How to genetate random number under constraint
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Muhammad Nabeel Hussain on 26 Sep 2019
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
Adam Danz on 26 Sep 2019
Edited: Adam Danz on 26 Sep 2019
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.
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;
% Throw error if the loop had to quit and missing values remain
error('The while-loop gave up. There are %d coordinates with missing values.',sum(isnan(xy(:,1))))
% 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
plot(xy(:,1),xy(:,2), 'ks', 'MarkerSize', 10)
These data in the figure above were produced in <0.08 sec and the minimum distance between coordinates is 205.52.
More Answers (2)
Jos (10584) on 26 Sep 2019
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) ;
if attempt_counter < 1000
plot(Pxy(:,1), Pxy(:,2),'bo') ;
disp('No positions found.') ;