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

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

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

5. 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

6. 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

7. 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”

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

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

10. 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

11. Genetic Algorithm

12. GA Operators

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

14. 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

15. Depth-First Search

16. Tabu Search - Performance

17. Performance of GA

18. 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

19. Questions ?