Help me implement genetic algorithm

I am trying to minimize a nonlinear objective:

||y- f(x_bar)||^2 + mu_s ||D_s x_bar||^2

Obviously, first term is data fitting term and second is regularization term involving spatial regularization. (more details about objective later).

The calculation of objective function is very time consuming which makes optimization also very time consuming. Also, I have to do it for 1/2 millon voxels (3d equivalent of pixels).

Fortunately I can precalculate my objective partwise and use it for each voxel. It seems that I can not use “lsqnonlin” as I can not input fixed step-size. I have the understanding that genetic algorithm can do this. I can easily map my objective to integer minimization.

Could someone please help me formulate this problem for genetic algorithm? Or some guidance would be highly appreciated.

Details about the objective:

In the objective, x_bar is a column vector consisting of αk (k = 1,..., N) and N is the number of voxel. I plan to choose αk from linearly spaced points as candidates (i.e. 0:005:0.35)

Of course, rather than solving entire ½ million at one go, I can solve 20 x 20 x 20 voxel (3D) at a time.

[Walter Roberson]

In your post, a word or letter appears to have gone missing between "in the objective," and "is a column vector".

[Dushyant]

Thanks for pointing out. It has been corrected.

[Anish Mitra]

Are you looking for implementation options of Genetic Algorithms in MATLAB?

If so, then the following links might be of help. They discuss the options of GA in detail.

http://www.mathworks.com/help/gads/examples/constrained-minimization-using-the-genetic-algorithm.html

http://www.mathworks.com/help/gads/examples/genetic-algorithm-options.html