static vs. dynamic populations in gas for coloring a dynamic graph cara monical...
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Static vs. Dynamic Populations in GAs for
Coloring a Dynamic Graph
Cara [email protected]
Forrest [email protected]
GECCO ’14July 16, 2014
Imagine You Want To…
Allocate
Registers
Frequencies
Batches
For Conflictin
gVariables
Devices
Jobs
In
Interpreted Program
Mobile Ad Hoc
Network
Management System
Dynamic Graph Coloring
GAs for Static Graph Coloring• Galinier & Hao ‘99• many others
Online Static Graph Coloring• Lovász et. al. ‘89
Ant-Based Dynamic Graph Coloring• Preuveneers & Berbers ‘04
Big Question
Dynamic
Problem
Genetic Algorith
m
[Jin & Branke ‘05]
Genetic Algorithm
Population of
solutions
Evaluate fitness
Select fit individua
ls
Perform Crossov
er
Perform Mutatio
n
4
3
5
6
7
2
9
8
10
1
1
2
5
8
10
7
3
6
9 4
Pop Size: 100
Greedy Decoder
Tournament, size 3
Evaluate fitness
Select fit individua
ls
Reproduction: OX1 & SWAP
Parent 1
Parent 2
Offspring
Population of
solutions
Perform Crossov
er
Perform Mutatio
n
AfterBefore
21 43 5 6 7 8 910
21 43 56 78 910
2 8910
* *
143 5 6 7
29810
1
43 5 6 7
21 3 5 6 8 910
3 5 6 74
Rate: 70% Rate: 50%
[Starkweather ‘91]
Experimental Setup
CD E A B
1. Graph 3. Dynamic Population (DGA)
2. DSATUR [Brélaz ‘79]
4. Static Population (SGA)
AE B D C
DC A E B
EC D B A
DA E B C
BA D C EE DCA B
AD B E C
EC D A B
0
0
0
CB D E A
AD B E C
CA E D B
AE B C D
4
3
EC D B A
DA B C E
DA E B C
AC D E B
3
4
4
3
3
3
3
3
4
3
A
E
DC
B
E DCA B
CB D E A
AD B E C
CA E D B
AE B C D
EC D B A
DA B C E
DA E B C
AC D E B
Experimental Setup1. Graph 3. Dynamic Population
(DGA)
2. DSATUR
4. Static Population (SGA)
DE B F C
FC B E D
BD F E CB CDF E
DB C F E
0
0
3
CB D E A
AD B E C
CA E D B
AE B C D
4
3
7
6
CB F D E
BD E C F
FC E D B
BE C F D
EB F D C
FC E D B
BD E C F
BE C F D
6
FC E D B
DE C F B
BD F E C
BD C F E
3
3
3
3
3
3
3
3
3
A
E
DC
B
F
B CDF E
EB F D C
FC E D B
BD E C F
BE C F D
FC E D B
DE C F B
BD F E C
BD C F E
Experimental Parameters
Graph Propertie
s DynamicPropertie
s
• n: Size, 100• p: Edge
density, .6• Structure
• G(n,p,cv) • Euclidean
• cv: Vertex change rate, .01
• e: Evolution a step, 1000
.05
.05
.05
.05
.025 .0167 .0125 .01
.1 .033 .2
.2
.075.15
.025
.0375
.1
.03
.067 .04
(Some) Big Answers (For this Problem & Algorithm)
Dynamic Problem ≥ Succession of
Static Problems
1.
Highly Dynamic Problem ≈
Succession of Static
Problems2.
Slightly Dynamic Problem
>Succession of
Static Problems
3.
Thank YouCentre College Department of Computer Science and Department of MathematicsCentre College, John C. Young Program
Contact Information
Cara MonicalUniversity of Illinois at Urbana-Champaign
Math Department
Forrest StonedahlAugustana College
CS and Math Departments
Performance vs. Edge Density
G(n,p,cv) Graphs Euclidean Graphs
Performance vs. Evolution
G(n,p,cv) Graphs Euclidean Graphs
