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Specify Starting Points and Values for surrogateopt, Problem-Based

For some solvers, you can pass the objective and constraint function values, if any, to solve in the x0 argument. This can save time in the solver. Pass a vector of OptimizationValues objects. Create this vector using the optimvalues function.

The solvers that can use the objective function values are:

  • ga

  • gamultiobj

  • paretosearch

  • surrogateopt

The solvers that can use nonlinear constraint function values are:

  • paretosearch

  • surrogateopt

For example, minimize the peaks function using surrogateopt, starting with values from a grid of initial points. Create a grid from -10 to 10 in the x variable, and –5/2 to 5/2 in the y variable with spacing 1/2. Compute the objective function values at the initial points.

x = optimvar("x",LowerBound=-10,UpperBound=10);
y = optimvar("y",LowerBound=-5/2,UpperBound=5/2);
prob = optimproblem("Objective",peaks(x,y));
xval = -10:10;
yval = (-5:5)/2;
[x0x,x0y] = meshgrid(xval,yval);
peaksvals = peaks(x0x,x0y);

Pass the values in the x0 argument by using optimvalues. This saves time for solve, as solve does not need to compute the values. Pass the values as row vectors.

x0 = optimvalues(prob,'x',x0x(:)','y',x0y(:)',...
    "Objective",peaksvals(:)');

Solve the problem using surrogateopt with the initial values.

[sol,fval,eflag,output] = solve(prob,x0,Solver="surrogateopt")
Solving problem using surrogateopt.

{"String":"Figure Optimization Plot Function contains an axes object. The axes object with title Best Function Value: -6.55113 contains an object of type line. This object represents Best function value.","Tex":[],"LaTex":[]}

surrogateopt stopped because it exceeded the function evaluation limit set by 
'options.MaxFunctionEvaluations'.
sol = struct with fields:
    x: 0.2283
    y: -1.6256

fval = -6.5511
eflag = 
    SolverLimitExceeded

output = struct with fields:
        elapsedtime: 46.1074
          funccount: 200
    constrviolation: 0
               ineq: [1x1 struct]
           rngstate: [1x1 struct]
            message: 'surrogateopt stopped because it exceeded the function evaluation limit set by ...'
             solver: 'surrogateopt'

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