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) = [4155524233553314525252443332351122254214531525243555353412335224522333512135321345513515]
(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) = [4125534233553314525252443332351122254214531525243555353412335224522333512135321345513515]
•Extensions
•Some ways this model could be made more realistic [3 marks]
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