Simulated Annealing

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Transcript of Simulated Annealing
 1. Simulated Annealing Katrina Ellison Geltman Hacker School February 20, 2014
2. What is simulated annealing? 3. Its an algorithm for nding a good solution to an optimization problem 4. Whats an optimization problem? 5. Its the problem of nding the best solution from all feasible solutions. (Wikipedia) 6. Canonical Example: Traveling Salesman 7. Canonical Example: Traveling Salesman The salesman needs to minimize the number of miles he travels. An itinerary is better if it is shorter. There are many feasible itineraries to choose from. We are looking for the best one. 8. Simulated annealing solves this type of problem. 9. Why annealing? 10. Simulated annealing is inspired by a metalworking process called annealing. It uses the equation that describes changes in a metals embodied energy during the annealing process 11. How does it work? 12. The Process ! ! ! 13. The Process Generate a random solution! Assess its cost! ! ! ! 14. The Process Generate a random solution! Assess its cost! Find a neighboring solution! Assess its cost! ! 15. The Process Generate a random solution! Assess its cost! Find a neighboring solution! Assess its cost! ! If cnew < cold: move!! If cnew > cold: maybe move 16. The Process Generate a random solution! Assess its cost! Find a neighboring solution! Assess its cost! ! If cnew < cold: move!! If cnew > cold: maybe move Why?? 17. To escape local maxima 18. To escape local maxima 19. To escape local maxima 20. To escape local maxima 21. To escape local maxima 22. The probability of accepting a worse solution depends on: > How much worse it is > Which iteration youre on 23. The probability of accepting a worse solution depends on: ! ! > How much worse it is! > Which iteration youre on 24. The probability of accepting a worse solution depends on: ! ! > How much worse it is! > Which iteration youre on Typically calculated using Metropolis Hastings algorithm 25. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration youre on 26. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration youre on (later iteration = less likely) 27. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration youre on Analogous to temperature in the physical annealing equation (later iteration = less likely) 28. Big jumps to worse states happen early. ! After many iterations, the algorithm hones in on a local optimum. ! So a goodenough solution is usually found. 29. The algorithms parameters must be tuned correctly, which requires some guesswork. 30. But overall, simulated annealing is generally considered a good choice for solving optimization problems. 31. The End!