# Mixed-Integer Surrogate Optimization

This example shows how to solve an optimization problem that involves integer variables. Beginning in R2019b, surrogateopt accepts integer constraints. In this example, find the point x that minimizes the multirosenbrock function over integer-valued arguments ranging from –3 to 6 in ten dimensions. The multirosenbrock function is a poorly scaled function that is difficult to optimize. Its minimum value is 0, which is attained at the point [1,1,...,1]. Code for the multirosenbrock function appears at the end of this example.

rng(1,'twister') % For reproducibility
nvar = 10; % Any even number
lb = -3*ones(1,nvar);
ub = 6*ones(1,nvar);
fun = @multirosenbrock;
intcon = 1:nvar; % All integer variables
[sol,fval] = surrogateopt(fun,lb,ub,intcon)

surrogateopt stopped because it exceeded the function evaluation limit set by
'options.MaxFunctionEvaluations'.
sol = 1×10

1     1     1     1     1     1     1     1     1     1

fval = 0

In this case, surrogateopt finds the solution.

### Helper Function

This code creates the multirosenbrock helper function.

function F = multirosenbrock(x)
% This function is a multidimensional generalization of Rosenbrock's
% function. It operates in a vectorized manner, assuming that x is a matrix
% whose rows are the individuals.
% Copyright 2014 by The MathWorks, Inc.
N = size(x,2); % assumes x is a row vector or 2-D matrix
if mod(N,2) % if N is odd
error('Input rows must have an even number of elements')
end
odds  = 1:2:N-1;
evens = 2:2:N;
F = zeros(size(x));
F(:,odds)  = 1-x(:,odds);
F(:,evens) = 10*(x(:,evens)-x(:,odds).^2);
F = sum(F.^2,2);
end