pour les arrêtes)
// cela va nous permettre d'utiliser notre propre méthode "dissimilarity" pour les noeuds et arrêtes
// gridg1.DynamicCastLabel(graph1.ListNodes[0].Label, graph1.ListEdges[0].Label);
// gridg2.DynamicCastLabel(graph2.ListNodes[0].Label, graph2.ListEdges[0].Label);
// nb variables du pb : matrices P(N*N), S(N*N) et T(N*N)
int nbCols = 3 * (N * N);
// nb contraintes du pb
int nbRows = N * N + N + N;
List <double> objList = new List <double>();
List <string> colNameList = new List <string>();
// coût des opérations d'édition des sommets (coeff de P dans la formule de la distance d'édition)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
double costNode = gridg1.ListNodes[i].Label.dissimilarity(gridg2.ListNodes[j].Label);
objList.Add(costNode);
//colNameList.Add("P[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
colNameList.Add("x_" + gridg1.ListNodes[i].Id + "," + gridg2.ListNodes[j].Id + "");
}
}
// coût des opérations d'édition des arrêtes (coeffs de S et T)
//Edge ee = new Edge((0).ToString());
//ee.Label = new LabelEdgeMutagen();
//ee.Label.Id = ConstantsAC.EPS_ID;
// coeff de S
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
// dans notre cas, l'opération est soit 0->1 ou 1->0 (insertion ou suppression d'une arrête)
// double costNode = ee.Label.dissimilarity(ee.Label) / 2.0;
double costNode = edgeepslabel.dissimilarity(edgeepslabel) / 2.0;
//double costNode = 0.5 / 2.0;
objList.Add(costNode);
colNameList.Add("S[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
}
}
// coeff de T
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
// dans notre cas, l'opération est soit 0->1 ou 1->0 (insertion ou suppression d'une arrête)
//double costNode = ee.Label.dissimilarity(ee.Label) / 2.0;
double costNode = edgeepslabel.dissimilarity(edgeepslabel) / 2.0;
// double costNode = 0.5 / 2.0;
objList.Add(costNode);
colNameList.Add("T[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
}
}
try
{
// Cplex cplex = new Cplex(); // creation du modèle CPLEX
//ILPMatrix lp_matrix = cplex.AddLPMatrix(); // matrice du pb (initialisée à 0 colonnes et 0 lignes)
cplex = new Cplex();
ilpMatrix = cplex.AddLPMatrix();
ColumnArray colonnes = cplex.ColumnArray(ilpMatrix, nbCols); // définition des variables-colonnes du pb
// ajout des variables-colonnes dans la matrice du pb (avec définition des bornes: P[i][j] = 0 ou 1, idem avec S et T)
INumVar[] x = cplex.NumVarArray(colonnes, 0, 1, NumVarType.Bool, colNameList.ToArray());
INumVar[,] P = new INumVar[N, N];
INumVar[,] S = new INumVar[N, N];
INumVar[,] T = new INumVar[N, N];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
P[i, j] = x[(N * i) + j];
}
}
// indice de S et T dans x (utilisés lors de la définition des contraintes)
int indicedebutS = N * N; // indice du 1er élément de S dans x
int indicedebutT = 2 * (N * N); // indice du 1er élément de T dans x
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
S[i, j] = x[indicedebutS + (N * i) + j];
}
}
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
T[i, j] = x[indicedebutT + (N * i) + j];
}
}
objCoef = objList.ToArray();
// ajout de la fonction objectif du pb
cplex.AddMinimize(cplex.ScalProd(x, objCoef));
// contrainte n°1
for (int i = 0; i < N; i++)
{
int[] coeffsA0 = new int[N]; // vecteur des coeffs ligne i de A0
INumVar[] coeffsP_A1 = new INumVar[N]; // vecteur des coeffs ligne i de P
for (int c = 0; c < N; c++)
{
coeffsA0[c] = (int)A0[i, c];
coeffsP_A1[c] = P[i, c];
}
for (int j = 0; j < N; j++)
{
INumVar[] coeffsP = new INumVar[N]; // vecteur des coeffs colonne j de P
int[] coeffsA1 = new int[N]; // vecteur des coeffs colonne j de A1
for (int c = 0; c < N; c++)
{
coeffsP[c] = P[c, j];
coeffsA1[c] = (int)A1[c, j];
}
cplex.AddEq(cplex.Sum(
cplex.Diff(
cplex.ScalProd(coeffsP, coeffsA0), cplex.ScalProd(coeffsP_A1, coeffsA1)),
cplex.Diff(
S[i, j], T[i, j]))
, 0);
/* (ANCIEN PRODUIT TERME A TERME)
* cplex.AddEq(cplex.Sum(
* cplex.Diff(
* cplex.Prod(A0[i,j],P[i,j]),cplex.Prod(P[i,j],A1[i,j])),
* cplex.Diff(
* S[i, j], T[i, j]))
* , 0); */
}
}
// contrainte n°2 (somme des lignes dans P = 1 et somme des colonnes dans P = 1)
for (int i = 0; i < N; i++)
{
INumVar[] sommeLignes = new INumVar[N];
INumVar[] sommeColonnes = new INumVar[N];
for (int j = 0; j < N; j++)
{
sommeLignes[j] = x[N * i + j];
sommeColonnes[j] = x[N * j + i];
}
cplex.AddEq(cplex.Sum(sommeLignes), 1);
cplex.AddEq(cplex.Sum(sommeColonnes), 1);
}
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception `" + e + "` caught");
}
}
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[] 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.NumVarArray(_nbIngot, 0.0, System.Double.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 Solution");
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");
}
}
private void decomp(int dim, int kts, int[][] dist, List <int> WorkList)
{
int[] lo = new int[dim];
int dk = dim * kts;
for (int i = 0; i < dim; i++)
{
lo[i] = 1;
}
Cplex cplex = new Cplex();
NumVarType varType = NumVarType.Bool;
INumVar[][] x = new INumVar[dim][];
for (int i = 0; i < dim; i++)
{
x[i] = cplex.NumVarArray(dk, 0, 1);
}
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dk; j++)
{
x[i][j] = cplex.BoolVar();
}
}
//****************************************
//Что тут происходит?
