Optimize function with Bayesian Optimization

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Pontus Vikstål
Pontus Vikstål 2019-4-10
编辑： Alan Weiss 2020-10-5
Hi,
I'm working with a simple example in trying to understand Bayesian Optimization.
Suppose I want to find the minimum of the 2-Dimensional Rastrigin function (this has a global minimum at coordinates (0,0)).
% Rastrigin function
fun = @(x,y)reshape(rastriginsfcn([x(:)/10,y(:)/10]),size(x));
fsurf(fun,[-30 30],'ShowContours','on')
title('rastriginsfcn([x/10,y/10])')
xlabel('x')
ylabel('y')
untitled.jpg
Now, I want to use Bayesian Optimization in order to minimize this function, but I can't seem to get it to work.w
Here is the code that I use.
% Variables for a Bayesian Optimization
X1 = optimizableVariable('x',[-30 30]);
X2 = optimizableVariable('y',[-30 30]);
vars = [X1,X2];
% Function to Optimize
fun = @(x)rastriginsfcn(x./10);
results = bayesopt(fun,vars,'AcquisitionFunctionName','expected-improvement-plus');
This code just gives me the error "Undefined function 'rdivide' for input arguments of type 'table'.".

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采纳的回答

Alan Weiss
Alan Weiss 2019-4-10
As clearly stated in the documentation for bayesopt, the function passes a TABLE of values. However, rastriginsfcn expects a 2-D double array. You need to write your own objective function for bayesopt, and cannot rely on those provided by Global Optimization Toolbox.
function fval = myrastrig(in)
x(1) = in.x;
x(2) = in.y;
fval = rastriginsfcn(x/10);
end
Then call the function as follows:
results = bayesopt(@myrastrig,vars)
Alan Weiss
MATLAB mathematical toolbox documentation
  2 个评论
Subhodip Biswas
Subhodip Biswas 2020-10-4
This example works well for a 2D functin. How can this code be automated if I have functions in 10D, 30D, and so on?
Alan Weiss
Alan Weiss 2020-10-5
编辑：Alan Weiss 2020-10-5
I think that you would be best served by surrogateopt rather than bayesopt for this case. The solvers have similar underlying mechanisms, but surrogateopt allows you to use higher-dimensional variables easily. bayesopt requires you to create variables one dimension at a time.
That said, is your problem very computationally demanding, with a slow-to-compute objective function? If not, then fmincon or patternsearch are usually better solvers for smooth and nonsmooth problems respecitvely.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation

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