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Simulated Annealing

A basic overview of the simulated annealing algorithm

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Simulated Annealing

  1. 1. Simulated Annealing Katrina Ellison Geltman Hacker School February 20, 2014
  2. 2. What is simulated annealing?
  3. 3. It’s an algorithm for finding a good solution to an optimization problem
  4. 4. What’s an optimization problem?
  5. 5. It’s the problem of finding the best solution from all feasible solutions. (Wikipedia)
  6. 6. Canonical Example: Traveling Salesman
  7. 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. 8. Simulated annealing solves this type of problem.
  9. 9. Why ‘annealing’?
  10. 10. • Simulated annealing is inspired by a metalworking process called annealing. • It uses the equation that describes changes in a metal’s embodied energy during the annealing process
  11. 11. How does it work?
  12. 12. The Process ! ! !
  13. 13. The Process • Generate a random solution! • Assess its cost! ! ! !
  14. 14. The Process • Generate a random solution! • Assess its cost! • Find a neighboring solution! • Assess its cost! !
  15. 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. 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. 17. … To escape local maxima
  18. 18. … To escape local maxima
  19. 19. … To escape local maxima
  20. 20. … To escape local maxima
  21. 21. … To escape local maxima
  22. 22. The probability of accepting a worse solution depends on: > How much worse it is > Which iteration you’re on
  23. 23. The probability of accepting a worse solution depends on: ! ! > How much worse it is! > Which iteration you’re on
  24. 24. The probability of accepting a worse solution depends on: ! ! > How much worse it is! > Which iteration you’re on Typically calculated using Metropolis- Hastings algorithm
  25. 25. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration you’re on
  26. 26. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration you’re on (later iteration = less likely)
  27. 27. The probability of accepting a worse solution depends on: > How much worse it is ! ! > Which iteration you’re on Analogous to temperature in the physical annealing equation (later iteration = less likely)
  28. 28. Big jumps to worse states happen early. ! After many iterations, the algorithm hones in on a local optimum. ! So a good-enough solution is usually found.
  29. 29. The algorithm’s parameters must be tuned correctly, which requires some guesswork.
  30. 30. But overall, simulated annealing is generally considered a good choice for solving optimization problems.
  31. 31. The End!

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