for (int j = 0; j < dim; j++)
{
INumExpr xcolSum = cplex.NumExpr();
for (int k = 0; k < kts; k++)
{
for (int i = 0; i < dim; i++)
{
xcolSum = cplex.Sum(xcolSum, x[i][k * dim + j]);
}
}
cplex.AddEq(lo[j], xcolSum);
}
varType = NumVarType.Float;
INumVar[] u = new INumVar[dk];
for (int j = 0; j < dk; j++)
{
u[j] = cplex.NumVar(0, 100000);
}
for (int j = 1; j < dk; j++)
{
cplex.AddGe(u[j], 0);
}
for (int k = 0; k < kts; k++)
{
for (int i = 1; i < dim; i++)
{
for (int j = 1; j < dim; j++)
{
if (i != j)
{
if (kts == 1)
{
cplex.AddLe(cplex.Sum(cplex.Diff(u[k * dim + i], u[k * dim + j]), cplex.Prod(dim, x[i][k * dim + j])), dim - 1);
}
else
{
cplex.AddLe(cplex.Sum(cplex.Diff(u[k * dim + i], u[k * dim + j]), cplex.Prod(dim, x[i][k * dim + j])), dim);
}
}
}
}
}
for (int i = 0; i < dim; i++)
{
INumExpr xrowSum = cplex.NumExpr();
for (int j = 0; j < dk; j++)
{
xrowSum = cplex.Sum(xrowSum, x[i][j]);
}
cplex.AddEq(lo[i], xrowSum);
}
//Условия независимости кластеров
if (kts > 1)
{
int[] a = new int[kts + 1];
for (int k = 1; k < kts; k++)
{
if (k > 1 && k < kts - 1)
{
continue;
}
int p;
for (int i = 1; i <= k; i++)
{
a[i] = i;
}
p = k;
while (p >= 1)
{
for (int m = 0; m < dim; m++)
{
INumExpr xcolrowSum = cplex.NumExpr();
for (int j = 1; j <= kts; j++)
{
bool row = false;
for (int i = 1; i <= k; i++)
{
if (a[i] == j)
{
row = true;
}
}
if (row)
{
for (int t = 0; t < dim; t++)
{
xcolrowSum = cplex.Sum(xcolrowSum, x[m][(j - 1) * dim + t]);
}
}
else
{
for (int t = 0; t < dim; t++)
{
xcolrowSum = cplex.Sum(xcolrowSum, x[t][(j - 1) * dim + m]);
}
}
}
cplex.AddLe(xcolrowSum, lo[m]);
}
if (a[k] == kts)
{
p--;
}
else
{
p = k;
}
if (p >= 1)
{
for (int i = k; i >= p; i--)
{
a[i] = a[p] + i - p + 1;
}
}
}
}
}
INumExpr costSum = cplex.NumExpr();
INumExpr[] costSum1 = new INumExpr[kts];
if (kts == 1)
{
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
costSum = cplex.Sum(costSum, cplex.Prod(x[i][j], dist[i][j]));
}
}
cplex.AddMinimize(costSum);
}
else
{
for (int k = 0; k < kts; k++)
{
costSum1[k] = cplex.NumExpr();
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
costSum1[k] = cplex.Sum(costSum1[k], cplex.Prod(x[i][k * dim + j], dist[i][j]));
}
}
//cplex.AddLe(costSum1[k], costSum);
}
costSum = cplex.Max(costSum1);
cplex.AddMinimize(costSum);
}
try
{
if (cplex.Solve())
{
textBox1.Text += "lambda = " + cplex.ObjValue + Environment.NewLine;
textBox1.Text += DateTime.Now.ToString() + Environment.NewLine;
WorkList.Clear();
int num_clust = 0;
for (int k = 0; k < kts; k++)
{
int dim1 = 0;
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
if (Convert.ToInt16(cplex.GetValue(x[i][k * dim + j])) == 1)
{
dim1++;
}
}
}
if (dim1 > 0)
{
num_clust++;
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
if (Convert.ToInt16(cplex.GetValue(x[i][k * dim + j])) == 1)
{
WorkList.Add(i);
break;
}
}
}
WorkList.Add(-1);
}
}
textBox1.Text += DateTime.Now.ToString() + Environment.NewLine;
}
else
{
textBox1.Text += "Нет решения" + Environment.NewLine;
textBox1.Text += DateTime.Now.ToString() + Environment.NewLine;
}
cplex.End();
}
catch (ILOG.Concert.Exception ex)
{
textBox1.Text += "Concert Error: " + ex + Environment.NewLine;
textBox1.Text += DateTime.Now.ToString() + Environment.NewLine;
}
}
static void Main(string[] args)
{
double[] Demand = new double[] { 15, 18, 14, 20 };
double[] Capacity = new double[] { 20, 22, 17, 19, 18 };
double[,] ShipCosts =
new double[,] { { 4000, 2500, 1200, 2200 },
{ 2000, 2600, 1800, 2600 },
{ 3000, 3400, 2600, 3100 },
{ 2500, 3000, 4100, 3700 },
{ 4500, 4000, 3000, 3200 } };
int nWarehouses = Capacity.Length;
int nCustomers = Demand.Length;
Cplex m = new Cplex();
INumVar[,] Ship = new INumVar[nWarehouses, nCustomers];
for (int i = 0; i < nWarehouses; ++i)
for (int j = 0; j < nCustomers; ++j)
Ship[i, j] = m.NumVar(0, System.Double.MaxValue, NumVarType.Float, "ship." + i + "." + j);
INumVar[] Shortage = new INumVar[nCustomers];
for (int j = 0; j < nCustomers; ++j)
Shortage[j] = m.NumVar(0, System.Double.MaxValue, NumVarType.Float, "shortage." + j);
INumVar TotalShortage = m.NumVar(0, System.Double.MaxValue, NumVarType.Float, "TotalShortage");
INumVar TotalShippingCost = m.NumVar(0, System.Double.MaxValue, NumVarType.Float, "TotalShippingCost");
IObjective obj = m.AddMinimize(TotalShippingCost);
IConstraint[] DemandCon = new IConstraint[nCustomers];
for (int j = 0; j < nCustomers; ++j)
{
INumExpr lhs = m.LinearNumExpr(0.0);
INumExpr rhs = m.LinearNumExpr(Demand[j]);
for (int i = 0; i < nWarehouses; ++i)
lhs = m.Sum(lhs, Ship[i, j]);
lhs = m.Sum(lhs, Shortage[j]);
DemandCon[j] = m.AddEq(lhs, rhs, "demand." + j);
}
IConstraint[] CapacityCon = new IConstraint[nWarehouses];
for (int i = 0; i < nWarehouses; ++i)
{
INumExpr lhs = m.LinearNumExpr(0.0);
for (int j = 0; j < nCustomers; ++j)
lhs = m.Sum(lhs, Ship[i, j]);
CapacityCon[i] = m.AddLe(lhs, Capacity[i], "capacity." + i);
}
INumExpr expr = m.Sum(Shortage);
IConstraint TotalShortageCon = m.AddEq(expr, TotalShortage, "total_shortage");
expr = m.LinearNumExpr(0.0);
for (int i = 0; i < nWarehouses; ++i)
for (int j = 0; j < nCustomers; ++j)
expr = m.Sum(expr, m.Prod(ShipCosts[i, j], Ship[i, j]));
IConstraint TotalShippingCon = m.AddEq(expr, TotalShippingCost, "total_shipping");
m.ExportModel("Facility.lp");
while (true)
{
Console.WriteLine("\nSolver Output:");
m.Solve();
double OptShortage = m.GetValue(TotalShortage);
double OptShipping = m.GetValue(TotalShippingCost);
Console.WriteLine("\nFacility Program Output:");
Console.WriteLine("\nTotalShortage = {0}", OptShortage);
Console.WriteLine("TotalShippingCost= {0}\n", OptShipping);
if (OptShortage < EPS) break;
INumVar[] varArr = new INumVar[26];
double[] ubs = new double[26];
double[] lbs = new double[26];
varArr[0] = TotalShortage;
varArr[1] = TotalShippingCost;
for (int i = 0; i < nWarehouses; ++i)
for (int j = 0; j < nCustomers; ++j)
varArr[4 * i + j + 2] = Ship[i, j];
for (int j = 0; j < nCustomers; ++j)
varArr[j + 22] = Shortage[j];
m.GetObjSA(lbs, ubs, varArr);
double ObjectiveBound = ubs[0];
m.SetLinearCoef(obj, ((1 + EPS) * ObjectiveBound), TotalShortage);
} // end while
for (int i = 0; i < nWarehouses; ++i)
for (int j = 0; j < nCustomers; ++j)
Console.WriteLine("{0} = {1}", Ship[i, j].Name, m.GetValue(Ship[i, j]));
for (int j = 0; j < nCustomers; ++j)
Console.WriteLine("{0} = {1}", Shortage[j].Name, m.GetValue(Shortage[j]));
Console.WriteLine("{0} = {1}", TotalShortage.Name, m.GetValue(TotalShortage));
Console.WriteLine("{0} = {1}", TotalShippingCost.Name, m.GetValue(TotalShippingCost));
} // end Main
/// <summary>
/// Getting maximum congruency for naming parameter sets A or B. Linear Programming optimization model.
