mean square error as genetic algorithm cost fuction

Hello to everyone,

I'm having problem by using the matlab ga function. In practice I have a SteadyStateThermalResults (basically the temperature associated to each node of a mesh), and I want to use a genetic algorithm to obtain the same thermal profile on the same geometry, by placing a heat source on it. Considering only circular heat sources, the output of the algo should be the position (x,y), the radius and the temperature of the source. I want to use the mean square error as cost function of my algo, and it should take the generated solution, place the heat source on the geometry, compute the thermal profile and make the mse with the original one. How can I specify this kind of cost function the the ga() matlab function?

Thank you in advance,

Antonio.

[Sam Chak]

Can you provide the equation for the mean square error?

[Torsten]

Maybe

error = sqrt(1/A * integral_(A) (T(SteadyStateThermalResults)-T(SimulationResultsWithHeatsource))^2 dA)

Answer 1

[R]

Hi Antonio,

To specify a custom cost function for the ga() function in MATLAB, you can define a function that takes the decision variables (position, radius, and temperature) as inputs and returns the mean square error (MSE) between the computed thermal profile and the original one.

Here's an example of how you can define the cost function:

function mse = customCostFunction1(x)
    % Extract decision variables
    xPosition = x(1);
    yPosition = x(2);
    radius = x(3);
    temperature = x(4);

    % Place the heat source on the geometry and compute the thermal profile
    % (Replace this with your own code)
    computedProfile = computeThermalProfile(xPosition, yPosition, radius, temperature);
    
    % Load the variable SteadyStateThermalResults from your workspace
    
    % Compute the mean square error with the original thermal profile
    mse = mean((computedProfile - SteadyStateThermalResults).^2);
end

In the above code, x is the decision variable vector, where x(1) and x(2) represent the x and y positions of the heat source, x(3) represents the radius, and x(4) represents the temperature. You need to replace computeThermalProfile() with your own function that computes the thermal profile based on the given heat source parameters.

To use this cost function with the ga() function, you can pass it as an argument:

% Define the options for the genetic algorithm
opts = optimoptions('ga','ConstraintTolerance',1e-6,'PlotFcn', @gaplotbestf);

% Run the genetic algorithm
[xOptimal, fval] = ga(@customCostFunction1, numVars, opts);

Also refer to the examples provided in the following MATLAB Documentation:

https://in.mathworks.com/help/gads/ga.html#d126e50475

This should provide a good starting point for you to implement a custom cost function.