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