/// Eq. (4) and Table II in DOI:10.1109/CEC.2019.8790261
/// The matrices need to be manually entered here in the script (cTopA, cTopB, cBtmA, cBtmB)
/// </summary>
internal static void IdentifyTwoBestParameterSets(string caseSolver)
{
Cplex cpl = new Cplex();
int N = 7;
//string caseSolver = "ES"; //"SGA" (default), "ES", "PSO", "FIPS"
int[] cTopA;
int[] cTopB;
int[] cBtmA;
int[] cBtmB;
switch (caseSolver)
{
default:
cTopA = new int[] { 11, 1, 1, 13, 0, 0, 2 };
cTopB = new int[] { 0, 5, 3, 0, 5, 5, 5 };
cBtmA = new int[] { 2, 12, 12, 0, 14, 14, 9 };
cBtmB = new int[] { 4, 0, 1, 4, 0, 0, 0 };
break;
case "ES":
cTopA = new int[] { 4, 6, 9, 3, 11, 11, 5 };
cTopB = new int[] { 2, 3, 1, 3, 1, 3, 3 };
cBtmA = new int[] { 4, 5, 2, 8, 0, 0, 6 };
cBtmB = new int[] { 3, 1, 3, 2, 5, 3, 2 };
break;
case "PSO":
cTopA = new int[] { 1, 3, 2, 3, 3, 7, 5 };
cTopB = new int[] { 12, 11, 3, 1, 7, 8, 5 };
cBtmA = new int[] { 7, 5, 6, 5, 5, 1, 3 };
cBtmB = new int[] { 0, 1, 9, 11, 5, 4, 7 };
break;
case "FIPS":
cTopA = new int[] { 6, 6, 7, 3, 5, 0, 8 };
cTopB = new int[] { 4, 6, 6, 9, 5, 9, 1 };
cBtmA = new int[] { 4, 4, 3, 7, 5, 10, 2 };
cBtmB = new int[] { 6, 4, 4, 1, 5, 1, 9 };
break;
}
INumVar[] xTopA = new INumVar[N];
INumVar[] xBtmB = new INumVar[N];
INumVar[] xTopB = new INumVar[N];
INumVar[] xBtmA = new INumVar[N];
ILinearNumExpr value = cpl.LinearNumExpr();
for (int n = 0; n < N; n++)
{
xTopA[n] = cpl.BoolVar();
xBtmB[n] = cpl.BoolVar();
xTopB[n] = cpl.BoolVar();
xBtmA[n] = cpl.BoolVar();
cpl.AddEq(cpl.Sum(xTopB[n], xTopA[n]), 1);
cpl.AddEq(cpl.Sum(xBtmA[n], xBtmB[n]), 1);
cpl.AddEq(cpl.Sum(xTopA[n], xBtmA[n]), 1);
cpl.AddEq(cpl.Sum(xTopB[n], xBtmB[n]), 1);
value.AddTerm(xTopA[n], cTopA[n]);
value.AddTerm(xTopB[n], cTopB[n]);
value.AddTerm(xBtmA[n], cBtmA[n]);
value.AddTerm(xBtmB[n], cBtmB[n]);
}
cpl.AddMaximize(value);
cpl.Solve();
Console.WriteLine("Parameter Grouping for Solver: {0}", caseSolver);
for (int n = 0; n < N; n++)
{
Console.WriteLine("n: {0}", n);
Console.WriteLine("xtopA: ;{0};, _____, xTopB: ;{1};", cpl.GetValue(xTopA[n]), cpl.GetValue(xTopB[n]));
Console.WriteLine("xbtmB: ;{0};, _____, xBtmA: ;{1};", cpl.GetValue(xBtmB[n]), cpl.GetValue(xBtmA[n]));
}
Console.WriteLine("cost: {0}", cpl.GetObjValue());
Console.ReadKey();
}
public static void Main (string[] args) {
int nMonths = cost.Length;
int nProducts = cost[0].Length;
try {
Cplex cplex = new Cplex();
INumVar[] produce = cplex.NumVarArray(nMonths, 0, System.Double.MaxValue);
INumVar[][] use = new INumVar[nMonths][];
INumVar[][] buy = new INumVar[nMonths][];
INumVar[][] store = new INumVar[nMonths][];
for (int i = 0; i < nMonths; i++) {
use[i] = cplex.NumVarArray(nProducts, 0.0, System.Double.MaxValue);
buy[i] = cplex.NumVarArray(nProducts, 0.0, System.Double.MaxValue);
store[i] = cplex.NumVarArray(nProducts, 0.0, 1000.0);
}
for (int p = 0; p < nProducts; p++) {
store[nMonths-1][p].LB = 500.0;
store[nMonths-1][p].UB = 500.0;
}
INumExpr profit = cplex.NumExpr();
for (int i = 0; i < nMonths; i++) {
// Not more than 200 tons of vegetable oil can be refined
cplex.AddLe(cplex.Sum(use[i][v1], use[i][v2]), 200.0);
// Not more than 250 tons of non-vegetable oil can be refined
cplex.AddLe(cplex.Sum(use[i][o1], use[i][o2], use[i][o3]), 250.0);
// Constraints on food composition
cplex.AddLe(cplex.Prod(3.0,produce[i]),
cplex.Sum(cplex.Prod(8.8, use[i][v1]),
cplex.Prod(6.1, use[i][v2]),
cplex.Prod(2.0, use[i][o1]),
cplex.Prod(4.2, use[i][o2]),
cplex.Prod(5.0, use[i][o3])));
cplex.AddGe(cplex.Prod(6.0, produce[i]),
cplex.Sum(cplex.Prod(8.8, use[i][v1]),
cplex.Prod(6.1, use[i][v2]),
cplex.Prod(2.0, use[i][o1]),
cplex.Prod(4.2, use[i][o2]),
cplex.Prod(5.0, use[i][o3])));
cplex.AddEq(produce[i], cplex.Sum(use[i]));
// Raw oil can be stored for later use
if (i == 0) {
for (int p = 0; p < nProducts; p++)
cplex.AddEq(cplex.Sum(500.0, buy[i][p]),
cplex.Sum(use[i][p], store[i][p]));
}
else {
for (int p = 0; p < nProducts; p++)
cplex.AddEq(cplex.Sum(store[i-1][p], buy[i][p]),
cplex.Sum(use[i][p], store[i][p]));
}
// Logical constraints:
// The food cannot use more than 3 oils
// (or at least two oils must not be used)
cplex.AddGe(cplex.Sum(cplex.Eq(use[i][v1], 0),
cplex.Eq(use[i][v2], 0),
cplex.Eq(use[i][o1], 0),
cplex.Eq(use[i][o2], 0),
cplex.Eq(use[i][o3], 0)), 2);
// When an oil is used, the quantity must be at least 20 tons
for (int p = 0; p < nProducts; p++)
cplex.Add(cplex.Or(cplex.Eq(use[i][p], 0),
cplex.Ge(use[i][p], 20)));
// If products v1 or v2 are used, then product o3 is also used
cplex.Add(cplex.IfThen(cplex.Or(cplex.Ge(use[i][v1], 20),
cplex.Ge(use[i][v2], 20)),
cplex.Ge(use[i][o3], 20)));
// Objective function
profit = cplex.Sum (profit, cplex.Prod(150, produce[i]));
profit = cplex.Diff(profit, cplex.ScalProd(cost[i], buy[i]));
profit = cplex.Diff(profit, cplex.Prod(5, cplex.Sum(store[i])));
}
cplex.AddMaximize(profit);
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine(" Maximum profit = " + cplex.ObjValue);
for (int i = 0; i < nMonths; i++) {
System.Console.WriteLine(" Month {0}", i);
System.Console.Write(" . buy ");
for (int p = 0; p < nProducts; p++)
