6.2. Assignment (lab06)

This ungraded assignment is a collection of 10 engineering problems that can be solved by optimization. In order to understand and solve the exercises, and more generally to gain the maximum benefit from this assignment, it is highly recommended that you revise Chapter 4 and Chapter 5.

6.2.1. Content

Activity	Topic	Difficulty
Quiz 1	Travel time	Easy
Quiz 2	Facility location	Easy
Quiz 3	Area fencing	Easy
Quiz 4	Topless box	Easy
	—
Quiz 5	Distance between polygons	Medium
Quiz 6	Shortest path	Medium
Quiz 7	Trilateration	Medium
	—
Quiz 8	Resection	Hard
Quiz 9	Inscribed circle	Hard
Quiz 10	Optimal trajectory	Hard

6.2.2. Required packages

For this assignment, you need to import the following packages.

• Numpy - The library for scientific computing in Python.

• Matplotlib - The library for plotting graphs in Python.

• Autograd - The library for automatic differentiation of Numpy code.

Installation: Open the terminal (‘Anaconda Prompt’ on Windows) and execute the following command.

pip install autograd

Add the flag --user for a local installation (only if you are not the admin).

6.2.3. Autograd caveats

Not all the NumPy features can be used with Autograd. Here is the list of operations that you must avoid inside your cost functions.

• Don’t use assignment to arrays A[0,0] = x, A[:,1] = y, …

  • Create new arrays through vectorized operations!

• Don’t create lists w = [x, y]

  • Create new arrays: w = np.array([x, y])

• Don’t implicitly cast lists to arrays A = np.sum([x, y])

  • Use explicit casts: A = np.sum(np.array([x, y]))

• Don’t use in-place operations such as a += b

  • Use binary opertions: a = a + b

• Don’t use the operation A.dot(B)

  • Use the operation: A @ B

• Never execute the line import numpy as np

  • Use the line: import autograd.numpy as np