Select 2D points respecting criteria

Hello,

I have som trouble to write some script part. I do have the optimization tool box, but I'm not sure how to apply properly them. I was considering to use GA, but any optimization would do.

I want to select a number (N) of 2D points from a larger pool of number. But under the constrains of Minimum distance between points X.

ex : I have 100 points (pool), and I want to select 10 (N) of these points with a minium distance of 10 (X)

Edited exemple using 'basic swapt' :

Pool=rand(100,2)*100;

N=10; % Number of points to be selected

X=10; % Mimumum distance

[~,te]=datasample(Pool,N,'Replace',false);

Base=Pool(te,:);

rest=Pool; rest(te,:)=[];

while sum(pdist(Base)<X)>1 % repeat until solution found

tested=sum(pdist(Base)<X); % Objective function

if tested>1

temp=Base;

[~,t1]=datasample(rest,1); % Randomly select one from 'available'

[~,t2]=datasample(Base,1); % Randomly select one from 'selected'

temp(t2,:)=[];

temp=[temp;rest(t1,:)];

if sum(pdist(temp)<X)<tested % if swapt improve results, then keep it

Base=temp;

rest(t1,:)=[];rest=[rest;Base(t2,:)];

end

end

end

scatter(Pool(:,1),Pool(:,2))

hold on

scatter(Base(:,1),Base(:,2),'*r')

The result would be 'Base' at the end. But I would prefer to use a matlab buitl-in function.

Any suggestions how to implement that ?

Thanks,