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Ant Colony Hyper-heuristics for Graph Colouring

Ant Colony Hyper-heuristics for Graph Colouring. Nam Pham ASAP Group, Computer Science School University of Nottingham. Overview. Hyper-heuristic Framework Problem Description Hyper-heuristic design for the problem An ant colony hyper-heuristic approach and experimental results

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Ant Colony Hyper-heuristics for Graph Colouring

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

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

  3. 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 • … Nam Pham

  4. Hyper-heuristic Framework Nam Pham

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

  6. 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 Nam Pham

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

  8. 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 1 2 3 4 5 6 7 8 Nam Pham

  9. 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) Nam Pham

  10. 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) Nam Pham

  11. 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) Nam Pham

  12. 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) Nam Pham

  13. 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 Nam Pham

  14. Results Nam Pham

  15. 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 Nam Pham

  16. 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. Nam Pham

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