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N-Queens

Boanerges Aleman-Meza Cheng Hu Darnell Arford Ning Suo Wade Ertzberger. N-Queens. Presentation Outline. Background Algorithms Traditional Depth First Search Tabu Search Genetic Algorithm Results & Conclusions Future Directions Questions. Characteristic Originated from 8-queens

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N-Queens

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  1. Boanerges Aleman-Meza Cheng Hu Darnell Arford Ning Suo Wade Ertzberger N-Queens

  2. Presentation Outline • Background • Algorithms • Traditional Depth First Search • Tabu Search • Genetic Algorithm • Results & Conclusions • Future Directions • Questions

  3. Characteristic Originated from 8-queens Studied for centuries Constraint satisfaction NP-complete AI techniques uninformed search depth first informed search Best first Background

  4. Depth-First Search • Tries placing a queen in the first available space • If no more queens can be placed without conflicts then the algorithm backtracks • Places queens and backtracks until all queens have been placed

  5. Depth-First Search • Because the search space is finite, if a solution exists then it will be found • For large N it is not efficient in respect to time complexity • Search space increases by a factorial

  6. Tabu Search • a Meta-Heuristic Approach • designed to guide other methods to scape of local optimality • recent moves are stored in a "tabu list" or “Tabu Memory”

  7. Tabu Search • Tabu Memory: • prevents reversals and repetitions of moves making them forbidden (tabu) • is the basis for intensifying and diversifying the search

  8. Q Q Q Q Q Q Q Q N-Queens Tabu Search a permutation problem • move strategy: "first-improving“ • random swaps done to avoid local optima in non-improving situations

  9. Genetic Algorithm • What’s GA? • Darwinism • Search • Features of GA • Optimization • large search space • environmental pressure • no clear relationship among problem features • find the fit solution

  10. Genetic Algorithm

  11. GA Operators

  12. GA In N-queens • Problem Representation Permutation encoding of n integers • Fitness Function Fitness = (N – conflict)2 • Partial Match Crossover (PMX)

  13. Results & Conclusions • Depth-First Search • Poor time and space complexity • Tabu Search • Fast but grows exponentially • Genetic Algorithms • Good performance for queens less than 1000 • Need optimization of crossover operator

  14. Depth-First Search

  15. Tabu Search - Performance

  16. Performance of GA

  17. Future Directions • Employ a variety of heuristics with the traditional approach. • Experiment with different “Tabu memory” sizes to find an optimal solution. • Genetic Algorithms • Apply heuristics in crossover • Other representation schemes

  18. Questions ?

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