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Applying Evolutionary Algorithm to Chaco Tool on the Partitioning of Power Transmission System
(CS448 Class Project)
Yan Sun
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Problem Statement
Overheads in Maxflow Calculation need to be minimized
Partition the Power Transmission System (PTS) using Chaco
An optimal set of parameters for Chaco
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Chaco
Developed by Bruce Hendrickson at Sandia National Lab
Available partitioning methods Inertial Spectral Kernighan-Lin Multilevel KL
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Chaco Parameters
Debugging Parameters Execution Parameters Extended Functionality Parameters
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Previous Experimentations
Austin and Brian’s experiments # partitions – 5 or 6 Degree as vertex weight 200 – 400 external message counts
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Experimental Procedure
Download and install Maxflow Run Chaco Take output from Chaco and create
XML file Run Maxflow
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EA Details -- Parameters
# partitions 5 6
# coarsening to 50 20
Partition method Bisection Quadrisection
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EA Details
Representation— array of 297 integers first 99 next 198 Both vertex weights and edge weights
Objective Function— number of message passed across partitions
Fitness Function—negative value of Object Function
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EA Details
Population Size = 20 Random Initialization
Offspring Size = 6
Parent Selection Tournament
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EA Details
Recombination Mutation Survivor Selection
Deterministic, Elitist, Steady State Termination Condition
Max # of generations No improvement Best solution found
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Parameter Sets
# Partitions # Coarsening to
Partition
Method Para 1 5 50 Bisection
Para 2 5 50 Quadrisection
Para 3 5 20 Bisection
Para 4 5 20 Quadrisection
Para 5 6 50 Bisection
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Average Fitness Values
Para 1 Para 2 Para 3 Para 4 Para 5
Terminating Average Fitness
-130.72 -138.32 -150.72 -134.26 -148.76
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Fitness vs. Generations
-350
-300
-250
-200
-150
-100
-50
0
gene
ratio
n 0
gene
ratio
n 10
gene
ratio
n 20
gene
ratio
n 30
gene
ratio
n 40
gene
ratio
n 50
gene
ratio
n 60
gene
ratio
n 70
gene
ratio
n 80
gene
ratio
n 90
gene
ratio
n 100
gene
ratio
n 110
gene
ratio
n 120
gene
ratio
n 130
gene
ratio
n 140
gene
ratio
n 150
generations
fitn
ess
valu
es
Para1
Para2
Para3
Para4
Para5
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Wilcoxon Rank-Sum Test
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Wilcoxon Rank-Sum Test
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Wilcoxon Rank-Sum Test
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Wilcoxon Rank-Sum Test
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Wilcoxon Rank-Sum Test
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# Generations to Reach Best Fitness
0
20
40
60
80
100
120
# generations to reach best fitness
values
Para1 Para2 Para3 Para4 Para5
parameter sets
Series1
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Wilcoxon Rank-Sum Test
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Conclusion
No difference found among parameter sets
Fewer external message counts 130-150 vs 200-400 Better partition?
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Problem
Non-deterministic evaluation results
population average fitness value
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Q/A?