Genetic Algorithm with nonlinear Constraints and Vectorization

Hi everyone,

I'm trying to solve an optimization problem with GA:

I have 100 binary variables writen in a vector k (1x100).

min: cost*k', where cost is a vector (1x100)

constraint: quantile(A*k', 0.05) > P, where A is a matrix with 10000x100 and P is a fixed value

Solving the problem without vectorization works perfectly, but if I'm setting 'UseVectorized' to true, it gives the following errors:

 Warning: This concatenation operation includes an empty array with an incorrect number of rows.
 Concatenation including empty arrays will require all arrays to have the same number of rows in a future release.

 Failure in initial user-supplied fitness function evaluation. GA cannot continue.

Here is the compact code for my problem:

N = 100;
ObjectiveFunction = @(k)costFunc(k, cost);
nvars = N;    % Number of variables
LB = zeros(1, N);   % Lower bound
UB = ones(1, N);  % Upper bound
ConstraintFunction = @(k)powerConstraint(k, A, P);

IntCon = 1:N;
options = optimoptions(@ga,'MaxStallGenerations',20,'FunctionTolerance',1e-10,...
                       'MaxGenerations',300, 'PopulationSize', 400, ...
                       'UseVectorized', true);

[k_best,kosten_best] = ga(ObjectiveFunction,nvars,[],[],[],[],LB,UB, ...
                       ConstraintFunction, IntCon, options);

function kosten = costFunc(k, cost)
 kosten = cost*k';
end

function [c, ceq] = powerConstraint (k, A, P)
 P_risk = quantile(A*k', 0.05);
 c = P - P_risk;
 ceq = [];
end

I discovered that Matlab exits with the Error, after an empty vector k is passed to the objective function.

EDIT: I attached a .mat file with an example for A, P and cost. The example is a little smaller, so one has to set N=19.

Thanks in advance for your help

Answer 1

[Alan Weiss]

Thank you for including a file so we could reproduce the issue.

The problem is that the quantile function returns a row vector, as documented. But a vectorized ga call wants a column, as documented but perhaps not documented so clearly. So change the constraint function to return a column:

function [c, ceq] = powerConstraint (k, A, P)
 P_risk = quantile(A*k', 0.05);
 P_risk = P_risk';
 c = P - P_risk;
 ceq = [];
end

Alan Weiss

MATLAB mathematical toolbox documentation

[Stefan M]

Hi Alan,

thanks for your answer. It works perfectly! I've read the documentation but did not look at the constraint function to closely because it returned a value without giving an error.

Thanks again very much for finding my error.

Answer 2

[Matt J]

See if this modification makes a difference.

   function kosten = costFunc(k, cost)

      if isempty(k), 
        kosten=[];
      else
       kosten = cost*k';
      end

   end

[Stefan M]

Hi Matt,

thanks for your answer. Unfortunately the error and the warning stay the same with this modification.

[Matt J]

The best thing would be to attach a .mat file to your original post with the variables A,P, and cost so that we can try the optimization ourselves.

[Stefan M]

I attached a file. The example is only for N=19, but everything else is the same