This preview shows page 1. Sign up to view the full content.
Unformatted text preview: informal and heuristic rather than analytic, youre right. In fact, some have argued that simulated annealing is not really an optimization method but rather a collec-tion of heuristic techniques that help in some cases. However, there is an important, recently discovered connection between the central idea of simulated annealing and use of Monte Carlo to approximate solutions to NP-hard problems, including de-termining the volume of a bounded convex region K in R n . If n is large, nding V ol ( K ) can be a very hard problem. The most well-developed approach is to dene a sequence of convex sets: K K 1 K 2 . . . K m = K where V ol ( K ) is easy to evaluate. For each i , perform a random walk in K i and count how many walkers happen to be in K i 1 . This gives an estimate of V ol ( K i 1 ) /V ol ( K i ) and the product of these estimates for all i is an estimate for...
View Full Document
- Fall '11