Mixed-Integer Surrogate Optimization

This example shows how to solve an optimization problem that involves integer variables. Beginning in R2019b,surrogateoptaccepts integer constraints. In this example, find the pointxthat minimizes themultirosenbrockfunction over integer-valued arguments ranging from –3 to 6 in ten dimensions. Themultirosenbrockfunction 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 themultirosenbrockfunction appears at theend of this example.

rng(1,'twister')% For reproducibilitynvar = 10;% Any even numberlb = -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 =1×101 1 1 1 1 1 1 1 1 1

fval = 0

In this case,surrogateoptfinds the solution.

functionF = 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 matrixifmod(N,2)% if N is odderror('Input rows must have an even number of elements')endodds = 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

See Also

surrogateopt

Related Topics

• Surrogate Optimization
• Mixed Integer ga Optimization