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I would like to pay attention to a series of applications by Samir Khan
http://www.maplesoft.com/applications/view.aspx?SID=153600
http://www.maplesoft.com/applications/view.aspx?SID=153599
http://www.maplesoft.com/applications/view.aspx?SID=153596
http://www.maplesoft.com/applications/view.aspx?SID=153598
My congratulations to the author on his work well done. New capacities of Global Optimization Toolbox are spectacular. For example, in the first application  an optimization
problem in 101 variables under 5050 nonlinear  constraints
(other than 202 bounds) is solved.
I think it requires a very powerful comp and much time.
I tried that  problem for n=20 with the good old DirectSearch
on my comp (4 GB RAM, Pentium Dual-Core CPU E5700@3GHz) by

soln2 := DirectSearch:-GlobalSearch(rc, {cons1, cons2, rc >= 0,
seq(`and`(vars[i] >= -70, vars[i] <= 70), i = 1 .. 2*n), rc <= 70},
variables = vars, method = quadratic, number = 140, solutions = 1,
evaluationlimit = 20000)

and obtained not so bad rc=69.9609360106765 (whereas www.packomania.com gives rc=58.4005674790451137175957) in about one hour.

Packing_by_DS.mw
For n=50 the memory of my comp cannot allocate calculations or the obtained result by the Search command is far away from the one in packomania.

 

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 have an equation of power (P)with 3 variables. The variables are R (resistance), ω (frequency) and K (spring stifness);

I would like to find out the optimum value of R and K to maximize the comulutive value of power when the ω is varying from ω1 to ω2. To do so, I should do the following steps:

 Step 1: Calculate the integral of Power when ω is changing from ω1 to ω2 : U(R,K...

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]);

How to play the Maple worksheet Alkylation Process Model Using DirectSearch

(http://www.maplesoft.com/applications/view.aspx?SID=1675)

There is some equivalence between GlobalOptimization commands: GetLastSolution and GlovalSolve and DirectSearch commands?

Gracias

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