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Data.xlsx

XY.mw

XYZ.mw

 

Hello,

I'm using the Global Optimization Toolbox to solve some examples and fit equations to a given data, finding "unknown" parameters. I generated the data on Excel, and I already know the values of these parameters.

The XY case is (there is no problem here, I just put as a example I follow):

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "I5:I25");
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "J5:J25");

> XY := zip( (X, Y) -> [X, Y] , X, Y);
> fig1 := plot(XY, style = point, view = [.9 .. 3.1, 6 .. 40]);


> Model := A+B*x+C*x^2+D*cos(x)+E*exp(x):
> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = -10 .. 10, D = 0 .. 10, E = 0 .. 10];

> ModelSubs := proc (x, val)

    subs({x = val}, Model)

    end proc;


> SqEr := expand(add((ModelSubs(x, X(i))-Y(i))^2, i = 1 .. 21));
> CoefList := GlobalSolve(SqEr, op(VarInterv), timelimit = 5000);

> Model := subs(CoefList[2], Model):

 

I could find the right values of A, B, C, D and E. 

 

My problem is in the XYZ case, where I don't know how to "write" the right instruction. My last attempt was:

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "Q5:Q25"); X2 := convert(X, list);
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "R5:R25"); Y2 := convert(Y, list);
> Z := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "S5:S25"); Z2 := convert(Z, list);
> NElem := numelems(X);

> pointplot3d(X2, Y2, Z2, axes = normal, labels = ["X", "Y", "Z"], symbol = box, color = red);

 

> Model := A*x+B*y+C*sin(x*y)+D*exp(x/y);

> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = 0 .. 10, D = 0 .. 10];

> ModelSubs:=proc({x,y},val)

subs({(x,y)=val},Model)

end proc:
Error, missing default value for option(s)

> SqEr := expand(add((ModelSubs(x, y, X(i), Y(i))-Z(i))^2, i = 1 .. NElem));
> CoefList := GlobalSolve(SqEr, op(Range), timelimit = 5000);
Error, (in GlobalOptimization:-GlobalSolve) finite bounds must be provided for all variables

 

My actual problem involves six equations, six parameters and four or five independent variables on each equation, but I alread developed a way to solve two or more equations simultaneously.

Thanks

Hello,

I'm using the Global Optimization Toolbox to solve some examples and fit equations to a given data, finding "unknown" parameters. I generated the data on Excel, and I already know the values of these parameters.

The XY case is (there is no problem here, I just put as a example I follow):

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "I5:I25");
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "J5:J25");

> XY := zip( (X, Y) -> [X, Y] , X, Y);
> fig1 := plot(XY, style = point, view = [.9 .. 3.1, 6 .. 40]);


> Model := A+B*x+C*x^2+D*cos(x)+E*exp(x):
> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = -10 .. 10, D = 0 .. 10, E = 0 .. 10];

> ModelSubs := proc (x, val)

    subs({x = val}, Model)

    end proc;


> SqEr := expand(add((ModelSubs(x, X(i))-Y(i))^2, i = 1 .. 21));
> CoefList := GlobalSolve(SqEr, op(VarInterv), timelimit = 5000);

> Model := subs(CoefList[2], Model):

 

I could find the right values of A, B, C, D and E. 

 

My problem is in the XYZ case, where I don't know how to "write" the right instruction. My last attempt was:

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "Q5:Q25"); X2 := convert(X, list);
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "R5:R25"); Y2 := convert(Y, list);
> Z := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "S5:S25"); Z2 := convert(Z, list);
> NElem := numelems(X);

> pointplot3d(X2, Y2, Z2, axes = normal, labels = ["X", "Y", "Z"], symbol = box, color = red);

 

> Model := A*x+B*y+C*sin(x*y)+D*exp(x/y);

> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = 0 .. 10, D = 0 .. 10];

> ModelSubs:=proc({x,y},val)

subs({(x,y)=val},Model)

end proc:
Error, missing default value for option(s)

> SqEr := expand(add((ModelSubs(x, y, X(i), Y(i))-Z(i))^2, i = 1 .. NElem));
> CoefList := GlobalSolve(SqEr, op(Range), timelimit = 5000);
Error, (in GlobalOptimization:-GlobalSolve) finite bounds must be provided for all variables

 

My actual problem involves six equations, six parameters and four or five independent variables on each equation, but I alread developed a way to solve two or more equations simultaneously.

Thanks.

We have just released a new, more powerful version of the Maple Global Optimization Toolbox.  

For this new release, Maplesoft has partnered with Noesis Solutions to develop a new version of the Maple Global Optimization Toolbox that is powered by Optimus technology. Optimus, from Noesis Solutions, is a platform for simulation process integration and design optimization that includes powerful optimization algorithms. This advanced technology is now available...

Hi,

   The error showed up whenever I tried to do the Maximum Likelihood Estimation with Global Optimization Toolbox.My objective (likelihood ) function f is defined as follows(A1 to A5 are intermediate variables; parameters  are x[1] to x[12]):

   f := 0;

   for j from 1 by 1 to 21 do

       A1 := exp(x[1]+x[2]*c[j]);

       A2 := exp(x[3]+x[4]*c[j]);

An optimal day...

February 09 2009 Tom 4 724 Global Optimization
0 0

Yesterday was one of those remarkable days when everything seems just about right. The highlight was an email message I received from a Prof. Fang from Ryerson University notifying us that we had been both nominated and awarded the Omond Solandt Award by the Canadian Operational Research Society for ongoing and outstanding contribution to the field of Operations Research (OR). No, it’s not a Nobel Prize or an Oscar, but whenever a group of smart people publically recognize our work, the honor and pride are genuine.

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