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Genetic Algorithm for points External To a Specific Volume

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I'm using the GA to select measurement points in a three-dimensional physics problem.
I can tell GA to select only N_points inside some specified plane above my problem simply as:
X.min = -10; X.max = 10; Y.min = -10; Y.max = 10; Z.min = 0; Z.max = 2;
lb = repmat([X.min Y.min Z.min],[1 N_points]);
ub = repmat([X.max Y.max Z.max],[1 N_points]); %Lower/Upper Boundaries [X,Y,Z]
Is it possible to instead set up constraints so points are only selected outside of some cube? For clarity, a physical example would be there exists volume which a measurement device cannot enter, so the problem searches for points external to that region.
Ideally, I would select points only within a hollow-cube: External to a specific volume, but extending to reasonable limits - thereby minimising the possible search space.

Accepted Answer

Matt J
Matt J on 10 Aug 2022
Edited: Matt J on 10 Aug 2022
You would have to use a non-linear constraint function for that:
function [cineq,ceq]=nonlcon(x)
x=reshape(x,3,[]); %reshape to 3xN_points
cineq(1,:)=vecnorm(x./[Xmax;Ymax;Zmax],inf)-1; %inside box of dimensions Xmax x Ymax x Zmax
cineq(2,:)=1-vecnorm(x./[Xmin;Ymin;Zmin],inf); %outside box of dimensions Xmin x Ymin x Zmin
Matt J
Matt J on 11 Aug 2022
Edited: Matt J on 11 Aug 2022
That would be,
ub=ones(3,N_points); lb=-ub; %outside box
function [cineq,ceq]=nonlcon(x)
x=reshape(x,3,[]); %reshape to 3xN_points
cineq=1-vecnorm(x./0.5,inf); %inner box

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