Numerical methods. Note 12


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N.B. Send me an email with the subject you propose for the last lecture. So far only one subject has been proposed: "Two-point boundary value problem".

Simulated annealing methods

Simulated annealing is a generic probabilistic algorithm for finding the global minimum in a large search space, continuous or discrete. In this method the steps uphill are sometimes accepted which is supposed to allow the routine to get off the local minimum and reach the global minimum. The uphill movements are controlled by the global temperature parameter T. The uphill step with the energy increase ΔE is accepted with the probability P=exp(-^ΔE/_T) (Metropolis algorithm). The downhill step is always accepted. The global temperature is gradually decreased and the routine turns into a normal downhill routine which converges to the nearest minimum.

Problems

Non-obligatory exercise: make a symbiotic hybrid of your simplex method with simulated annealing algorithm.