System.Console.Write("{0,8:F2} ", cplex.GetValue(buy[i][p]));
System.Console.WriteLine();
System.Console.Write(" . use ");
for (int p = 0; p < nProducts; p++)
System.Console.Write("{0,8:F2} ", cplex.GetValue(use[i][p]));
System.Console.WriteLine();
System.Console.Write(" . store ");
for (int p = 0; p < nProducts; p++)
System.Console.Write("{0,8:F2} ", cplex.GetValue(store[i][p]));
System.Console.WriteLine();
}
}
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
public static void Main(string[] args)
{
if ( args.Length < 1 ) {
System.Console.WriteLine("Usage: Transport <type>");
System.Console.WriteLine(" type = 0 -> convex piecewise linear model");
System.Console.WriteLine(" type = 1 -> concave piecewise linear model");
return;
}
try {
Cplex cplex = new Cplex();
int nbDemand = 4;
int nbSupply = 3;
double[] supply = {1000.0, 850.0, 1250.0};
double[] demand = {900.0, 1200.0, 600.0, 400.0};
INumVar[][] x = new INumVar[nbSupply][];
INumVar[][] y = new INumVar[nbSupply][];
for (int i = 0; i < nbSupply; i++) {
x[i] = cplex.NumVarArray(nbDemand, 0.0, System.Double.MaxValue);
y[i] = cplex.NumVarArray(nbDemand, 0.0, System.Double.MaxValue);
}
for (int i = 0; i < nbSupply; i++) // supply must meet demand
cplex.AddEq(cplex.Sum(x[i]), supply[i]);
for (int j = 0; j < nbDemand; j++) { // demand must meet supply
ILinearNumExpr v = cplex.LinearNumExpr();
for(int i = 0; i < nbSupply; i++)
v.AddTerm(1.0, x[i][j]);
cplex.AddEq(v, demand[j]);
}
double[] points;
double[] slopes;
if ( args[0].ToCharArray()[0] == '0' ) { // convex case
points = new double[] {200.0, 400.0};
slopes = new double[] { 30.0, 80.0, 130.0};
}
else { // concave case
points = new double[] {200.0, 400.0};
slopes = new double[] {120.0, 80.0, 50.0};
}
for (int i = 0; i < nbSupply; ++i) {
for (int j = 0; j < nbDemand; ++j) {
cplex.AddEq(y[i][j],
cplex.PiecewiseLinear(x[i][j],
points, slopes, 0.0, 0.0));
}
}
ILinearNumExpr expr = cplex.LinearNumExpr();
for (int i = 0; i < nbSupply; ++i) {
for (int j = 0; j < nbDemand; ++j) {
expr.AddTerm(y[i][j], 1.0);
}
}
cplex.AddMinimize(expr);
if ( cplex.Solve() ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine(" - Solution: ");
for (int i = 0; i < nbSupply; ++i) {
System.Console.Write(" " + i + ": ");
for (int j = 0; j < nbDemand; ++j)
System.Console.Write("" + cplex.GetValue(x[i][j]) + "\t");
System.Console.WriteLine();
}
System.Console.WriteLine(" Cost = " + cplex.ObjValue);
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine(exc);
}
}
public Dictionary <EdgePair, Double> Solve(FCTPGraph ti)
{
Dictionary <EdgePair, Double> edgeFlows = new Dictionary <EdgePair, Double>();
Dictionary <String, Edge> edgeMap = new Dictionary <String, Edge>();
Dictionary <String, INumVar> varMap = new Dictionary <String, INumVar>();
String currentVar = "";
try {
//Model
Cplex cplex = new Cplex();
IModel model = cplex.GetModel();
//model.Set(GRB.StringAttr.ModelName, "tranportation");
ILinearNumExpr expr = cplex.LinearNumExpr();
//edges
foreach (Edge e in ti.Edges)
{
String xij = edgeVarName(e.Source, e.Sink);
edgeMap.Add(xij, e);
INumVar var = cplex.NumVar(0, System.Double.MaxValue);
var.Name = xij;
varMap.Add(xij, var);
expr.AddTerm(e.C, var);
}
//objective min Sum c_{ij} x_{ij}
model.Add(cplex.Minimize(expr));
//supply constraints
foreach (Node ssource in ti.Sources)
{
List <INumExpr> sourceConstraint = new List <INumExpr>();
foreach (Node ssink in ti.Sinks)
{
String name = edgeVarName(ssource.Id, ssink.Id);
sourceConstraint.Add(varMap[name]);
}
cplex.AddEq(cplex.Sum(sourceConstraint.ToArray()), ssource.Amount);
}
//demand constraints
foreach (Node dsink in ti.Sinks)
{
List <INumExpr> sinkConstraint = new List <INumExpr>();
foreach (Node dsource in ti.Sources)
{
String name = edgeVarName(dsource.Id, dsink.Id);
sinkConstraint.Add(varMap[name]);
}
cplex.AddEq(cplex.Sum(sinkConstraint.ToArray()), dsink.Amount);
}
cplex.SetParam(Cplex.BooleanParam.Threads, 1);
cplex.ExportModel("mipTranportationCplex.lp");
bool status = cplex.Solve();
Console.WriteLine("Status: " + status);
foreach (String s in edgeMap.Keys)
{
currentVar = s;
double flow = cplex.GetValue(varMap[s]);
Edge e = edgeMap[s];
EdgePair ep = new EdgePair(e.Source, e.Sink);
edgeFlows.Add(ep, flow);
}
cplex.End();
} catch (ILOG.Concert.Exception e) {
Console.Out.WriteLine(currentVar + " - is current var");
Console.Out.WriteLine(e.ToString());
}
return(edgeFlows);
}
public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
int nbWhouses = 4;
int nbLoads = 31;
INumVar[] capVars =
cplex.NumVarArray(nbWhouses, 0, 10,
NumVarType.Int); // Used capacities
double[] capLbs = {2.0, 3.0, 5.0, 7.0}; // Minimum usage level
double[] costs = {1.0, 2.0, 4.0, 6.0}; // Cost per warehouse
// These variables represent the assigninment of a
// load to a warehouse.
INumVar[][] assignVars = new INumVar[nbWhouses][];
for (int w = 0; w < nbWhouses; w++) {
assignVars[w] = cplex.NumVarArray(nbLoads, 0, 1,
NumVarType.Int);
// Links the number of loads assigned to a warehouse with
// the capacity variable of the warehouse.
cplex.AddEq(cplex.Sum(assignVars[w]), capVars[w]);
}
// Each load must be assigned to just one warehouse.
