How set properly a multiobjective optimization problem

Hello everyone

I am trying to use multiobjective genetic algorithim to find the values for the variables r1,r2,r3,l1,l2,l3 that produces the minimum pressure drop and minimum volumen, this are the equations:

Delta_pressure = ((2*k*l1)/r1)*(((3+1/n)*v_melt)/(pi*r1^3))^n + ((2*k*l2)/r2)*(((3+1/n)*v_melt)/(pi*r2^3))^n + ((2*k*l3)/r3)*(((3+1/n)*v_melt)/(pi*r3^3))^n;

and

volume = (pi*r1^2)*l1+(pi*r2^2)*l2+(pi*r3^2)*l3

Where k,n, v_melt are constant

I am using the optimize live editor, but so far I dont know how to use properly

This is one of my attemps to make it work, I use the volume equation as constrain function, train to make the volumen always minor that 1.5 times the part volume (v_part)

I am not sure what should write on "fixed input a" or "optimization input"

Thanks for any help

Answer 1

[Alan Weiss]

I think that you need to understand that the optimization variables all need to be in one variable, typically called x. See Writing Scalar Objective Functions. Furthermore, if you choose gamultiobj before you try to create the objective function, you will get a more useful template than the one you are using. Finally, your nonlinear constraint function must return c(x) that is less than zero for feasible points. I think that you need

c = (pi*r1^2)*l1 + pi*(r2^2*l2) + (pi*r3^2)*l3 - 1.5*v_part;

One more thing. You might want to set r and l as vectors, not as separate variables for each component. So you would write r(2) instead of r2. Again, these woould be parts of the x vector. So you might have something like

function f1 = obj(x)
r = x(1:3);
l = x(4:6);
% Then write things in terms of r and l.
end

You might need to use extra variables for fixed parameters such as k and v_melt. You would put them in your workspace and then your function might look like

function f1 = obj(x,k,v_melt)
% Code goes here
end

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation