Interpret surrogateoptplot

R2026b
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The surrogateoptplot plot function provides a good deal of information about the surrogate optimization steps.

Minimize Bounded Function

For example, consider the plot of the steps surrogateopt takes on the test function rastriginsfcn, which is available when you run this example. This function has a global minimum value of 0 at the point [0,0].

Create a surface plot of rastriginsfcn.

fsurf(@(x,y)reshape(rastriginsfcn([x(:),y(:)]),size(x)));

3-D surface plot of Rastrigin's function showing many local minima over a 2-D domain

Plot Minimization Process

By giving asymmetric bounds, you encourage surrogateopt to search away from the global minimum. Set asymmetric bounds of [-3,-3] and [9,10]. Set options to use the surrogateoptplot plot function, and then call surrogateopt.

lb = [-3,-3];
ub = [9,10];
options = optimoptions("surrogateopt",PlotFcn="surrogateoptplot");
rng(100)
[x,fval] = surrogateopt(@rastriginsfcn,lb,ub,options);

Surrogate optimization plot showing random samples, adaptive samples, best values, and a surrogate reset

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

Interpret Plot

Begin interpreting the plot from its left side. For details of the algorithm steps, see Surrogate Optimization Algorithm.

  • The first points are colored triangles, indicating quasirandom samples of the function within the problem bounds. These points, labeled "Random Samples" in the legend, come from the Construct Surrogate phase.

  • Next are dots indicating the adaptive points, the points created in the Search for Minimum phase. These points are labeled "Adaptive Samples" in the legend.

  • The circles (overlapping to look like a thick line) represent the best (lowest) objective function value found. These points are labeled "Best" in the legend. Shortly after evaluation number 30, surrogateopt is stuck in a local minimum with an objective function value near 8. Zoom in to see this behavior more clearly.

xlim([10 50])
ylim([0 15])

Zoomed plot showing best value near 10 for evaluations 10 to 50, with one random sample near 12

  • Near evaluation number 90, a vertical line indicates a surrogate reset. At this point, the algorithm returns to the Construct Surrogate phase.

  • The colored x points represent the incumbent, which are the best points found since the previous surrogate reset.

  • After evaluation number 115, the incumbent improves on the previous best point a few times, attaining a value of about 1. Zoom in to see this behavior more clearly.

xlim([110 140])
ylim([0 10])

Zoomed plot showing best value improving from 8 to about 1 between evaluations 110 and 140

  • The solver has another surrogate reset near evaluation 180.

  • The optimization halts at evaluation number 200 because it is the default function evaluation limit for a 2-D problem.

Problem with Nonlinear and Integer Constraints

The surrogateoptplot display changes when you have nonlinear constraints. Impose the constraint that x(1) is integer-valued, and the nonlinear constraint that x2≥x12-2. For the function that implements this constraint, see rasfcn at the end of this example.

fun = @rasfcn;

Set integer constraints by setting intcon = 1, and run the minimization.

intcon = 1;
[x,fval] = surrogateopt(fun,lb,ub,intcon,options);

Surrogate optimization plot with feasible and infeasible samples for integer-constrained problem

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

The plot now shows colored markers where surrogateopt evaluates infeasible points. The final point is close to the true minimum point of [0,0].

disp(x)
         0    0.0407

The integer constraint likely helps surrogateopt find the true minimum by reducing the search space.

function F = rasfcn(x)
F.Fval = rastriginsfcn(x);
F.Ineq = x(1)^2 - 2 - x(2);
end

See Also

Topics