How to genetate random number under constraint

I want to genetate two vector X(size=37x1) and Y(size=37x1) 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

[Bruno Luong]

Let see so you have 37 numbers and they must be separate by at least by a distance of 200, so you need a total length of 200x36 = 7200 which is larger than 1800. So you requirement simply is not possible to meet.

[Muhammad Nabeel Hussain]

Sir, The figure given met the condition i have described. My goal is to generate such cordinates for x and y so that no turbine is in 200 meter radius of any other turbine. This is acheived in figure. but i want to do it efficeintly.

[Adam]

Do they have to be random? You can create a regular grid that would put them maximal distance apart far more easily than you could create random locations. Or you can use a regular grid as a start point and add random perturbations from that if you wish. As ever when people ask for something random though the question is 'How random?' There's lots of different ways to produce a set of random numbers, that may all be considered 'random' by some criterion.

[Bruno Luong]

Then your description "such that difference between any two numbers of one vector X or Y should be greater than 200." is incorrect. The two points

(100,1000)
(150, 100)

are separated by a distance larger than 200. But it is not satisfied what you have originally stated: since the difference of X is 50.

Please clarify your question.

[Adam Danz]

This is actually fairly easy to do if you just monitor the distance between the turbines rather than the distance between each x and y coordinate.

Your question states "any two numbers of one vector X or Y should be greater than 200." In that case, the turbines cannot be any closer than 200*sqrt(2).

Instead of choosing values of x and y individually that have a minimum distance of 200, you just need to monitor the distance between the turbine coordinates.

[Adam Danz]

@Muhammad Nabeel Hussain, I'm curous how you plotted the plane symbols. Mind explaining?

Answer 1

[Adam Danz]

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.

[Muhammad Nabeel Hussain]

Thankyou Adam Danz. It solved my problem.

[Adam Danz]

Glad I could help.

@Muhammad Nabeel Hussain, I'm curous how you plotted the plane symbols. Mind explaining?

[Siavash Soltanahmadi]

Dear @Adam Danz,

Is there a way we could generate a second set of random number within the same range specified for the first set of random number, where the numbers in the second set are constrained by a different value to the first constraint?

To clarify, imagine within a same space we aim to obtain 12 coordinates, the minimum separation between 10 random coordinates has to be “2” and the minimum separation between another 2 coordinates (and between these 2 and the first 10 coordinates) has to be “5”.

Thanks,

Sia

Answer 2

[Bruno Luong]

Similar question has been answered in this thread

Answer 3

[Jos (10584)]

Brute force attempt:

N = 20 ;
xyRange = [100 1900] ;
minimumDistance = 200 ;
attempt_counter = 1 ; 
Distances = 0 ;
while any(Distances < minimumDistance) && attempt_counter < 10000
    attempt_counter = attempt_counter + 1 ;
    Pxy = randi(xyRange, N, 2) ; 
    Distances = pdist(Pxy) ;
end
if attempt_counter < 1000
    plot(Pxy(:,1), Pxy(:,2),'bo') ;
else
    disp('No positions found.') ;
end