1. Ant Colony Hyper-heuristics for Graph Colouring Nam Pham ASAP Group, Computer Science School University of Nottingham

2. Nam Pham Overview Hyper-heuristic Framework Problem Description Hyper-heuristic design for the problem An ant colony hyper-heuristic approach and experimental results Future works

3. Nam Pham Hyper-heuristic “Heuristics that choose heuristics”  High level heuristics: Meta-heuristics Choice Function Ant Algorithm Case-based Reasoning …  Low level heuristics: different moving strategies, constructive heuristics …

4. Nam Pham Hyper-heuristic Framework

5. Nam Pham Graph Colouring Problem Assignment of “colours” to vertices in a graph Adjacent vertices have different colours Objective: minimise the number of required colours

6. Nam Pham Hyper-heuristic Design Constructive hyper-heuristics Search for sequence of heuristics [Ross 2002] Each heuristic is applied for colouring one vertex Evaluation function is defined as the number of required colours when applying heuristic sequence

7. Nam Pham Graph Example Heuristic 1 (H1) Heuristic 2 (H2) Heuristic 3 (H3) 8 12 7 6 4 3 5

8. Nam Pham Search Space of Heuristic Sequences We are looking for a heuristic sequence that produces smallest number of used colours Decisions H 1 H 2 H 3 Sequence 12345678

9. Nam Pham Ant Colony Hyper-heuristics Ant algorithms are well-known if used as low level heuristics There are only two papers using ant algorithms as hyper-heuristics so far (reference at the end)

10. Nam Pham Ant Colony Hyper-heuristics Ant algorithm is well-known if used as a low level heuristic There are only two papers using ant algorithm as hyper-heuristic so far (reference at the end)

11. Nam Pham Ant Colony Hyper-heuristics Ant algorithm is well-known if used as a low level heuristic There are only two papers using ant algorithm as hyper-heuristic so far (reference at the end)

12. Nam Pham Ant Colony Hyper-heuristics Ant algorithm is well-known if used as a low level heuristic There are only two papers using ant algorithm as hyper-heuristic so far (reference at the end)

13. Nam Pham Experiment Heuristics employed include:  Largest Degree First (LD)  Largest Colour Degree First (LCD)  Least Saturation Degree First (SD) University of Toronto Benchmark Data ftp://ftp.mie.utoronto.ca/pub/carter/testprob ftp://ftp.mie.utoronto.ca/pub/carter/testprob

14. Nam Pham Results LDLCDSDAnt Algorithm HHBest known Car913735312928 Car923233 2928 Ear8326252322 Hec9219201917 Kfu9320212019 Lse91171817 Pur933640353235 Rye9322232221 Sta8313 Tre9223262320 Uta9232333230 Ute9210 Yor8322242219

15. Nam Pham Future works Compare ant colony hyper-heuristic with other population based hyper-heuristics – evolutionary algorithms, genetic algorithm, swarm intelligence… Do research on characteristics of heuristic search space Expand to exam timetabling problem

16. Nam Pham Reference Burke, E.K., Kendall, G., Landa Silva, J.D., O'Brien, R.F.J., Soubeiga, E.: An ant algorithm hyperheuristic for the project presentation scheduling problem. Cuesta-Cañada, A., Garrido, L., Terashima-Marín, H.: Building Hyper-heuristics Through Ant Colony Optimization for the 2D Bin Packing Problem.