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

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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

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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 …

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Nam Pham Hyper-heuristic Framework

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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

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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

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

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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

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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)

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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)

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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)

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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)

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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

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

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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

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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.

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