2. Intro
â Annealing â cooling temperature in metallargy
â An optimization algo inspired by Stastical
Mechanics
â Combination of â
1) MCMC Algo
2) Metropilos Algo
3. MCMC Algo
â Marcov Chain Monte Carlo
â Involves a Stochastic element (random)
â This helps computer to take random decisions
â Depends on state and transition between 2
states in MM
4. Metropolis Algo
â Randomly generates perturbations of current
state (approx soln)
â Accepts or rejects them based on how the
probability of state is effected
â Like a schedule of lovering temperature
5. Example â Minimizing a function
â F = (x1.....xn) and f>=0
â If f â represemtsenergy of a stastical
mechanical system
â We have states S=(x1....xn)
â Hence the probability of state S at temperature T
is given by
â p(S) =
Boltzmann-gibbs distribution
6. â If there are m states
â Limits P(S) = 1/m (is Sis at ground state)
t->0 = 0 (if otherwise)
â Hence we could stimulate the system at
temperature near 0, we get ground state
7. â But MCMC and Metropolis fail to generate
Minima
â Because, movement in state space is inhibited
by regions of low probability and by high energy
barriers
â Simulated Anneling overcomes this problem
8. â Starts at high temp and progresses to lower temp
â Annealing Schedule is given By -
â
â
â Hence as algo proceeds â inc in energy is less
likely
â And hence minima of energy could be acheived