Metropolis Monte Carlo walk

In the Monte Carlo method to estimate a many-dimensional integral by sampling the integrand. Metropolis Monte Carlo or, more generally, Markov chain Monte Carlo (MCMC), to which this volume is mainly devoted, is a sophisticated version of this where one uses properties of random walks to solve problems in high-dimensional spaces, particularly those arising in statistical mechanics. 

Simulated annealing is a global, multivariate optimization technique based on the Metropolis Monte Carlo search algorithm. The method starts from an initial random state, and walks through the state space associated with the problem of interest by generating a series of small, stochastic steps. An objective function maps each state into a value in EH that measures its fitness. In the problem at hand, a state is a unique -membered subset of compounds from the n-membered set, its fitness is the diversity associated with that set, and the step is a small change in the composition of that set (usually of the order of 1-10% of the points comprising the set). While downhill transitions are always accepted, uphill transitions are accepted with a probability that is inversely proportional to... 

In Monte Carlo minimization, an additional step is inserted after the random walk before Metropolis evaluation. This step is a... 

The crucial point to note is that the above average combines information about both the accepted and the rejected state of a trial move. Note that the Monte Carlo algorithm used to generate the random walk among the states n need not be the same as the one corresponding to TTnm- For instance, we could use standard Metropolis to generate the random walk, and use the S3Tnmetric rule [4]... 

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