Optimize the more than one variable in bayesopt

Hi;

I am using 2d(input) and want to find the expected value of the predictive function of the surrogate model(GPR)

I am not sure either I am treating my optimizableVariable correctly or not because its not working properly.

Any help could be a huge favor.

X1 = optimizableVariable('X1',[0,1]); % variable to optimize on interval [0,1]
X2 = optimizableVariable('X2',[0,1]); %variable to optimize on interval[0,1]
opt_v = [X1,X2];
    % function handle to optimize x on
    objective_function = @(x)expectedvalue(x,model); %define objective function to be optimize
      rng(1); %for reproducibility
        BO_expectedvalue = bayesopt(objective_function,opt_v,...
            'IsObjectiveDeterministic',true,...
            'PlotFcn',[],'verbose',1,'MaxObjectiveEvaluations',30,...
            'NumSeedPoints',10);  % Bayesian optimization loop of expected value                                       % Important: this is a sub-optimization problem, which is solved here again, with Bayesian Optimization
    
        x_maximum = bestPoint(BO_expectedvalue,'Criterion','min-observed').X1;  % argmax of the expectedvalue function
        y_maximum = predict(model,x_maximum);
        
        %objective function is: 
function objective = expectedvalue(x,model)
%this function serves as the objective function in an optimization routine
       [y_pred,~] = predict(model,x.opt_v);%generates expected value of predictive function of the surrogate model
      
       objective = -y_pred;    % must be negative since objective is minimized in MATLAB routine "bayesopt"
     
end

[xu supeng]

Not sure whether this can help, but I finally change my previous program in a more clean way like this, then you don't need to use predict, and I don't understand your question clearly(from email), if you want to use more variables, just set it, if you want to optimize multi-objective function, then you may need to combine them into one objective function.

xrange = optimizableVariable('v1',[-2,2],'Type','real');
yrange = optimizableVariable('v2',[-5,5],'Type','real');

var=[xrange yrange];

bayesObject = bayesopt(@(tbl)mdlfun(tbl),var,...
    'MaxObjectiveEvaluations',50);   % iteration numbers

function rel = mdlfun(tbl)
x=tbl.v1;
y=tbl.v2;
rel=f(x,y);
end

function output=f(x,y)
output=x^2+(y-2)^2;
end

Answer 1

[Alan Weiss]

I believe that the error is in this line:

[y_pred,~] = predict(model,x.opt_v);

The software passes a table of values in x, with the two values x.X1 and x.X2. I am not sure what predict accepts as an argument, but x.opt_v is not passed and is not available, only x is passed. So you might need a line or two of code to convert the passed value x to whatever form predict accepts.

Alan Weiss

MATLAB mathematical toolbox documentation