The University of Queensland
School of Information Technology Electrical Engineering
Engg7302 Advanced Computational Techniques in Engineering
Assignment 2: Optimisation
Due date: 18 Oct 18 17:00
Where to submit: Submit the assignment report via the Blackboard turnitin
assignment submission system.
This assignment is worth 20% of the total marks for the course.
For this assignment, you are required to carry out the process of attempting to solve
different optimisation problems. For each question, you are required to report your
results in details. It should include your best solution and its corresponding solution
procedures. If you are asked to solve those sub-questions using MATLAB, then their
MATLAB source code is required.
Marks will be awarded based on how well your submission addresses the above
points.
Question 1
Suppose a linear equation is to be fit predicting raw material price as a linear
function of the quantity of product A and produce B (made of the same raw material)
sold given the following data:
Price of raw material Quantity of product A sold Quantity of product B sold
5 9 1
2 13 8
9 17 3
10 8 5
4 10 9
6 15 2
Assume the prediction equation is 0 1 1 2 2i i iy c c x c x , where 12,ccare the prediction
parameters on the quantity of products A and B sold, respectively, and 0c is the
intercept. Define 12,iixx as the observations on the quantity of products A and B sold,
respectively, and iy as the observed price. i identifies the thi observation.
(1) Suppose the desired criterion for equation fit is that the fitted data exhibit
minimum of the largest absolute deviation between the raw material price and its
prediction.
Please define a LP model to minimize the largest absolute deviation.
- Write down the tabular form. of the formed LP problem.
(15 marks)
- Solve the formed LP problem using the MATLAB function-linprog.
2
(15 marks)
(2) Suppose the desired criteria for equation fit is that the fitted data exhibit
minimum sum of the squared deviations between the raw material price and its
prediction. You are then asked to solve the formed least square (LS) problem.
- Write down the linear system equation (Ax=B) of the LS problem.
(15 marks)
- Solve the LS problem using the normal equations approach.
(10 marks)
Question 2
You have certain types of chicken wire to build a temporary enclosure for holding
chicken at your backyard. You plan to build a rectangular enclosure (see Figure 1)
Figure 1 Rectangular enclosure (chicken house)
You have 50m of Type-1 chicken wire, and you want to maximise the area of the
enclosure for your given materials.
- Please find the lengths of rectangular sides x1, x2 using the Lagrange
Multipliers method. (suggestion: consider a two dimensional (2D) optimisation
procedure)
(15 marks)
- Please find the rectangular sides x1, x2 using the Golden Section Search
method. Please provide your matlab code. (Suggestion: please convert the
2D optimisation problem to a 1D optimisation problem using the relationship:
2*(x1+x2) = 50 x2 = 25-x1.
(15 marks)
- Please find the rectangular sides x1, x2 using the Newton’s Method. Please
provide your matlab code.
(15 marks)