INonLoVariable.InitApproximation

Syntax

InitApproximation: Array;

Description

The InitApproximation property determines array of initial approximations for controlling variable. If calculation could not be completed because of array elements lack, then values of the IVarConstraint.LowerBound property are used as values of missing elements. If value of the IVarConstraint.LowerBound property is not defined, initial approximation "0,01" is taken.

Example

Add a link to the Cp system assembly.

Sub UserProc;
Var
 Optima: NonLinearOptimization;
 Vars: INonLoVariables; //variables list
 Vrbl: INonLoVariable; //variable
 VarConstr: IVarConstraint; //variable constraint
 VarConstrs: IVarConstraints; //list of variable constraints
 RetroX1: Array[3] Of Double;
 RetroX2: Array[3] Of Double;
 RetroU: Array[3] Of Double;
 RetroV: Array[3] Of Double;
 Funstions: Array[2] Of String;
 InitAp: Array[3] Of Double;
 Res: INonLoResults;
 TimeInterval: Integer;
 s: String;
 ci: ICultureInfo;
 j, i: Integer;
 val: Double;
Begin
 Optima := New NonLinearOptimization.Create;
// Values of variables
 RetroX1[0] := 2;
 RetroX1[1] := 2.1;
 RetroX1[2] := 2.2;
 RetroX2[0] := 1;
 RetroX2[1] := 0.9;
 RetroX2[2] := 0;
 RetroU[0] := 1;
 RetroU[1] := 1.5;
 RetroU[2] := 0;
 RetroV[0] := 0.5;
 RetroV[1] := 0.75;
 RetroV[2] := 0;
// Variables and constraints
 Vars := Optima.Variables;
 Vrbl := Vars.Add("x1");
 Vrbl.Retrospective := RetroX1;
 Vrbl.CoefficientsOrder := "x1[t];x1[t-1];x1[t-2];x1[t-3]";
 VarConstrs := Vrbl.Constraints;

 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -101;
 VarConstr.UpperBound := 101;
 VarConstr.Lag := 3;
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -102;
 VarConstr.UpperBound := 102;
 VarConstr.Lag := 2;

 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -10030;
 VarConstr.UpperBound := 10030;
 VarConstr.Lag := 1;
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -13040;
 VarConstr.UpperBound := 13040;
 VarConstr.Lag := 0;
 Vars := Optima.Variables;
 Vrbl := Vars.Add("x2");
 Vrbl.Retrospective := RetroX2;
 Vrbl.CoefficientsOrder := "x2[t];x2[t-1];x2[t-2]";
 VarConstrs := Vrbl.Constraints;

 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -201;
 VarConstr.UpperBound := 201;
 VarConstr.Lag := 3;
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -202;
 VarConstr.UpperBound := 202;
 VarConstr.Lag := 2;

 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -203;
 VarConstr.UpperBound := 203;
 VarConstr.Lag := 1;
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := -12040;
 VarConstr.UpperBound := 12040;
 VarConstr.Lag := 0;
//Controlling variable
 Vars := Optima.Variables;
 Vrbl := Vars.Add("u");
 Vrbl.Name := "Controlling variable 1";
 Vrbl.Retrospective := RetroU;
 Vrbl.ControlVariable := True;
 Vrbl.CoefficientsOrder := "u[t];u[t-1]";
 For i := 0 To 2 Do
 InitAp[i] := 0.1 * i;
 End For;
 Vrbl.InitApproximation := InitAp;
 VarConstrs := Vrbl.Constraints;
 For i := 0 To 3 Do
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := 0;
 VarConstr.UpperBound := 1;
 VarConstr.Lag := i;
 End For;
//Controlling variable
 Vars := Optima.Variables;
 Vrbl := Vars.Add("v");
 Vrbl.Name := "Controlling variable 2";
 Vrbl.Retrospective := RetroV;
 Vrbl.ControlVariable := True;
 Vrbl.CoefficientsOrder := "v[t];v[t-1]";
 For i := 0 To 2 Do
 InitAp[i] := 8.8 * i;
 End For;
 Vrbl.InitApproximation := InitAp;
 VarConstrs := Vrbl.Constraints;
 For i := 0 To 3 Do
 VarConstr := VarConstrs.Add;
 VarConstr.LowerBound := 0.8;
 VarConstr.UpperBound := 4;
 VarConstr.Lag := i;
 End For;

 Funstions := New string[2];
 Funstions[0] := "0.3 * x1[t-1] + 0.1 * x2[t-2] + u[t-1] * x1[t-1] *x2[t-1]";
 Funstions[1] := "-0.2 * x1[t-1] + 0.4 *x2[t-1] + (x1[t-1] * x2[t-2])/v[t-1]";
 Optima.Equations := Funstions;
    Optima.CriterionFunction := "x1[t] * x1[t] - x1[t] * x2[t]";     TimeInterval := 4;     Optima.NodesCount := 2;     Optima.MaxIterationsCount := 5000;     Optima.MethodType := CpNonLinearMethodType.SequentialQP;     Optima.Tolerance := 0.1;     Optima.Extremum := ExtremumType.Maximum;     Res := Optima.Evaluate(TimeInterval) As INonLoResults;          s := "Optimal value: " + Res.OptimalValue.ToString;     Debug.WriteLine(s);     s := "     ";     For j := 1 To Vars.Count Do         Vrbl := Vars.Item(j - 1);         s := s + Vrbl.Id + "        ";     End For;     Debug.WriteLine(s);          ci := CultureInfo.Current;     For i := 1 To TimeInterval Do         s := "t=" + i.ToString + ", ";         For j := 1 To Vars.Count Do             Vrbl := Vars.Item(j - 1);             Val := Res.VarValues(Vrbl.Id)[i - 1];             s := s + ci.FormatDoublePrec(Val, 6) + ", ";         End For;         Debug.WriteLine(s);     End For;          s := "Status : " + Res.Status.ToString;     Debug.WriteLine(s);     s := "Error : " + Res.ErrorMsg;     Debug.WriteLine(s); End Sub UserProc;

After executing this example the calculation results are displayed in console window:

Optimal value:- 5222824.6794125168
x1 x2 u v
t=1, 2,690000, 3,600000, 1,000000, 0,800000,
t=2, 10,591000, 4,264500, 1,000000, 0,800000,
t=3, 48,702620, 47,247100, 1,000000, 4,000000,
t=4, 2 316,094770, 61,081568, 0,000000, 0,800000,
Status : 21
Error: The solution is found, but the iteration sequence did not converge with the required accuracy