MATLAB: How to find intermediate points and plot following problem in MATLAB

optimizationpareto

I have three variables x, y and z. Each variable value can be between [0 0.5]. I want to generate 20 equidistant points for each variable such that sum of x y and z is 0.5. For e.g. 0 0 0.5, 0.495 0.05 0 etc. Kindly tell me how to proceed. Basically it is a Pareto front for DTLZ1 test function.

Best Answer

Much more efficient and actually yielding all possible combinations:
N = 101;
x = linspace(0,0.5,N);
%-------------------------------------------------
%This bit here is more efficient than the one below. Loops can be your friend.
tic
numVals = numel(x);
total_elements = sum(1:numel(x));
results = ones(total_elements,3);
pos = 1;
for ii = 1:numVals;
    idx = pos + numVals - ii;
    results(pos : idx, 1) = x(end - ii + 1:-1:1);
    results(pos : idx, 2) = x(1:end - ii + 1);
    results(pos : idx, 3) = x(ii);
    pos = idx + 1;
end
toc
%---------------------------------------------------
%KSSV's answer:
tic
y = linspace(0,0.5,N) ;
z = linspace(0,0.5,N) ;
[X,Y,Z] = ndgrid(x,y,z) ;
x = X(:) ; y = Y(:) ; z = Z(:) ;
thesum = x+y+z ;
% get the sum 0.5
idx = find(thesum==0.5) ;
iwant = [x(idx) y(idx) z(idx)];
toc
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