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Linkage Tree Genetic Algorithm

Linkage Tree Genetic Algorithm. Wei-Ming Chen. Papers. The Linkage Tree Genetic Algorithm, Dirk Thierens , 2010 Pairwise and Problem-Specific Distance Metrics in the Linkage Tree Genetic Algorithm, Martin Pelikan , Mark W. Hauschild , Dirk Thierens , 2011.

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Linkage Tree Genetic Algorithm

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  1. Linkage Tree Genetic Algorithm Wei-Ming Chen

  2. Papers The Linkage Tree Genetic Algorithm, Dirk Thierens, 2010 Pairwise and Problem-Specific Distance Metrics in the Linkage Tree Genetic Algorithm, Martin Pelikan, Mark W. Hauschild, Dirk Thierens, 2011

  3. The Linkage Tree Genetic Algorithm Dirk Thierens GECCO 2010

  4. GA mechanism Evaluation Selection Initialization Until termination Replacement Crossover Mutation

  5. Introduction • Construct the variables to a tree • Hierarchical Clustering • Assign each variable to a single cluster. • Repeat until one cluster left • Join two nearest clusters ciand cj into cij

  6. Clustering Entropy H : Distance D :

  7. Genetic Algorithm Choose a pair of chromosome Crossover mask : apart chromosome into two subsets Replacement : If one of the offspring is better than both of the parents

  8. Example (1/4)

  9. Example (2/4)

  10. Example (3/4)

  11. Example (4/4)

  12. Algorithm Initial : Create initial population of size N Repeat Build the linkage tree For every pair while the tree is not fully traversed traversed a step and set crossover mask do crossover do replacement if necessary

  13. Result • Test problems • Trap function • NK landscape • Result • The problems are solved in polynomial time • Similar with ECGA and DSMGA

  14. Pairwise and Problem-Specific Distance Metrics in the Linkage Tree Genetic Algorithm Martin Pelikan, Mark W. Hauschild, Dirk Thierens GECCO 2011

  15. local search To improves the quality of the solution In first iteration, do local search before proceeding with the first iteration Based on single-bit neighborhoods choose the step which improves the quality of the solution most Until find the local optimum

  16. Speed up • Original : • Pairwise matrix : • Problem-Specific Metric • decomposable problem composed of m subproblems • prefer decompositions which minimize the sizes of subsets • If two variables in the same subset, the distance of them is 1

  17. Result • Test problems • Trap-5, Trap-6, Trap 7 • NK landscape • 2D spin glass • Result • The problems are solved in polynomial time • Trap functions : almost same • NK landscape : Original< Pairwise < Problem • 2D spin glass : Original < Problem < Pairwise

  18. Conclusion • LTGA : • Small population size • Solve all the problems in low-order polynomial time • Future work : • Problem-specific metrics • Construct all the variables to only one tree ? • Change the minimum mask size ?

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