Using Column Generation Techniques To Create

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Lecture 21 Using Column Generation Techniques To
Create Node Disjoint Working Backup Paths
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Working and backup paths from node 1 to node 4.
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1
3
4
Figure 1. A graph with crossing links
We want to avoid paths with crossing links.
3
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
4
Distance Matrix (KM)
ATL BOS CHI DAL LA NY SF
ATL - - 1126 1287 3540 1368 -
BOS - 1609 - - 322 -
CHI - 1448 - 1287 3540
DAL - 2253 - 2816
LA - - 644
NY - -
SF -
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Figure 3. DA (US network with average node
degree of 3.15)
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10
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Legend 1 Brussels 2 Copenhagen 3 Paris 4 Berlin 5
Athens 6 Dublin 7 Rome 8 Luxembourg 9 Amsterdam 1
0 Oslo 11 Lisbon 12 Madrid 13 Stockholm 14 Zurich
15 London 16 Zagreb 17 Prague 18 Vienna
2
6
4
9
15
1
8
3
17
14
18
16
7
11
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Figure 4. KL (European network with average node
degree of 3.89)
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See data4 See runP4 See outP4
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BOS-SF
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O-D BOS-SF Path 1
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
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O-D BOS-SF Path 2
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
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ATL-CHI
12
O-D ATL-CHI Path 1
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
13
O-D ATL-CHI Path 2
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
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O-D ATL-CHI Path 3
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
15
O-D ATL-CHI Path 4
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
16
O-D ATL-CHI Path 5
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup
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BOS-DAL
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O-D Bos-Dal Path 1
Boston
2
Chicago
3
6
San Francisco
New York
7
5
1
Los Angeles
4
Atlanta
Dallas
Working Backup