INonLoVariable.InitApproximation

Syntax

InitApproximation: Array;

Description

The InitApproximation property determines an array of initial approximations for controlling variable. If calculation cannot be completed because of array elements lack, values of the IVarConstraint.LowerBound property are used as values of missing elements. If value of the IVarConstraint.LowerBound property is not determined, 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 the example the calculation results are displayed in the 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