Applying Evolutionary Algorithm to Chaco Tool on the Partitioning of Power Transmission System

(CS448 Class Project)

Yan Sun

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

Chaco

Developed by Bruce Hendrickson at Sandia National Lab

Available partitioning methods Inertial Spectral Kernighan-Lin Multilevel KL

Chaco Parameters

Debugging Parameters Execution Parameters Extended Functionality Parameters

Previous Experimentations

Austin and Brian’s experiments # partitions – 5 or 6 Degree as vertex weight 200 – 400 external message counts

Experimental Procedure

Download and install Maxflow Run Chaco Take output from Chaco and create

XML file Run Maxflow

EA Details -- Parameters

# partitions 5 6

# coarsening to 50 20

Partition method Bisection Quadrisection

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

EA Details

Population Size = 20 Random Initialization

Offspring Size = 6

Parent Selection Tournament

EA Details

Recombination Mutation Survivor Selection

Deterministic, Elitist, Steady State Termination Condition

Max # of generations No improvement Best solution found

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

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

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

Wilcoxon Rank-Sum Test

Wilcoxon Rank-Sum Test

Wilcoxon Rank-Sum Test

Wilcoxon Rank-Sum Test

Wilcoxon Rank-Sum Test

# 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

Wilcoxon Rank-Sum Test

Conclusion

No difference found among parameter sets

Fewer external message counts 130-150 vs 200-400 Better partition?

Problem

Non-deterministic evaluation results

population average fitness value

Q/A?