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Ameisenalgorithmen Ant Colony Optimization

12.11.2003. Ant Colony Optimization. 2. Optimization . Given a graph with two specified vertices A and B, find a shortest path from A to B. Given a set of cities and pairwise distances, find a shortest tour.Given a sequence of amino acids of a protein, find the structure of the protein.Where is

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Ameisenalgorithmen Ant Colony Optimization

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    1. 12.11.2003 Ant Colony Optimization 1 Ameisenalgorithmen – Ant Colony Optimization Lehrprobe zur Habilation, Barbara Hammer, AG LNM, Universität Osnabrück

    2. 12.11.2003 Ant Colony Optimization 2 Optimization Given a graph with two specified vertices A and B, find a shortest path from A to B. Given a set of cities and pairwise distances, find a shortest tour. Given a sequence of amino acids of a protein, find the structure of the protein. ‘Where is my manuscript for the talk, I put it on this pile of papers...’

    3. 12.11.2003 Ant Colony Optimization 3 Ant colony

    4. 12.11.2003 Ant Colony Optimization 4 Ant Colony Optimization (ACO): a heuristic optimization method for shortest path and other optimization problems which borrows ideas from biological ants

    5. 12.11.2003 Ant Colony Optimization 5 Ant Colony Optimization Outline History: ACO for shortest paths Traveling salesperson and ACO-metaheuristic Protein folding - state of the art ACO General comments - where is my manuscript?

    6. 12.11.2003 Ant Colony Optimization 6 History: ACO for shortest paths …

    7. 12.11.2003 Ant Colony Optimization 7 History: ACO for shortest paths Goss et al. 1989, Deneuborg et al. 1990 experiments with Argentine ants: ants go from the nest to the food source and backwards after a while, the ants prefer the shortest path from the nest to the food source stigmercy: the ants communicate indirectly laying pheromone trails and following trails with higher pheromone length gradient ? pheromone will accumulate on the shortest path Dorigo et al. 1991 applications to shortest path problems

    8. 12.11.2003 Ant Colony Optimization 8 History: ACO for shortest paths I:directed A first ACO for a simple shortest path problem: directed acyclic graph (V={0,...,N}, E={i?j}), ant hill: 0, food source: N

    9. 12.11.2003 Ant Colony Optimization 9 History: ACO for shortest paths I:directed

    10. 12.11.2003 Ant Colony Optimization 10 History: ACO for shortest paths II:general ...a more complex undirected cyclic graph ...

    11. 12.11.2003 Ant Colony Optimization 11 History: ACO for shortest paths II:general

    12. 12.11.2003 Ant Colony Optimization 12 History: ACO for shortest paths II:general

    13. 12.11.2003 Ant Colony Optimization 13 History: ACO for shortest paths II:general

    14. 12.11.2003 Ant Colony Optimization 14 History: ACO for shortest paths

    15. 12.11.2003 Ant Colony Optimization 15 Traveling salesperson and ACO-metaheuristic …

    16. 12.11.2003 Ant Colony Optimization 16 Traveling salesperson

    17. 12.11.2003 Ant Colony Optimization 17 Traveling salesperson

    18. 12.11.2003 Ant Colony Optimization 18 Traveling salesperson

    19. 12.11.2003 Ant Colony Optimization 19 Traveling salesperson

    20. 12.11.2003 Ant Colony Optimization 20 Traveling salesperson Results for a 30 cities instance (10 runs, one hour) Results for larger instances (25000 constructed tours, best tour documented)

    21. 12.11.2003 Ant Colony Optimization 21 ACO-metaheuristic Optimization problem for ACO: over a set of basic components C = {c1,...,cn} partial solutions are subsets s in C feasible (partial) solutions F in C solutions S in C cost function f for solutions Goal: iteratively expand feasible partial solutions by components to reach a solution s with minimum f(s), pheromone attached to each component ci guides the search

    22. 12.11.2003 Ant Colony Optimization 22 ACO-metaheuristic

    23. 12.11.2003 Ant Colony Optimization 23 Protein folding - state of the art ACO …

    24. 12.11.2003 Ant Colony Optimization 24 Protein folding

    25. 12.11.2003 Ant Colony Optimization 25 Protein folding Dill, 1985: the HP model preserves important information of the biological conformation Crescenzi et al. and Berger/Leighton, 1998: the problem is NP hard Shmygelska/Hoss, 2003: ACO

    26. 12.11.2003 Ant Colony Optimization 26 Protein folding start at the left end and iteratively fold one amino acid into a relative direction R,S,R,R,L,L,R,S,R,R,L,R,L,L,R,R,S,R in {R,S,L}length-2 basic components: an element in {i-R,i-S,i-L} represents the local structural motif at position (i-1,i,i+1) pheromone values ti-D , i = 2.. length-1, D = L,S,R

    27. 12.11.2003 Ant Colony Optimization 27 Protein folding components: local structural motifs i-D partial solutions: subsets of local structural motifs feasible partial solutions: sequences of consecutive structural motifs without overlap of the amino acids in the 2D lattice solutions: final folds cost function to be maximized: number of 1-1 contacts in the 2D lattice

    28. 12.11.2003 Ant Colony Optimization 28 Protein folding

    29. 12.11.2003 Ant Colony Optimization 29 Protein folding Best reported results for different size instances

    30. 12.11.2003 Ant Colony Optimization 30 General comments - where is my manuscript …

    31. 12.11.2003 Ant Colony Optimization 31 General comments ACOs: nice, powerful, and robust metaheuristic for NP hard, possibly non -static optimization problems, the solutions of which decompose into single components Applications for (* = state of the art results for some settings): quadratic assignment problems * vehicle routing * sequential ordering * shortest common supersequence * scheduling * graph coloring and partitioning telecommunication networks and routing * ... more info on ACOs: Swarm Intelligence, From Natural to Artificial Systems, E.Bonabeau, M.Dorigo, G.Theraulaz, Santa Fe, 1999 http://iridia.ulb.ac.be/~mdorigo/ACO/ Duft der Daten, Der Spiegel, November 13, 2000 Swarm smarts, Scientific American, March 2000

    32. 12.11.2003 Ant Colony Optimization 32 General comments Are ACO’s better than other metaheuristics for general optimization problems?

    33. 12.11.2003 Ant Colony Optimization 33

    34. 12.11.2003 Ant Colony Optimization 34

    35. 12.11.2003 Ant Colony Optimization 35 ACO-metaheuristic ACO-metaheuristic applicable to general optimization problems as stated above robust and tolerant to changes, e.g. in non-static problems yields state of the art solvers for some problems with modifications daemon actions: improve the found solutions using local search (e.g. k-opt for TSP) elitism: update pheromone only for the (local or global) best ants ...

    36. 12.11.2003 Ant Colony Optimization 36 Protein folding – state of the art ACO

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