MATLAB: How to genetate random number under constraint

constraintrandom number generation

I want to genetate two vector X(size=37×1) and Y(size=37×1) of random numbers between
100 to 1900 such that difference between any two numbers of one vector X or Y should be greater than 200.
I have tried generating random number again and again while rejecting if they dont met constraint.
but it make infinte loop.
Actually X and Y are cordinates of turbines. Constraint is no turbine can be in the 200 meter radius of any other turbine. Any idea for doing this very fast? Thanks

Best Answer

This takes milliseconds.
The main idea is to start off with a set of random coordinates and continually replace coordinates that are too close to another coordinate until either 1) all distances are less than the minimum distance requirement or 2) 100 attempts were made per coordinate.
%Define parameters
nPoints = 37;       %number of coordinates
lim = [100,1900];   %bounds of random numbers
minDist = 200;      %minimum distance between turbines
% Create random coordinates and continually replace coordinates
% that are too close to another point.  Stop when minimum distance
% is satisfied or after making nPoints*100 attempts.
xy = nan(nPoints,2);
c = 0; %Counter
while any(isnan(xy(:))) && c<(nPoints*100)
    % Fill NaN values with new random coordinates
    xy(isnan(xy)) = rand(1,sum(isnan(xy(:)))) * (lim(2)-lim(1)) + lim(1);
    % Identify rows that are too close to another point
    [~,isTooClose] = find(triu(squareform(pdist(xy)) < minDist,1));
    % Replace too-close coordinates with NaN
    xy(isTooClose,:) = NaN; 
    c = c+1;
end
% Throw error if the loop had to quit and missing values remain
if any(isnan(xy(:)))
    error('The while-loop gave up. There are %d coordinates with missing values.',sum(isnan(xy(:,1))))
end
% Display number of attempts 
fprintf('%d number of attempts.\n', c)
% Show the minimum distance 
distances = squareform(pdist(xy)); 
fprintf('Min distance = %.2f\n', min(distances(distances~=0)))
% Plot results
 figure() 
 plot(xy(:,1),xy(:,2), 'ks', 'MarkerSize', 10)
 grid on
These data in the figure above were produced in <0.08 sec and the minimum distance between coordinates is 205.52.
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