And circles with an unknown radius inside a half circle without overlapping each other.
So the first constraint that should be satisfied is that the any pair of two circles should not have
any overlap with each other.
So this the distance between their centers should be bigger than our eye.
Plus, R.G. Square on our eye and RJ are the unknown parameters of the model, the radius of those small
circles, and also they should not be out of the circle.
OK, and finally, why should be bigger than our eye.
OK, so in order to see how can we code it in Python, um, I will show you quickly how we can do it.
OK, so first of all, as before, we have to import um package required packages Palomo matplotlib
a numpty and then we define the abstract.
So here you can see that um we have a set I, we have a set J which is the alias of says I parmeter
r um we have to give the model the radius of each small circle and also and we have some variables,
decision variables are X, Y and radius.
So um X can be between zero and for example the big number 15 is a big number for this purpose on initialize
it with some number and also y um can be initialized.
And as for but the bound for WI is between our eye and 15, OK, so on the are the radius is a bigger
bound, has been chosen for radius.
And also we can say, OK.
And if I is less than J, then this constraints should be satisfied.
So, um, and then we can, um, everything is defined here, so there is another constraint telling
us that, um.
Um, all the circles should be inside the big circle, and the solver is chosen as the EPOP since it's
non-linear and also the data of the model which contains the.
The radius of each circle is also specified, so you can see the data file here.
OK, and once we know that you can change the radius of each circle, that should be fine.
Um, and also, finally, you can plot the results at the end.
So I run the model and the whole model and, uh, check the results for you.
OK, so you can see here that, um, the results are obtained here.
I can rerun that.
See if it gives any other response.
OK, so it is solving and the minimum radius is this number if I give any other kind of initial solution
for that.
So let's change the initial solution.
Let's say X is three and why is let's say five and and rerun the whole model again.
And check the results.
OK, you can see that it gives you an another, um, answer.
OK, so since the problem is non-linear, then it is expected to be sensitive to the initial, um,
value you assign to your variables.
OK, so by changing the initial value, you can see the objective function is changed.
Thank you very much.