for (int l = 0; l < nbLoads; l++) {
INumVar[] aux = new INumVar[nbWhouses];
for (int w = 0; w < nbWhouses; w++)
aux[w] = assignVars[w][l];
cplex.AddEq(cplex.Sum(aux), 1);
}
cplex.AddMinimize(cplex.ScalProd(costs, capVars));
cplex.SetParam(Cplex.Param.MIP.Strategy.Search, Cplex.MIPSearch.Traditional);
if ( cplex.Solve(new SemiContGoal(capVars, capLbs)) ) {
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine("--------------------------------------------");
System.Console.WriteLine();
System.Console.WriteLine("Solution found:");
System.Console.WriteLine(" Objective value = " + cplex.ObjValue);
System.Console.WriteLine();
for (int w = 0; w < nbWhouses; w++) {
System.Console.WriteLine("Warehouse " + w + ": stored "
+ cplex.GetValue(capVars[w]) + " loads");
for (int l = 0; l < nbLoads; l++) {
if ( cplex.GetValue(assignVars[w][l]) > 1e-5 )
System.Console.Write("Load " + l + " | ");
}
System.Console.WriteLine(); System.Console.WriteLine();
}
System.Console.WriteLine("--------------------------------------------");
}
else {
System.Console.WriteLine(" No solution found ");
}
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception caught: " + e);
}
}
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 static void Main(string[] args)
{
if (args.Length < 1)
{
System.Console.WriteLine("Usage: Transport <type>");
System.Console.WriteLine(" type = 0 -> convex piecewise linear model");
System.Console.WriteLine(" type = 1 -> concave piecewise linear model");
return;
}
try {
Cplex cplex = new Cplex();
int nbDemand = 4;
int nbSupply = 3;
double[] supply = { 1000.0, 850.0, 1250.0 };
double[] demand = { 900.0, 1200.0, 600.0, 400.0 };
INumVar[][] x = new INumVar[nbSupply][];
INumVar[][] y = new INumVar[nbSupply][];
for (int i = 0; i < nbSupply; i++)
{
x[i] = cplex.NumVarArray(nbDemand, 0.0, System.Double.MaxValue);
y[i] = cplex.NumVarArray(nbDemand, 0.0, System.Double.MaxValue);
}
for (int i = 0; i < nbSupply; i++) // supply must meet demand
{
cplex.AddEq(cplex.Sum(x[i]), supply[i]);
}
for (int j = 0; j < nbDemand; j++) // demand must meet supply
{
ILinearNumExpr v = cplex.LinearNumExpr();
for (int i = 0; i < nbSupply; i++)
{
v.AddTerm(1.0, x[i][j]);
}
cplex.AddEq(v, demand[j]);
}
double[] points;
double[] slopes;
if (args[0].ToCharArray()[0] == '0') // convex case
{
points = new double[] { 200.0, 400.0 };
slopes = new double[] { 30.0, 80.0, 130.0 };
}
else // concave case
{
points = new double[] { 200.0, 400.0 };
slopes = new double[] { 120.0, 80.0, 50.0 };
}
for (int i = 0; i < nbSupply; ++i)
{
for (int j = 0; j < nbDemand; ++j)
{
cplex.AddEq(y[i][j],
cplex.PiecewiseLinear(x[i][j],
points, slopes, 0.0, 0.0));
}
}
ILinearNumExpr expr = cplex.LinearNumExpr();
for (int i = 0; i < nbSupply; ++i)
{
for (int j = 0; j < nbDemand; ++j)
{
expr.AddTerm(y[i][j], 1.0);
}
}
cplex.AddMinimize(expr);
if (cplex.Solve())
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
System.Console.WriteLine(" - Solution: ");
for (int i = 0; i < nbSupply; ++i)
{
System.Console.Write(" " + i + ": ");
for (int j = 0; j < nbDemand; ++j)
{
System.Console.Write("" + cplex.GetValue(x[i][j]) + "\t");
}
System.Console.WriteLine();
}
System.Console.WriteLine(" Cost = " + cplex.ObjValue);
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine(exc);
}
}
void solve()
{
Cplex Model = new Cplex();
// decision variables
#region
//x1-tjs (first stage t = 1),length of a collection period (in days) at collection point j during time period t
//INumVar[][][] X1 = new INumVar[period][][];
//for (int i = 0; i < period; i++)
//{
// X1[i] = new INumVar[cpoint][];
// for (int ii = 0; ii < cpoint; ii++)
// {
// X1[i][ii] = new INumVar[scenario];
// X1[i][ii] = Model.NumVarArray(scenario, 1, 7, NumVarType.Int);
// }
//}
//x2-tpjks ,volume of products returned from collection point j to recycling center k during time period t
INumVar[][][][][] X2 = new INumVar[period][][][][];
for (int a = 0; a < period; a++)
{
X2[a] = new INumVar[ptype][][][];
for (int aa = 0; aa < ptype; aa++)
{
X2[a][aa] = new INumVar[cpoint][][];
for (int bb = 0; bb < cpoint; bb++)
{
X2[a][aa][bb] = new INumVar[rcenter][];
for (int cc = 0; cc < rcenter; cc++)
{
X2[a][aa][bb][cc] = new INumVar[scenario];
X2[a][aa][bb][cc] = Model.NumVarArray(scenario, 0, System.Double.MaxValue, NumVarType.Int);
}
}
}
}
//x3-tij ,Binary decision variable equals ‘1’ if customer i is allocated to collection point j during time period t and ‘0’ otherwise
INumVar[][][] X3 = new INumVar[period][][];
for (int aa = 0; aa < period; aa++)
{
X3[aa] = new INumVar[customer][];
for (int bb = 0; bb < customer; bb++)
{
X3[aa][bb] = new INumVar[cpoint];
X3[aa][bb] = Model.NumVarArray(cpoint, 0.0, 1.0, NumVarType.Bool);
}
}
//x4-tj ,Binary decision variable equals ‘1’ if collection point j is rented during time period t and ‘0’ otherwise
INumVar[][] X4 = new INumVar[period][];
for (int i = 0; i < period; i++)
{
X4[i] = new INumVar[cpoint];
X4[i] = Model.NumVarArray(cpoint, 0.0, 1.0, NumVarType.Bool);
}
//x5-k ,Binary decision variable equals ‘1’ if recycling center k is established and ‘0’ otherwise
INumVar[] X5 = new INumVar[rcenter];
X5 = Model.NumVarArray(rcenter, 0, 1, NumVarType.Bool);
//x6 maximum capacity level option for recycling center k
INumVar[] X6 = new INumVar[rcenter];
X6 = Model.NumVarArray(rcenter, 1, 3, NumVarType.Int);
//X7-tjs Auxiliary variable x7 the frequency of recylce during a period
//INumVar[][][] X7 = new INumVar[period][][];
//for (int i = 0; i < period; i++)
//{
// X7[i] = new INumVar[cpoint][];
// for (int ii = 0; ii < cpoint; ii++)
// {
// X7[i][ii] = new INumVar[scenario];
// X7[i][ii] = Model.NumVarArray(scenario, 30, wday, NumVarType.Int);
// }
//}
#endregion
Double M = 100000;
// constraints
#region
// formulation （4）
INumExpr[] expr1 = new INumExpr[1];
for (int aa = 0; aa < period; aa++)
{
for (int bb = 0; bb < customer; bb++)
{
expr1[0] = X3[0][0][0];
for (int cc = 0; cc < cpoint; cc++)
{
expr1[0] = Model.Sum(expr1[0], X3[aa][bb][cc]);
}
expr1[0] = Model.Sum(expr1[0], Model.Prod(-1.0, X3[0][0][0]));
Model.AddEq(expr1[0], 1);
}
}
// formulation （5）
INumExpr[] expr2 = new INumExpr[1];
INumExpr[] expr3 = new INumExpr[1];
