MATLAB: GA fails to get optimal solution for linear programming problem

fmincongagloballinearOptimization Toolboxpatternsearchprogrammingsocp

When I compare the solutions between "fmincon" and GA solver, I get 2 different results. It is also clear that "fmincon" gives better solution:
n = 22;
AssetMean = [...
0
0.0044
0
0.0510
0
0.0397
0.0295
0
0
0
0.0397
0.0295
0.0397
0.0510
0
0
0
0
0
0
0.0200
0];
LowerBound = zeros(n,1);
UpperBound = [...
0.7500
0.7500
0
0.1500
0
0.1500
0.1500
0
0
0
0.1500
0.1500
0.1500
0.1500
0
0
0
0.7500
0
0
0
0];
%%fmincon
of = @(x) -(AssetMean'*x);
[x, y] = fmincon(of, (1/n)*ones(n,1), [], [], ones(n,1)', 1, LowerBound, UpperBound)
%%GA
of = @(x) -(x*m.AssetMean);
[x1, y1] = ga(of, n, [], [], ones(n,1)', 1, LowerBound, UpperBound);
x1 = x1'
y1

Best Answer

"fmincon" uses second derivative information to find a solution.

On the other hand, for GA, the algorithm is converging but slowly because it is not using any derivative information.

For a linear programming problem, it is recommended to use the "linprog" function.

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