Genetic Algorithm for points External To a Specific Volume

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.

Answer 1

[Matt J]

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
 
 ceq=[];
 
end

[Matt J]

In fact, though, cineq(1,:) is unnecessary. You could and probably should use the lb, ub argument for that, as you have been.

[ADSW121365]

The comment has confused me slightly, please forgive me, my initial thought is that cineq(2:) would be better suited to the existing lb,ub.

An example may help me: Take a 2 unit cube, where we wish to ignore a central unit cube.

• In this case, the outside box has limits ranging from -1:1 in XYZ.
• The inner box, which should be excluded from the search, then has limits ranging from -0.5:0.5 in XYZ.

For this explicit case, what would be your recommended syntax to achieve my intention?

[Matt J]

That would be,

ub=ones(3,N_points); lb=-ub;  %outside box


x=ga(fun,numel(ub),[],[],[],[],lb,ub,@nonlcon);


function [cineq,ceq]=nonlcon(x)

 x=reshape(x,3,[]); %reshape to 3xN_points

 cineq=1-vecnorm(x./0.5,inf); %inner box
 
 ceq=[];
 
end

[ADSW121365]

Perfect I understand now, thankyou!