for (int aa = 0; aa < period; aa++)
{
for (int bb = 0; bb < cpoint; bb++)
{
expr2[0] = X3[0][0][0];
expr3[0] = X4[0][0];
for (int cc = 0; cc < customer; cc++)
{
Model.Sum(expr2[0], X3[aa][cc][bb]);
}
expr2[0] = Model.Sum(expr2[0], Model.Prod(-1.0, X3[0][0][0]));
expr3[0] = Model.Prod(M, X4[aa][bb]);
expr3[0] = Model.Sum(expr3[0], Model.Prod(-1.0, X4[0][0]));
Model.AddLe(expr2[0], expr3[0]);
}
}
// formulation （6）
INumExpr[] expr4 = new INumExpr[1];
INumExpr[] expr5 = new INumExpr[1];
INumExpr[] expr6 = new INumExpr[1];
for (int aa = 0; aa < period; aa++)
{
for (int cc = 0; cc < scenario; cc++)
{
for (int bb = 0; bb < cpoint; bb++)
{
expr5[0] = X3[0][0][0];
for (int dd = 0; dd < customer; dd++)
{
for (int ee = 0; ee < ptype; ee++)
{
expr5[0] = Model.Sum(expr5[0], Model.Prod(Model.Prod(r[dd, ee, aa, cc], X3[aa][dd][bb]), vlength));
}
}
expr5[0] = Model.Sum(expr5[0], Model.Prod(-1.0, X3[0][0][0]));
expr6[0] = X2[0][0][0][0][0];
for (int ff = 0; ff < rcenter; ff++)
{
for (int ee = 0; ee < ptype; ee++)
{
expr6[0] = Model.Sum(expr6[0], X2[aa][ee][bb][ff][cc]);
}
}
expr6[0] = Model.Sum(expr6[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
Model.AddEq(expr5[0], expr6[0]);
}
}
}
// formulation （7-1）
INumExpr[] expr7 = new INumExpr[1];
for (int aa = 0; aa < period; aa++)
{
for (int bb = 0; bb < rcenter; bb++)
{
for (int cc = 0; cc < scenario; cc++)
{
for (int dd = 0; dd < cpoint; dd++)
{
expr7[0] = X2[0][0][0][0][0];
for (int ee = 0; ee < ptype; ee++)
{
expr7[0] = Model.Sum(expr7[0], X2[aa][ee][dd][bb][cc]);
}
expr7[0] = Model.Sum(expr7[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
Model.AddLe(expr7[0], Model.Prod(X5[bb], M));
}
}
}
}
// formulation （7-2）
INumExpr[] expr71 = new INumExpr[1];
for (int aa = 0; aa < period; aa++)
{
for (int bb = 0; bb < rcenter; bb++)
{
for (int cc = 0; cc < scenario; cc++)
{
for (int dd = 0; dd < cpoint; dd++)
{
expr71[0] = X2[0][0][0][0][0];
for (int ee = 0; ee < ptype; ee++)
{
expr71[0] = Model.Sum(expr71[0], X2[aa][ee][dd][bb][cc]);
}
expr71[0] = Model.Sum(expr71[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
Model.AddLe(expr71[0], Model.Sum(Model.Prod(X6[bb], 1000), Model.Prod(Model.Sum(1, Model.Prod(X5[bb], -1)), M)));
}
}
}
}
// formulation （8）
INumExpr[] expr8 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
expr8[0] = X4[0][0];
for (int b = 0; b < cpoint; b++)
{
expr8[0] = Model.Sum(expr8[0], X4[a][b]);
}
expr8[0] = Model.Sum(expr8[0], Model.Prod(-1.0, X4[0][0]));
Model.AddGe(expr8[0], 1);
}
// formulation （9）
INumExpr[] expr9 = new INumExpr[1];
expr9[0] = X5[0];
for (int a = 0; a < rcenter; a++)
{
expr9[0] = Model.Sum(expr9[0], X5[a]);
}
expr9[0] = Model.Sum(expr9[0], Model.Prod(-1.0, X5[0]));
Model.AddGe(expr9[0], 1);
// formulation （10）
INumExpr[] expr10 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
for (int b = 0; b < rcenter; b++)
{
for (int c = 0; c < scenario; c++)
{
for (int d = 0; d < cpoint; d++)
{
expr10[0] = X2[0][0][0][0][0];
for (int e = 0; e < ptype; e++)
{
expr10[0] = Model.Sum(expr10[0], X2[a][e][d][b][c]);
}
expr10[0] = Model.Sum(expr10[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
Model.AddGe(expr10[0], X5[b]);
}
}
}
}
// formulation （11）
for (int a = 0; a < period; a++)
{
for (int c = 0; c < customer; c++)
{
for (int b = 0; b < cpoint; b++)
{
Model.AddLe(Model.Prod(d1[c, b], X3[a][c][b]), l);
}
}
}
// formulation （12）
for (int a = 0; a < period; a++)
{
for (int aa = 0; aa < ptype; aa++)
{
for (int b = 0; b < cpoint; b++)
{
for (int c = 0; c < rcenter; c++)
{
for (int d = 0; d < scenario; d++)
{
Model.AddGe(X2[a][aa][b][c][d], 0);
}
}
}
}
}
// #endregion
//formulation (15) //formulation (1) objective function -1
// collection points rent cost
INumExpr[] expr11 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
expr11[0] = X4[0][0];
for (int b = 0; b < cpoint; b++)
{
expr11[0] = Model.Sum(expr11[0], Model.Prod(X4[a][b], e1[b]));
}
expr11[0] = Model.Sum(expr11[0], Model.Prod(-1.0, X4[0][0]));
}
INumExpr[] expr12 = new INumExpr[1];
INumExpr[] expr121 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
for (int b = 0; b < rcenter; b++)
{
expr121[0] = X5[0];
for (int c = 0; c < cpoint; c++)
{
for (int d = 0; d < ptype; d++)
{
for (int e = 0; e < customer; e++)
{
expr12[0] = X2[0][0][0][0][0];
for (int f = 0; f < scenario; f++)
{
expr12[0] = Model.Sum(expr12[0], Model.Prod(Model.Prod(X2[a][d][c][b][f], e2[d, c, b]), wday / vlength));
}
expr12[0] = Model.Sum(expr12[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
}
}
}
expr121[0] = Model.Sum(expr121[0], Model.Prod(expr12[0], X5[b]));
}
}
INumExpr[] expr13 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
for (int b = 0; b < rcenter; b++)
{
expr13[0] = X5[0];
for (int bb = 0; bb < elevel; bb++)
{
expr13[0] = Model.Sum(expr13[0], Model.Prod(X5[b], e3[b, bb]));
}
expr13[0] = Model.Sum(expr13[0], Model.Prod(-1.0, X5[0]));
}
}
Model.AddLe(Model.Prod(wday, Model.Sum(expr11[0], expr13[0])), e); //expr12[0], ,)
// #endregion
// //formulation (1) objective function -1
// #region
INumExpr[] expr15 = new INumExpr[1];
expr15[0] = X4[0][0];
for (int i = 0; i < period; i++)
{
for (int ii = 0; ii < cpoint; ii++)
{
expr15[0] = Model.Sum(expr15[0], Model.Prod(a[ii], X4[i][ii]));
}
}
expr15[0] = Model.Sum(expr15[0], Model.Prod(-1.0, X4[0][0]));
// ok
INumExpr[] expr17 = new INumExpr[1];
for (int a = 0; a < period; a++)
{
for (int aaa = 0; aaa < scenario; aaa++)
{
for (int bb = 0; bb < cpoint; bb++)
{
for (int bbb = 0; bbb < customer; bbb++)
{
expr17[0] = X3[0][0][0];
for (int aa = 0; aa < ptype; aa++)
{
expr17[0] = Model.Sum(expr17[0], Model.Prod(Model.Prod(r[bbb, aa, a, aaa] * b[aa], X3[a][bbb][bb]), (vlength + 1) * 0.5));
}
expr17[0] = Model.Sum(expr17[0], Model.Prod(-1.0, X3[0][0][0]));
}
}
}
}
INumExpr[] expr18 = new INumExpr[1];
INumExpr[] expr41 = new INumExpr[1];
expr18[0] = X5[0];
for (int a = 0; a < period; a++)
{
for (int aa = 0; aa < rcenter; aa++)
{
for (int bb = 0; bb < cpoint; bb++)
{
for (int b = 0; b < ptype; b++)
{
for (int aaa = 0; aaa < customer; aaa++)
{
expr41[0] = X2[0][0][0][0][0];
for (int bbb = 0; bbb < scenario; bbb++)
{
expr41[0] = Model.Sum(expr41[0], Model.Prod(Model.Prod(X2[a][b][bb][aa][bbb], z[bb, aa, b]), vlength));
