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. I am programming in Matlab.
Details about the objective:
In the objective, is a column vector consisting of αk (k = 1,..., N) and N is the number of voxel. Of course, rather than solving entire ½ million at one go, I can solve 20 x 20 x 20 voxel (3D) at a time. I plan to choose αk from linearly spaced points as candidates (i.e. 0:005:0.35)
Hi Dushyant
You may see the following documentation.
http://www.mathworks.com/help/gads/solving-a-mixed-integer-engineering-design-problem-using-the-genetic-algorithm.html?refresh=true
MATLAB 12b and above have facilities to handle mix-integer programming problem through GA.
TYPE
Solve the Mixed Integer Optimization Problem USING GENETIC ALOGRITM
in google
click on try in matlab
openExample('globaloptim/steppedCantileverExample')
Run the command by entering it in the MATLAB Command Window
Number of m files will be loaded.
You can take help of these m files
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