1. 1 Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem Kuo-Hsien Chuang 2008/11/05

2. 2 Introduction Output graph Fitness = 2 Input graph

3. 3 Literature review Maximum vertex covering algorithm

4. 4 Literature review MVCA applying Pilot method –Let C = empty set of labels –Set C = {all c 屬於 ( L – C), min(comp(C + c))}

5. 5 Exploited metaheuristics MGA

6. 6 Exploited metaheuristics MGA

7. 7 Exploited metaheuristics MGA

8. 8 Exploited metaheuristics GRASP

9. 9 Exploited metaheuristics

10. 10 Exploited metaheuristics

11. 11 Exploited metaheuristics

12. 12 Exploited metaheuristics VNS

13. 13 Exploited metaheuristics

14. 14 Exploited metaheuristics

15. 15 Exploited metaheuristics

16. 16 Computational results

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20. 20 Conclusion All the results allow us to state that VNS and GRASP are fast and extremely effective metaheuristics for the MLST problem Future research : an algorithm based on Ant Colony Optimisation (ACO) is currently under study in order to try to obtain a larger diversification capability by extending the current greedy MVCA local search.