Simulated
Annealing (SA) is a method that simulates the thermodynamic process in which
metal is heated to its melting temperature and then slowly cooled to its
crystal configuration of lowest energy. The system is in thermal equilibrium
when the probability of a certain state is governed by a Boltzmann distribution:
(18)
with
E as energy, T as temperature and k
as Boltzmann's constant. Kirkpatrick et al. [133]
applied SA to an optimization problem. During the minimization of a multivariate
function, a candidate solution is generated by randomly perturbing the current
configuration and the energy (similar to the fitness of GA) is calculated. If
the new energy is lower than the current, the displacement is accepted. If the
energy is higher, the displacement is accepted with a probability given by the
Boltzmann distribution . These uphill steps allow the algorithm to escape
from local minima. The probability of accepting an uphill step is a function
of the change of the energy and of the temperature, which is gradually lowered
during the search process. Due to the similar approach with random steps in
the search process, SA has several times been compared with GA for the selection
of variables whereby SA achieved comparable or slightly worse results and consequently
will not be used in this study [91]-[96].
Ph. D. Thesis