[SOLVED] algorithm math matlab ECE3093 Assignment 2: Melbourne 2050

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]