}
expr41[0] = Model.Sum(expr17[0], Model.Prod(-1.0, X2[0][0][0][0][0]));
}
}
}
expr18[0] = Model.Prod(expr41[0], X5[aa]);
}
}
expr18[0] = Model.Sum(expr18[0], Model.Prod(-1.0, X5[0]));
INumExpr[] expr19 = new INumExpr[1];
for (int i = 0; i < period; i++)
{
for (int ii = 0; ii < rcenter; ii++)
{
for (int iii = 0; iii < elevel; iii++)
{
expr19[0] = X5[0];
for (int iiii = 0; iiii < capacity; iiii++)
{
expr19[0] = Model.Sum(expr19[0], Model.Prod(q[ii, iii, iiii], X5[ii]));
}
}
}
}
expr19[0] = Model.Sum(expr19[0], Model.Prod(-1.0, X5[0]));
#endregion
INumExpr[] expr21 = new INumExpr[1];
expr21[0] = Model.Prod(Model.Sum(expr15[0], Model.Prod(expr17[0], wday), expr18[0], expr19[0]), lambda); //
INumExpr[] expr22 = new INumExpr[1];
expr22[0] = Model.Prod(Model.Sum(expr11[0], expr12[0], expr13[0]), delta); // Model.Prod(Model.Prod(wday, Model.Sum(expr11[0], expr12[0], expr13[0])),delta);
Model.AddMinimize(Model.Sum(expr21[0], expr22[0])); //
Model.ExportModel("RLND.LP");
if (Model.Solve())
{
Console.WriteLine("statue=" + Model.GetStatus());
Console.WriteLine("obj=" + Model.ObjValue);
Console.WriteLine("X2的结果");
for (int aa2 = 0; aa2 < period; aa2++)
{
for (int bb2 = 0; bb2 < ptype; bb2++)
{
for (int cc = 0; cc < cpoint; cc++)
{
for (int dd = 0; dd < rcenter; dd++)
{
for (int ee = 0; ee < scenario; ee++)
{
Console.WriteLine(Model.GetValue(X2[aa2][bb2][cc][dd][ee]));
Console.WriteLine();
}
}
}
}
}
//for (int a = 0; a < X6.Length; a++)
//{
// Console.WriteLine("result[" + a + "] = " + Model.GetValue(X6[a]));
//}
//Console.WriteLine();
Model.End();
}
else
{
Model.End();
Console.WriteLine();
Console.WriteLine("cannot be solved");
}
}
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);
}
}
/// <summary>
/// The example's main function.
/// </summary>
public static void Main(string[] args)
{
int retval = 0;
Cplex cplex = null;
try
{
cplex = new Cplex();
/* ***************************************************************** *
* *
* S E T U P P R O B L E M *
* *
* We create the following problem: *
* Minimize *
* obj: 3x1 - x2 + 3x3 + 2x4 + x5 + 2x6 + 4x7 *
* Subject To *
* c1: x1 + x2 = 4 *
* c2: x1 + x3 >= 3 *
* c3: x6 + x7 <= 5 *
* c4: -x1 + x7 >= -2 *
* q1: [ -x1^2 + x2^2 ] <= 0 *
* q2: [ 4.25x3^2 -2x3*x4 + 4.25x4^2 - 2x4*x5 + 4x5^2 ] + 2 x1 <= 9.0
* q3: [ x6^2 - x7^2 ] >= 4 *
* Bounds *
* 0 <= x1 <= 3 *
* x2 Free *
* 0 <= x3 <= 0.5 *
* x4 Free *
* x5 Free *
* x7 Free *
* End *
* *
* ***************************************************************** */
INumVar[] x = new INumVar[7];
x[0] = cplex.NumVar(0, 3, "x1");
x[1] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x2");
x[2] = cplex.NumVar(0, 0.5, "x3");
x[3] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x4");
x[4] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x5");
x[5] = cplex.NumVar(0, System.Double.PositiveInfinity, "x6");
x[6] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x7");
IRange[] linear = new IRange[4];
linear[0] = cplex.AddEq(cplex.Sum(x[0], x[1]), 4.0, "c1");
linear[1] = cplex.AddGe(cplex.Sum(x[0], x[2]), 3.0, "c2");
linear[2] = cplex.AddLe(cplex.Sum(x[5], x[6]), 5.0, "c3");
linear[3] = cplex.AddGe(cplex.Diff(x[6], x[0]), -2.0, "c4");
IRange[] quad = new IRange[3];
quad[0] = cplex.AddLe(cplex.Sum(cplex.Prod(-1, x[0], x[0]),
cplex.Prod(x[1], x[1])), 0.0, "q1");
quad[1] = cplex.AddLe(cplex.Sum(cplex.Prod(4.25, x[2], x[2]),
cplex.Prod(-2, x[2], x[3]),
cplex.Prod(4.25, x[3], x[3]),
cplex.Prod(-2, x[3], x[4]),
cplex.Prod(4, x[4], x[4]),
cplex.Prod(2, x[0])), 9.0, "q2");
quad[2] = cplex.AddGe(cplex.Sum(cplex.Prod(x[5], x[5]),
cplex.Prod(-1, x[6], x[6])), 4.0, "q3");
cplex.AddMinimize(cplex.Sum(cplex.Prod(3.0, x[0]),
cplex.Prod(-1.0, x[1]),
cplex.Prod(3.0, x[2]),
cplex.Prod(2.0, x[3]),
cplex.Prod(1.0, x[4]),
cplex.Prod(2.0, x[5]),
cplex.Prod(4.0, x[6])), "obj");
/* ***************************************************************** *
* *
* O P T I M I Z E P R O B L E M *
* *
* ***************************************************************** */
cplex.SetParam(Cplex.Param.Barrier.QCPConvergeTol, 1e-10);
cplex.Solve();
/* ***************************************************************** *
* *
* Q U E R Y S O L U T I O N *
* *
* ***************************************************************** */
double[] xval = cplex.GetValues(x);
double[] slack = cplex.GetSlacks(linear);
double[] qslack = cplex.GetSlacks(quad);
double[] cpi = cplex.GetReducedCosts(x);
double[] rpi = cplex.GetDuals(linear);
double[] qpi = getqconstrmultipliers(cplex, xval, ZEROTOL, x, quad);
// Also store solution in a dictionary so that we can look up
// values by variable and not only by index.
IDictionary <INumVar, System.Double> xmap = new Dictionary <INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
xmap.Add(x[j], xval[j]);
}
/* ***************************************************************** *
* *
* C H E C K K K T C O N D I T I O N S *
* *
* Here we verify that the optimal solution computed by CPLEX *
* (and the qpi[] values computed above) satisfy the KKT *
* conditions. *
* *
* ***************************************************************** */
// Primal feasibility: This example is about duals so we skip this test.
// Dual feasibility: We must verify
// - for <= constraints (linear or quadratic) the dual
// multiplier is non-positive.
// - for >= constraints (linear or quadratic) the dual
// multiplier is non-negative.
for (int i = 0; i < linear.Length; ++i)
{
if (linear[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (rpi[i] > ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
}
else if (linear[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (rpi[i] < -ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
}
else
{
// nothing to do for equality constraints
}
}
for (int i = 0; i < quad.Length; ++i)
{
if (quad[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (qpi[i] > ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
}
else if (quad[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (qpi[i] < -ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
}
else
{
// nothing to do for equality constraints
}
}
// Complementary slackness.
