Class exercise: Ice cream cone

Fig. 11 ice cone

We want to minimize the surface area of a cone, while not making the gap on the top too big (in terms of area). Let’s define this as a multi-objective optimization problem with

1. the first objective to minimize the ice cream cone area \(\pi r \sqrt{r^2+h^2}\)

2. the second objective to minimize the ice cream cone area + the area of the gap \(\pi r \sqrt{r^2+h^2} + \pi r^2\).

The total volume inside the cone must be at least 200.

Find the pareto front using normalized objective functions

Exercise 39 (Model)

Write out the model of this problem.

Exercise 40 (Method)

Now let’s solve this problem using an optimization method.

Click –> Live Code to activate live coding on this page!

import scipy as sp 
import numpy as np

#YOUR CODE HERE