Static vs Dynamic Populations in GAs for Coloring

Static vs. Dynamic Populations in GAs for Coloring a Dynamic Graph GECCO ’ 14 July 16, 2014 Cara Monical cmonica 2@illinois. edu Forrest Stonedahl forreststonedahl@augustana. edu

Imagine You Want To… Allocate For Conflicting In Registers Variables Interpreted Program Devices Mobile Ad Hoc Network Jobs Management System Frequencies Batches

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 [Jin & Branke ‘ 05] Dynamic Problem Genetic Algorithm

Genetic Algorithm 4 9 1 10 10 8 1 3 7 5 6 5 8 2 6 Pop Size: 100 Population of solutions 9 4 Greedy Decoder Tournament, size 3 Evaluate fitness Select fit individuals 2 Perform Crossover Perform Mutation

Reproduction: OX 1 & SWAP [Starkweather ‘ 91] 1 Population of solutions 3 2 3 6 9 1 * 4 5 6 7 9 10 Parent 1 7 2 5 Parent 2 8 * 1 10 8 4 9 2 3 4 5 6 7 1 10 8 Offspring 2 3 4 5 6 7 8 9 10 Before After Evaluate fitness Select fit individuals Rate: 70% Rate: 50% Perform Crossover Perform Mutation

Experimental Setup 3. Dynamic Population (DGA) 1. Graph A E B C D 2. DSATUR [Brélaz ‘ 79] A B E C D 4 0 3 D A C E D A B 3 E A B D C 3 B C D A E A B 3 D A B E C 4 4. Static Population (SGA) 0 3 C E D B A 3 A D B E C 4 A D B E D B C C E 3 C A E D A E B 3

Experimental Setup 3. Dynamic Population (DGA) 1. Graph F A E B C D 4 0 7 2. DSATUR F E B D C 3 63 0 D A C B C F E D C B F 3 E A B B C C F D 3 B C E D F D E A C E 3 D C A B F B E D C E B C F 3 4. Static Population (SGA) 63 C E F D E B D F B C 3 E C D F C B F E B D 3 D B F E C 3 D B B D C F E 3

Experimental Parameters Graph Properties Dynamic Properties • n: Size, 100 • p: Edge density, . 6 • Structure • G(n, p, cv) • Euclidean • cv: Vertex change rate, . 01 • e: Evolution a step, 1000

. 05 . 025 . 0167 . 1 . 05 . 033 . 15 . 075 . 0375 . 03 . 067 . 05 . 04 . 2 . 1 . 0125 . 01 . 2

(Some) Big Answers (For this Problem & Algorithm) 1. Dynamic Problem 2. Highly Dynamic Problem 3. Slightly Dynamic Problem ≥ ≈ > Succession of Static Problems

Thank You Centre College Department of Computer Science and Department of Mathematics Centre College, John C. Young Program Contact Information Cara Monical Forrest Stonedahl University of Illinois at Urbana-Champaign Math Department cmonica 2@illinois. edu Augustana College CS and Math Departments forreststonedahl@augustana. edu

Performance vs. Edge Density G(n, p, cv) Graphs Euclidean Graphs

Performance vs. Evolution G(n, p, cv) Graphs Euclidean Graphs