// For any constraint the product of primal slack and dual multiplier
// must be 0.
for (int i = 0; i < linear.Length; ++i)
{
if (System.Math.Abs(linear[i].UB - linear[i].LB) > ZEROTOL &&
System.Math.Abs(slack[i] * rpi[i]) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for row " + linear[i]
+ ": " + System.Math.Abs(slack[i] * rpi[i]));
}
}
for (int i = 0; i < quad.Length; ++i)
{
if (System.Math.Abs(quad[i].UB - quad[i].LB) > ZEROTOL &&
System.Math.Abs(qslack[i] * qpi[i]) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for quad " + quad[i]
+ ": " + System.Math.Abs(qslack[i] * qpi[i]));
}
}
for (int j = 0; j < x.Length; ++j)
{
if (x[j].UB < System.Double.PositiveInfinity)
{
double slk = x[j].UB - xval[j];
double dual = cpi[j] < -ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
}
if (x[j].LB > System.Double.NegativeInfinity)
{
double slk = xval[j] - x[j].LB;
double dual = cpi[j] > ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
}
}
// Stationarity.
// The difference between objective function and gradient at optimal
// solution multiplied by dual multipliers must be 0, i.E., for the
// optimal solution x
// 0 == c
// - sum(r in rows) r'(x)*rpi[r]
// - sum(q in quads) q'(x)*qpi[q]
// - sum(c in cols) b'(x)*cpi[c]
// where r' and q' are the derivatives of a row or quadratic constraint,
// x is the optimal solution and rpi[r] and qpi[q] are the dual
// multipliers for row r and quadratic constraint q.
// b' is the derivative of a bound constraint and cpi[c] the dual bound
// multiplier for column c.
IDictionary <INumVar, System.Double> kktsum = new Dictionary <INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
kktsum.Add(x[j], 0.0);
}
// Objective function.
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)cplex.GetObjective().Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = it.Value;
}
// Linear constraints.
// The derivative of a linear constraint ax - b (<)= 0 is just a.
for (int i = 0; i < linear.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)linear[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - rpi[i] * it.Value;
}
}
// Quadratic constraints.
// The derivative of a constraint xQx + ax - b <= 0 is
// Qx + Q'x + a.
for (int i = 0; i < quad.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)quad[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - qpi[i] * it.Value;
}
for (IQuadNumExprEnumerator it = ((IQuadNumExpr)quad[i].Expr).GetQuadEnumerator();
it.MoveNext(); /* nothing */)
{
INumVar v1 = it.NumVar1;
INumVar v2 = it.NumVar2;
kktsum[v1] = kktsum[v1] - qpi[i] * xmap[v2] * it.Value;
kktsum[v2] = kktsum[v2] - qpi[i] * xmap[v1] * it.Value;
}
}
// Bounds.
// The derivative for lower bounds is -1 and that for upper bounds
// is 1.
// CPLEX already returns dj with the appropriate sign so there is
// no need to distinguish between different bound types here.
for (int j = 0; j < x.Length; ++j)
{
kktsum[x[j]] = kktsum[x[j]] - cpi[j];
}
foreach (INumVar v in x)
{
if (System.Math.Abs(kktsum[v]) > ZEROTOL)
{
throw new System.SystemException("Stationarity test failed at " + v
+ ": " + System.Math.Abs(kktsum[v]));
}
}
// KKT conditions satisfied. Dump out the optimal solutions and
// the dual values.
System.Console.WriteLine("Optimal solution satisfies KKT conditions.");
System.Console.WriteLine(" x[] = " + arrayToString(xval));
System.Console.WriteLine(" cpi[] = " + arrayToString(cpi));
System.Console.WriteLine(" rpi[] = " + arrayToString(rpi));
System.Console.WriteLine(" qpi[] = " + arrayToString(qpi));
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("IloException: " + e.Message);
System.Console.WriteLine(e.StackTrace);
retval = -1;
}
finally
{
if (cplex != null)
{
cplex.End();
}
}
System.Environment.Exit(retval);
}
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");
}
}
private void button1_Click(object sender, EventArgs e)
{
int[,] A = new int[, ]
{
{ 1, 1, 1, 1, 0 },
{ 1, 1, 0, 1, 1 },
{ 0, 1, 1, 1, 1 }
};
double[] L = new double[] { 8, 5, 7, 8, 4 };
double G = 10.7;
double[] N_Max = new double[] { 2, 2, 2 };
int nbOfWorkers = A.GetLength(0);
int nbOfTasks = A.GetLength(1);
Cplex cplex = new Cplex();
INumVar[,] X = new INumVar[nbOfWorkers, nbOfTasks]; // C라는 2차원 인덱스가 0이면, 행의 개수을 받겠다
// C라는 2차원 인덱스가 1이면 열의 개수를 받겠다.
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
X[i, j] = cplex.BoolVar();
}
}
List <INumVar> D_negative = new List <INumVar>();
for (int i = 0; i < nbOfWorkers; i++)
{
D_negative.Add(cplex.NumVar(0, double.MaxValue));
}
List <INumVar> D_positive = new List <INumVar>();
for (int i = 0; i < nbOfWorkers; i++)
{
D_positive.Add(cplex.NumVar(0, double.MaxValue));
}
//목적함수
ILinearNumExpr objectiveFunction = cplex.LinearNumExpr();
for (int i = 0; i < nbOfWorkers; i++)
{
objectiveFunction.AddTerm(1, D_negative[i]);
}
for (int i = 0; i < nbOfWorkers; i++)
{
objectiveFunction.AddTerm(1, D_positive[i]); // C[i, j], X[i, j] 두개를 곱해서 objectiveFunction 에 넣겠다.
}
//과제
for (int i = 0; i < nbOfWorkers; i++)
{
ILinearNumExpr constLeft1 = cplex.LinearNumExpr();
for (int j = 0; j < nbOfTasks; j++)
{
constLeft1.AddTerm(L[j], X[i, j]);
}
constLeft1.AddTerm(1, D_negative[i]);
constLeft1.AddTerm(-1, D_positive[i]);
cplex.AddEq(constLeft1, G);
}
for (int j = 0; j < nbOfTasks; j++)
{
ILinearNumExpr constLeft2 = cplex.LinearNumExpr();
for (int i = 0; i < X.GetLength(0); i++)
{
constLeft2.AddTerm(1, X[i, j]);
}
cplex.AddEq(constLeft2, 1);
}
for (int i = 0; i < nbOfWorkers; i++)
{
for (int j = 0; j < nbOfTasks; j++)
{
cplex.AddLe(X[i, j], A[i, j]);
}
}
for (int i = 0; i < nbOfWorkers; i++)
{
ILinearNumExpr constLeft4 = cplex.LinearNumExpr();
for (int j = 0; j < nbOfTasks; j++)
{
constLeft4.AddTerm(1, X[i, j]);
}
cplex.AddLe(constLeft4, N_Max[i]);
}
cplex.AddMinimize(objectiveFunction);
cplex.Solve();
string solution = "";
double tolerance = cplex.GetParam(Cplex.Param.MIP.Tolerances.Integrality); //tolerance를 정의함
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
if (cplex.GetValue(X[i, j]) >= 1 - tolerance)
{
solution += "(" + (i + 1).ToString() + " ," + (j + 1).ToString() + ")";
}
}
}
MessageBox.Show("목적함수 값은 =" + cplex.GetObjValue() + "\r\n" + "선택된 변수는 =" + solution);
}
