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Optimize Function Using simulannealbnd, Problem-Based

This example shows how to minimize a function using simulated annealing in the problem-based approach when the objective is a function file, possibly of unknown content (a "black box" function). The function to minimize, dejong5fcn(x), is included with Global Optimization Toolbox. Plot the function.

dejong5fcn

Figure contains an axes object. The axes object contains 2 objects of type surface, contour.

Create a 2-D optimization variable x. The dejong5fcn function expects the variable to be a row vector, so specify x as a 2-element row vector.

x = optimvar("x",1,2);

To use dejong5fcn as the objective function, convert the function to an optimization expression using fcn2optimexpr.

fun = fcn2optimexpr(@dejong5fcn,x);

Create an optimization problem with the objective function fun.

prob = optimproblem("Objective",fun);

Set variable bounds from –50 to 50 in all components. When you specify scalar bounds, the software expands the bounds to all variables.

x.LowerBound = -50;
x.UpperBound = 50;

Set a pseudorandom initial point within the bounds. The initial point is a structure with field x.

rng default % For reproducibility
x0.x = x.LowerBound + rand(size(x.LowerBound)).*x.UpperBound;

Solve the problem, specifying the simulannealbnd solver.

[sol,fval] = solve(prob,x0,"Solver","simulannealbnd")
Solving problem using simulannealbnd.
Optimization terminated: change in best function value less than options.FunctionTolerance.
sol = struct with fields:
    x: [-32.0371 -31.8792]

fval = 0.9980

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