genetic algorithm matlab minimization

Hi, I would like to use the Optimization-ToolBox of Matlab that provide a tool for the Genetic Algorithms. I have a small equation (Score= alpha*(\sum(L[i])^(1/alpha) + Beta*(\sum(R[i])^(1/Beta)) that compute a score where L and R are vectors of values that I computed before and alpha and beta are parameters that I want to optimize via the GA. The constraint is that the scores should be close to another vector of scores called ground truth. We can formalize this constraint by : " |score - ground_truth_score|_2^{2}=0"

So for every L[i] and R[i], an Alpha and Beta would optimize the constraint defined before.

I'm trying to discover the GA in Matlab, however, I don't know how to formalize the constraint with the fitness function (the equation).

Answer 1

[Alan Weiss]

Perhaps the constrained minimization example will help.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Anass]

Hi, thank you for your response, but i've already seen this example, they are talking about the constraint on the input data (variable x of the function), however, in my case, i'm talking about the constraint on the value returned by the function. This one must be close to my ground truth. I don't find a way to make a constraint on this.

[Anass]

After reading this example, which i think is a similar problem as mine http://fr.mathworks.com/help/gads/examples/coding-and-minimizing-a-fitness-function-using-the-genetic-algorithm.html?prodcode=GD&language=fr

I made this objective function to manage the minimization of my problem, however i'm not sure if it's the right answer:

function y=parametrized_fitness_fct(x,ground_truth_score)

 y=x(1)*(L^(1/x(1))) + x(2)*(R^(1/x(2))) + ground_truth_score;
      % ground_truth_score, L and R are single values
end
FitnessFunction =@(x) parametrized_fitness_fct(x,ground_truth_score);
[x,score] = ga(FitnessFunction,numberOfVariables)%numberOfVariables=2
%x will be a vector containing the searched values "alpha and beta",    
%and score is the score optimized to be close to the ground_truth_score