1
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And circles with an unknown radius inside a half circle without overlapping each other.

2
00:00:08,370 --> 00:00:19,350
So the first constraint that should be satisfied is that the any pair of two circles should not have

3
00:00:19,350 --> 00:00:20,550
any overlap with each other.

4
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So this the distance between their centers should be bigger than our eye.

5
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Plus, R.G. Square on our eye and RJ are the unknown parameters of the model, the radius of those small

6
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circles, and also they should not be out of the circle.

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OK, and finally, why should be bigger than our eye.

8
00:00:49,870 --> 00:01:00,810
OK, so in order to see how can we code it in Python, um, I will show you quickly how we can do it.

9
00:01:00,840 --> 00:01:08,010
OK, so first of all, as before, we have to import um package required packages Palomo matplotlib

10
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a numpty and then we define the abstract.

11
00:01:12,480 --> 00:01:22,160
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

12
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r um we have to give the model the radius of each small circle and also and we have some variables,

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decision variables are X, Y and radius.

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So um X can be between zero and for example the big number 15 is a big number for this purpose on initialize

15
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it with some number and also y um can be initialized.

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And as for but the bound for WI is between our eye and 15, OK, so on the are the radius is a bigger

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bound, has been chosen for radius.

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And also we can say, OK.

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And if I is less than J, then this constraints should be satisfied.

20
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So, um, and then we can, um, everything is defined here, so there is another constraint telling

21
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us that, um.

22
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Um, all the circles should be inside the big circle, and the solver is chosen as the EPOP since it's

23
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non-linear and also the data of the model which contains the.

24
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The radius of each circle is also specified, so you can see the data file here.

25
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OK, and once we know that you can change the radius of each circle, that should be fine.

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Um, and also, finally, you can plot the results at the end.

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So I run the model and the whole model and, uh, check the results for you.

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OK, so you can see here that, um, the results are obtained here.

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I can rerun that.

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See if it gives any other response.

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OK, so it is solving and the minimum radius is this number if I give any other kind of initial solution

32
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for that.

33
00:03:41,240 --> 00:03:44,270
So let's change the initial solution.

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Let's say X is three and why is let's say five and and rerun the whole model again.

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And check the results.

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OK, you can see that it gives you an another, um, answer.

37
00:04:03,210 --> 00:04:13,100
OK, so since the problem is non-linear, then it is expected to be sensitive to the initial, um,

38
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value you assign to your variables.

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00:04:16,080 --> 00:04:23,960
OK, so by changing the initial value, you can see the objective function is changed.

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Thank you very much.