Modify surrogateopt Options

This example uses:

Open Live Script

This example shows how to search for a global minimum by running surrogateopt on a two-dimensional problem that has six local minima. The example then shows how to modify some options to search more effectively.

Define the objective function sixmin as follows.

sixmin = @(x)(4*x(:,1).^2 - 2.1*x(:,1).^4 + x(:,1).^6/3 ...
    + x(:,1).*x(:,2) - 4*x(:,2).^2 + 4*x(:,2).^4);

Plot the function.

[X,Y] = meshgrid(linspace(-2.1,2.1),linspace(-1.2,1.2));
Z = sixmin([X(:),Y(:)]);
Z = reshape(Z,size(X));
surf(X,Y,Z,EdgeColor="none")
view(-139,31)

Figure contains an axes object. The axes object contains an object of type surface.

The function has six local minima and two global minima.

Run surrogateopt on the problem using the "surrogateoptplot" plot function in the region bounded in each direction by [-2.1,2.1]. To understand the "surrogateoptplot" plot, see Interpret surrogateoptplot.

rng default
lb = [-2.1,-2.1];
ub = -lb;
opts = optimoptions("surrogateopt",PlotFcn="surrogateoptplot");
[xs,fvals,eflags,outputs] = surrogateopt(sixmin,lb,ub,opts);

Figure Optimization Plot Function contains an axes object. The axes object with title Best: -1.03163 Incumbent: -1.03162 Current: -1.03161, xlabel Number of Function Evaluations, ylabel Objective Function contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent Best, Incumbent, Random Samples, Adaptive Samples, Surrogate Reset.

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.

Set a smaller value for the MinSurrogatePoints option to see whether the change helps the solver reach the global minimum faster.

opts.MinSurrogatePoints = 4;
[xs2,fvals2,eflags2,outputs2] = surrogateopt(sixmin,lb,ub,opts);

Figure Optimization Plot Function contains an axes object. The axes object with title Best: -1.03163 Incumbent: -1.03163 Current: -1.0316, xlabel Number of Function Evaluations, ylabel Objective Function contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent Best, Incumbent, Random Samples, Adaptive Samples, Surrogate Reset.

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.

The smaller MinSurrogatePoints option does not noticeably change the solver behavior.

Try setting a larger value of the MinSampleDistance option.

opts.MinSampleDistance = 0.05;
[xs3,fvals3,eflags3,outputs3] = surrogateopt(sixmin,lb,ub,opts);

Figure Optimization Plot Function contains an axes object. The axes object with title Best: -0.939739 Incumbent: 1.4033 Current: 6.89693, xlabel Number of Function Evaluations, ylabel Objective Function contains 12 objects of type line. One or more of the lines displays its values using only markers These objects represent Best, Incumbent, Random Samples, Adaptive Samples, Surrogate Reset.

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.

Changing the MinSampleDistance option has a small effect on the solver. This setting causes the surrogate to reset more often, and causes the best objective function to be slightly higher (worse) than before.

Try using parallel processing. Time the execution both with and without parallel processing on the camelback function, which is a variant of the sixmin function. To simulate a time-consuming function, the camelback function has an added pause of one second for each function evaluation.

function y = camelback(x)

y = (4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ...
    + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4);
pause(1)
end

Run the solver, and return the solution time.

opts = optimoptions("surrogateopt",UseParallel=true,PlotFcn="surrogateoptplot");
tic
[xs4,fvals4,eflags4,outputs4] = surrogateopt(@camelback,lb,ub,opts);

Figure Optimization Plot Function contains an axes object. The axes object with title Best: -1.03163 Incumbent: Inf Current: -1.03048, xlabel Number of Function Evaluations, ylabel Objective Function contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent Best, Incumbent, Random Samples, Adaptive Samples, Surrogate Reset.

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.

toc
Elapsed time is 58.567754 seconds.

Time the solver when run on the same problem in serial.

opts.UseParallel = false;
tic
[xs5,fvals5,eflags5,outputs5] = surrogateopt(@camelback,lb,ub,opts);

Figure Optimization Plot Function contains an axes object. The axes object with title Best: -1.03163 Incumbent: -1.0308 Current: 10.2073, xlabel Number of Function Evaluations, ylabel Objective Function contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent Best, Incumbent, Random Samples, Adaptive Samples, Surrogate Reset.

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.

toc
Elapsed time is 221.516376 seconds.

For time-consuming objective functions, parallel processing significantly improves the speed, without overly affecting the results.

See Also

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