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Heuristic search

Heuristic search. heuristic search attempts to find the best tree, without looking at all possible trees. heuristic search methods tend to be greedy. heuristic search methods may fail to find the best solution. global optimum. local optimum. Moving through the trees.

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Heuristic search

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  1. Heuristic search heuristic search attempts to find the best tree, without looking at all possible trees

  2. heuristic search methods tend to be greedy

  3. heuristic search methods may fail to find the best solution global optimum local optimum

  4. Moving through the trees nearest neighbour interchanges ‘swap’ adjacent branches to find alternative trees Nearest-neighbour interchanges a c b e d

  5. Moving through the trees nearest neighbour interchanges starts by erasing an internal branch Nearest-neighbour interchanges a c b e d

  6. Moving through the forest and then erases the two braches connected to it at each end Nearest-neighbour interchanges a c b e d

  7. Moving through the forest the four subtrees are now hooked together in all possible ways Nearest-neighbour interchanges a c b e d e a b ((a+c) + e) + (b+d) c d

  8. Moving through the forest Nearest-neighbour interchanges c a b ((a+e) + c) + (b+d) a c b e d e d e a b c d

  9. Moving through the forest now a second internal branch is erased and the procedure is repeated Nearest-neighbour interchanges c a b a a c c b b e d e e d d e a b c d

  10. Moving through the forest Nearest-neighbour interchanges d c c a b b a a c c b b e e d a e e d d b e a c a b c e d d

  11. Moving through the forest Nearest-neighbour interchanges d c c a b b a a c c b b e e d a e e d d b e a c a b c e d d

  12. d c b d a a d c b c e b e c b e a e d a a c b d e b c a e b a d e c d e b b a d a d c b b a a d c c e e c d e e c a b c a a b c b d e d d e a b d e c

  13. [9] [11] d c b d a a [11] d c b [11] c e b e c b e a e d a [11] a c b [11] d e [11] b c a e b a d e c d e [11] b b a [9] d a [9] [9] d c b b a a d c c e [10] [10] e c d e e c a b [8] c a a b c b d e d d e [9] a b d e c

  14. [9] [11] [11] d c b d a a [11] d c b [11] c e b e c b e a e d a [11] a c b [11] d e [11] b c a e b a d e c d e [11] b b a [9] d a [9] [9] d c b b a a d c c e [10] [10] e c d e e c a b [8] c a a b c b d e d d e [9] a b d e c

  15. [9] [11] [11] d c b d a a [11] d c b [11] c e b e c b e a e d a [11] a c b [11] d e [11] b c a e b a d e c d e [11] b b a [9] d a [9] [9] d c b b a a d c c e [10] [10] e c d e e c a b [8] c a a b c b d e d d e [9] a b d e c

  16. [9] [11] [11] d c b d a a [11] d c b [11] c e b e c b e a e d a [11] a c b [11] d e [11] b c a e b a d e c d e [11] b b a [9] d a [9] [9] d c b b a a d c c e [10] [10] e c d e e c a b [8] c a a b c b d e d d e [9] a b d e c

  17. [9] [11] [11] d c b d a a [11] d c b [11] c e b e c b e a e d a [11] a c b [11] d e [11] b c a e b a d e c d e [11] b b a [9] d a [9] [9] d c b b a a d c c e [10] [10] e c d e e c a b [8] c a a b c b d e d d e [9] a b d e c

  18. Moving through the forest in SPR, a branch with a subtree is removed… Nearest-neighbour interchanges Subtree pruning and regrafting (SPR) b g c f d i a h e j k

  19. Moving through the forest … and reinserted in all possible places. Nearest-neighbour interchanges Subtree pruning and regrafting b f g c i d a h j e k

  20. Moving through the forest Nearest-neighbour interchanges Subtree pruning and regrafting b f g c i d a h j e k

  21. Moving through the forest Nearest-neighbour interchanges Subtree pruning and regrafting b f i g c h a j d e k

  22. Moving through the forest in TBR, the tree is first bisected … Nearest-neighbour interchanges Subtree pruning and regrafting (SPR) Tree bisection and reconnection (TBR) b g c f d i a h e j k

  23. Moving through the forest and then all possible connections are made between a branch of one subtree and a branch of the other Nearest-neighbour interchanges Subtree pruning and regrafting Tree bisection and reconnection b g c f d i a h j e k

  24. Moving through the forest Nearest-neighbour interchanges Subtree pruning and regrafting Tree bisection and reconnection h i b j g f c a d e k

  25. Moving through the forest many more rearrangement methods exist and new ones are being developed Nearest-neighbour interchanges Subtree pruning and regrafting Tree bisection and reconnection …

  26. Sequential addition the sequential addition strategy starts with a simple tree and adds species one by one a c b

  27. Sequential addition every new tree is evaluated on the way,... a a a c b b [8] [9] [7] b d d c c d a c b

  28. Sequential addition … and the most promising path is taken e a b c d a b a [9] b b a a e d c [9] c b [9] d e e c [9] [11] d e d c a a a c b b [8] [9] [7] b d d c c d a c b

  29. a Star decomposition e f a e f b c a d b c f e a d e f c b d b c d star decomposition starts out with an unresolved tree and sequentially pairs species: e.g. UPGMA and neighbour-joining techniques

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