ECE3093 Assignment 2: Melbourne 2050
April 2019
Name: ________________________ Student ID: _________________
Electronic submission of this assignment is due on Moodle by 9am on Monday 6 May 2019. You are required to submit this file as pdf, and the source code (Matlab script). Note: you may insert scans or photos of your handwritten notes for any of the answers requiring mathematics.
• Locating a single IMEX in the plane
• How many local & global minima does this function have? (Give reasons) [2 marks]
• Formula for calculating an optimal IMEX location [2 marks]
• Global Optimal solution: [2 marks]
x-coordinate
y-coordinate
100
100
f =
4,466,571
• Locating a single IMEX using Manhattan distances
• Formulate as a linear program [5 marks] .
• Write down the dual of this linear program. [5 marks]
• Solution found from solving the linear program [5 marks]
x-coordinate
y-coordinate
50
50
g =
68,089
• Bonus Question: Direct method for computing the primal & dual solution [5 marks]
• Locating multiple IMEXs in the plane
(
• Code for computing best allocation vector and locations, starting with random [5 marks]
• Analysis of algorithm [4 marks]
• Solution of the 5 IMEX problem [5 marks]
1st IMEX
2nd IMEX
3rd IMEX
4th IMEX
5th IMEX
20
100
80
31
50
20
100
30
95
40
h =
87,059
Allocation (k) = [ 4 1 5 5 5 2 4 2 3 3 5 5 3 3 1 4 5 2 5 2 5 2 4 4 3 3 3 2 3 5 1 1 2 2 2 5 4 2 1 4 5 3 1 5 2 5 2 4 3 5 5 5 3 5 3 4 1 2 3 3 5 2 2 4 5 2 2 3 3 3 5 1 2 1 3 5 3 2 1 3 4 5 5 1 3 5 1 5]
(list allocation to 1st to 5th IMEX in the order of locations in the spreadsheet)
• The discrete IMEX location problem
• Analysis of enumeration approach [2 marks]
• Integer Linear Programming Formulation [5 marks]
• Code corresponding to the above formulation [0 marks]
• Solution [5 marks]
1st IMEX
2nd IMEX
3rd IMEX
4th IMEX
5th IMEX
k
1
2
4
23
16
q
232
303
267
149
314
u
67
39
80
47
45
v
54
111
46
96
66
h =
76,290
Allocation (k) = [ 4 1 2 5 5 3 4 2 3 3 5 5 3 3 1 4 5 2 5 2 5 2 4 4 3 3 3 2 3 5 1 1 2 2 2 5 4 2 1 4 5 3 1 5 2 5 2 4 3 5 5 5 3 5 3 4 1 2 3 3 5 2 2 4 5 2 2 3 3 3 5 1 2 1 3 5 3 2 1 3 4 5 5 1 3 5 1 5]
• Extensions
• Some ways this model could be made more realistic [3 marks]